jANL-78-XX-95

Energy Level Structure and Transition Probabilities

in the Spectra of the Trivalent Lanthanides in LaF-

W. T. Carnal!Chemistry Division

Argonne National Laboratory

Hannah Crosswhite and H. M. CrosswhiteDepartment of Physics

The Johns Hopkins University

- N O T I C E -

Thi* report w u prepared u an account of worksponsored by the United Slates Covemment. Neither theUnited State* nor ih* United States Department ofEnergy, nor any of their employees, nor *ny of theircontractors, nbcontradon, or their employees, mikesany wininty, expreis ot implied, or aitumei any legalliability or responsibility for the accuracy, completeneaor tisefulrten of any information, apparatus, product orprocen disclosed, or represent! that its tat would notinfringe privately owned rights.

filSTBlBimoN OF THIS DOCUMENT Ig UNJ4MIXS&

BLANK PAGE

CONTENTSPage

I. Introduction 2

II. Physical and Crystal!ographic Properties of LaF., 5

Fig. 1. LaF3 Structure Viewed Down the C-axis 6

III. Treatment of Experimental Data 8

Fig. 2. Crystal-field Parameters for Ln3+:LaCl3 and Ln3+:LaF3 13

IV. Energy Level Correlations - Survey of Experimental Data 14

1. f2(f12) 14

2. f3(f]1) 14

3. fV°) 16

4. f5(f9) 16

5. f6(f8) 17

6. f7 17

V. Theoretical Interpretation of Excited State Relaxation 19

A. Theoretical Treatment of Absorption Spectra 19

1. General Concepts 19

2. Induced Electric-Dipole Transitions 21

3. Magnetic Dipole Transitions 23

4. Comparison of Calculated and Observed TransitionProbabilities 24

B. Relaxation of Excited States 24

1. General Considerations 24

2. Radiative Relaxation 253+

Fig. 3. Energy-level diagrams of Ln :LaCl, 273. Non-radiative Relaxation 28

4. Comparison of Computed Excited State Lifetimes with

Those Observed Experimentally 30

5. Comments on the Use of the Tables 31

Acknowledgements 33

References 34

APPENDIX Ii.

Fig. 1. Variation of the Slater Parameter F with Lanthanide Atomic Number.

Fig. 2. Variation of the Spin-Orbit Constant with Lanthanide Atomic Number.

Table 1. Parameters for Ln3+:LaCl,. **

Table 2. Relativistic Hartree-Fock Integrals for 4fN(IV).

APPENDIX II3+

Table 1. Atomic Parameters for Ln :LaF3-

Table 2. Crystal-Field Parameters for Ln rLaFj.

APPENDIX III

Table 1. Experimental and Calculated Energy Levels for Pr :LaF,.

Table 2. Matrix Elements of [U ( A*] 2 for Selected 4f2-transitions.

APPENDIX IV3+ N

Table 1. Experimental and Calculated Energy Levels for Nd :LaF,.

Table 2. Matrix Elements of [ U ^ ] 2 for Selected 4 f 3 - t rans i t ions . •*

Figs. 1-21. Tlie Absorption Spectrum of Nd :LaF, in the Region -\4000-50000 cm"

recorded at A K.

APPENDIX V

Table 1. Computed Energy Levels for Pm :LaF,.

Table 2. Matrix Elements of [l/ x*] 2 for Selected 4f4-transitions.

APPENDIX VI

Table 1. Experimental and Calculated Energy Levels for Sm :LaFg.

Table i. Matrix Elements of [irX*]2 for Selected 4f5-transitions.APPENDIX VII

3+Table 1. Computed Energy Levels for Eu :LaFg. '•'

Table 2. Matrix Elements of [U ( X , ] 2 for Selected 4f6-transitions.

4-*

APPENDIX VIII

Table 1. Experimental and Calculated Energy Levels for Gd :LaF,.

Table 2. Matrix Elements of [ U ^ ] 2 for Selected 4f7-transitions.

APPENDIX IX

Table 1. Experimental and Calculated Energy Levels for Tb3+:LaF .

Table 2. Matrix Elements of [U ( X )] 2 for Selected 4f8-transitions.

APPENDIX X

Table 1. Experimental and Calculated Energy Levels for Dy :LaF .

Table 2. Matrix Elements of [U*X']2 for Selected 4f9-transitions.

APPENDIX XI3+Table 1. Experimental and Calculated Energy Levels for Ho :LaF3.

Table 2. Matrix Elements of [U ( X*] 2 for Selected 4f10-transitions.

APPENDIX XII.3+Table 1. Experimental and Calculated Energy Levels for Er :LaF,.

Table 2. Matrix Elements of [U ( X )] 2 for Selected 4fn-transitions.

-3+.,

APPENDIX X I I I .

Table 1. Experimental and Calculated Energy Levels for TmOT:LaF3

Table 2. Matrix Elements of [U ( X* ] 2 for Selected 4f12-transitions.

APPENDIX XIV

Table 1. Calculated Values of Qx for Ln3+:LaF3-

Table 2. Observed and Calculated Excited State Lifetimes for Ln3+:LaF,

Table 3. Partial Lifetimes and Branching Ratios in the Relaxation of

Excited States in Tb3+:LaFo.

FOREWORD

The spectroscopic investigations of lanthanide doped LaF^ crystals

and their theoretical interpretation reported here are the result of an

extensive joint effort of the Argonne National Laboratory and The Johns

Hopkins University over the last decade. It had its roots in similar

studies at both laboratories of other crystal hosts, particularly LaCl3>

for which a summary is also given in an appendix to this report. This

work was supported at Argonne by the United States Atomic Energy

Commission and the United States Energy Research and Development

Administration, and at Hopkins by the United States Army Research Office

and the National Science Foundation. An identical report is being

issued under separate cover by each institution.

-2-

I. Introduction

The low-temperature absorption spectra of trivalent lanthanide compounds

reveal the sharp-line structure characteristic of transitions between states

within the 4f -configuration, induced by the ionic environment. These transi-

tions can be directly represented as upper-state energy levels. In some cases,

notably ions in LaC13 host crystals, the empirical levels have been interpreted

in terns of a model which exhibits in detail the structure of the 4f elec-

tronic configuration itself. The atomic parameters derived from these studies

vary slowly and systematically across the lanthanide series and in fact are

depressed from corresponding values derived from atomic and ionic vapor

spectra.

G. H. Dieke has given a definitive review of the spectra of lanthanides

in crystals including a comprehensive summary of the data in LaCl3 host crys-

tals, Dieke (1968). The early interpretive papers concentrated on analysis of

the crystal-field parameters. More recently, the emphasis has been on devel-

oping models which include structural details of the 4fN configurations them-

selves with simultaneous diagonalization of the complete Hamiltonian rather

than a perturbation-theory treatment. The most recent analyses have been

given in a series of papers, Crosswhite et al. (1976), Carnall et al. (1976),

Crosswhite et al. (1977). These include effective two-body and three-body

operators approximating the electrostatic effects of configuration-mixing

interactions, plus two-body double-vector effective operators which allow for

the variation of spin-orbit interactions with spectroscopic term and for the

spin-other-orbit corrections for relativistic effects. The present analysis

of spectroscopic data for the lanthanides in single-crystal U F ~ employs the

most recent model.

'•&',

-3-

As a crystal matrix in which to study the absorption spectra of lantha-

nide ions, laFg has several advantageous features. In addition to being a „ >

transparent host over a wide region of the spectrum, it is chemically inert

so that the crystals can be handled in air. Thus even though the site SJW- **

metry of the metal ion is low, the commercial availability of the crystals in

a wide range of dopings has encouraged extensive experimental studies.

We report here two types of correlation with experimental results. For

even-f-electron systems we have computed a center of gravity based on the en-

ergies of the observed states, and calculated optimized sets of atomic energy

level parameters. For odd-electron systems we have performed complete crystal-

field calculations in which the parameters of both the atomic and crystal-

field parts of the interaction have been adjusted to experimental data. Trends >

in the free-ion parameters over the series have been examined and in some cases y

further restrictions on their values are set, based on observed parametric reg- f

ularities across the periodic series. The crystal field parameters for the I

odd-f-electron ions have also been compared and regularities over the series >

are noted. The end result of this effort is a set of eigenvectors for all of

the ionic states in each configuration. We then turn to the interpretation of

intensities of absorption bands and develop the basis for computing transition

probabilities using a semi-empirical theory of induced electric dipole transi-

tions. Finally, we apply the results of the analysis of absorption spectra at

\ „ room temperature to the related process of excited state relaxation, and pro-

' vide the basis for computing the radiative lifetime for any given state in any

!> •'->-,• member of the series.

Spectroscopic results for all lanthanides doped into LaF, (Ln :LaF,)

' ",,, > except Pm3+ and Eu3+ are reported. Since the crystals were obtained from

S;- commercial sources, the fact that the only isotope of Pm available in macro

-4-

amounts is ' Pm which is g"-unstable with a relatively short half-life, ex-

cluded it from consideration. The tendency of EuF3 to reduce to EuF2 at high

temperatures even in the presence of F., vapors, and the very strong broad band2+structure associated with Eu in the visible and ultraviolet range due to

4f -+ 4f 5d transitions, made it impossible to obtain the requisite experi-3+

mental data for the Eu-system. The energy level schemes for Pm :LaFo and

Eu :LaF_ were therefore calculated using parameters obtained by interpolation.

Some of the experimental results utilized in the analyses represent as

yet unpublished work done over a period of years in the Chemistry Division of

Argonne National Laboratory with the help of senior thesis students and guest

scientists. These results were obtained using several different instruments.

Spectra in the range ^OOO-ieOOO cm" were recorded using a Cary Model 14R

(crystal-grating- 0.5 meter) recording spectrophotometer. In the region

15000-50000 c m , both a 1-meter Hilger-Engis Model 1000 spectrograph equipped

with an EMI 9558 Q photomultiplier, and the Argonne 30' Paschen-Runge spectro-

graph (in second order) were used. Observations were made at ^298, 77, and

4 K. Crystals of LaF, doped with selected lanthanides in various concentra-

tions were obtained from Optovac Inc., North Brookfield, Mass. 01535.

There continues to be a wide interest in lanthanide-doped crystals and

glasses as laser materials. In some cases quantitative intensity calculations

have been carried out and related to the fluorescing properties in a given

host. The most extensive calculations have been limited to the f (f ) and3 11

f (f ) members of the series since the matrix elements of the tensor opera-

tors connecting the states of interest required ir the intensity analysis formore complex systems have not been published. We report here a consistent set

of the matrix elements for all 4f -configurations based on the systematic atomic

parameters generated in this work.

-5-

II. Physical and Crystal!ographic Properties of LaF-

There have been conflicting reports suggesting both C2V, Oftedal (1929,

1931) and D 3 h, Schlyter (1953), site symmetries of the La3+ ions in LaFy

More recent studies, Mansmann (1964, 1965), Zalkin et al. (1966), Lowndes

et al. (1969), indicate that the nine nearest-neighbor F" ions present a suf-

ficiently distorted environment so that the symmetry is D 3 d (P3cl) with a C2

site symmetry, Fig. 1. A recent powder neutron-diffraction study of LaF, and

CeF,, Cheetham et al. (1976), provided additional confirmation of the latter

structure. Isostructural members of the series are LaF-, CeF,, PrF,, and

NdF,; SmFo and the heavier trifluorides are dimorphic. They also crystallize

in the orthorhombic YF3 lattice where each Y3 + has 8-F" at 2.3 A and one at

2.6 A, Zalkin and Templeton (1953).

The crystallographic evidence for a low site symmetry in LaF3 is con-

sistent with the results of an early spectroscopic study of PrF, in which

Sayre and Freed (1955) pointed out that the number of lines observed at low

temperature for electronic transitions associated with several excited states

excluded a site symmetry higher than C2y. The Raman spectrum of LaF, has been

interpreted in terms of a C2 site symmetry of the La , but these results also

emphasize that the deviation of the symmetry from more symmetric models is

small indeed, Bauman and Porto (1967). Spectroscopic evidence for hidden3+selection rules in the polarized spectrum of Nd :LaF3 is also suggestive of

an approach to a symmetry higher than C2> Wong et al. (1963b), Kumar et al.

(1976).

A recant investigation of the normal and vacuum ultraviolet absorption

bands of trivalent lanthanides doped into LaF3 has provided evidence that LaF3o

is transparent down to the normal ultraviolet limit of ^000 A, Heaps et al.

(1976).

Fig. 1

LoF3 STRUCTURE VIEWED DOWN THE c-AXIS

FK08)

0 I 2A

oo = 7.185 ± O.OOI A

c0 = 7.351 ± 0.001 A

A. Zalkin, D. H. Templeton, J.E.HopkinsInorg. Chem. 5, 1466 (1966)

Space Group0jd-P3ClSite symmetry C2

- 7 -

Refractive index (n) measurements using films of LaF3> CeF,, and NdF,,

Haas et al. (1959), provided the following values in the 0.25-2.0 p range:

x(u)2.0

1.2

0.8

0.6

n__

1.57

1.575

1.58

1.585

0.45

0.40

0.30

0.27

n

1.60

1.61

1.625

1.65

For single-crystal LaF_, the expression obtained for the variation of the re-

fractive index (ordinary ray) with wavelength in the visible-near ultraviolet,

Wirich (1966), was

n = 1.57376 + 1 5 3 - 1 3 7

0 X(A) - 686.2

2536.5 1.65587 1.65652

3131.5 - 1.63639

3663.3 - 1.62520

4046.5 1.61797 1.61933

4358.3 1.61664 1.61546

5460.7 1.60597 1.60583

The M.P. of LaF3 is 1493°C and its density is 5.94 gm/cm3, Brown (1958).

-8-

III. Treatment of Experimental Data

In recent years there have been numerous reports of the spectroscopic

properties of different lanthanides in host LaF,, and many of these investiga-

tions have included low-temperature spectra. Consequently, the energies of

the crystal-field components associated with many of the free-ion states have

been recorded. The extensive data available led us to begin a systematic

theoretical analysis of the 4f energy level structures over the series.

Part of the motivation to undertake a systematic analysis of the data

stemmed from the results described in two papers by Onopko (1968a,b) in which

he pointed out that the energies of crystal-field components of several of the

lowest-lying free-ion states in Nd3+:LaF3 and Er3+:LaF3 could be computed in

reasonably good agreement with experiment by assuming that the site symmetry

approaches D,.. The approximation also appeared to be justified in treating

the crystal-field levels in Gd :LaF3, Schwiesow and Crosswhite (1969). We

had already developed computer programs that allow a complete diagonalization

of the atomic and crystal-field Hamiltonian for the 4f3(4f11) case in D 3 h~

symmetry. We had also determined the atomic parameters for both Nd :NdF33+

and Er :LaF3. We therefore extended the analysis using Onopko's crystal-

field parameters. The initial results confirmed the validity of Onopko's

analysis by providing a computed set of crystal-field levels that were in

reasonably good agreement with experiment throughout the spectral range to

^50,000 c m .

The analysis was extended by assigning the experimentally observed en-

ergy to those crystal-field states identified by the initial computation.

This permitted a least-squares adjustment of the original crystal-field param-

eters. Additional assignments were made based entirely on the correlation

-9-

between the optimized crystal-field parameter calculations and observed levels.

We then proceeded to perform a similar crystal-field calculation for other Ian-

than ides using the optimized values for Nd and Er' as the basis for beginning

the analysis.

For odd-electron systems the crystal field will split a level into J +

1/2 separate components in all site symmetries except cubic and octahedral.

The number of possible components therefore is the same for C2 and D 3 h, and

because D ^ appears to be a good approximation to the actual one, it is not

difficult to correlate the experimental and computed levels.3+ 2

On the contrary, in even-electron systems such as Pr (4f ), crystal-

field calculations based on D~u symmetry do not remove the degeneracy of the

vi = ±1, ±2 states. It has been pointed out that the number of lines observed

in the spectrum of Pr :LaF, implies a low site symmetry consistent with the

complete removal of symmetry-related degeneracy in the indicated levels. Sayre

and Freed (1955), Carnall et al. (1969). This leads to ambiguities in making

the necessary crystal-field correlations. We have therefore attempted complete

crystal-field analyses only for odd-electron systems. For the even-electron

cases we have made the approximation of fitting the centers of the crystal

groups to the free-ion Hamiltonian only.

The basic theory used to interpret the structure observed experimentally

in lanthanide crystal spectra has been considerably refined in recent years.

A semi-empirical approach has been employed in which the attempt is made to

identify those effective interactions operating within the f -configuration

that reproduce the observed structure. Judd (1963), Wybourne (1965), Judd et

al. (1968), Crosswhite et al. (1968). Based on this method of interpretation,

the total Hamiltonian of the system can be written:• A

glSTBlBUTlON OF XHiS JJOQUMJSNT Ig UHU«££gR

-10-

E " EF + ECF

where Ep is the atomic part of the interaction:

k=0.2,4,6Fk(nf,nf)f.

k aL(L+l) YF(R7)

1=2,3,4,6,7,8Mkm.

kk=0,2,4 k=2,4,6

kThe F , i k k-j., a, 3, y, T , M and P are parameters and their associated terms

are the corresponding operators. E C F represents the crystal-field interaction.

Following Onopko (1968a,b) we assumed that the symmetry of the lanthanide site

in LaF3 was approximately hexagonal (Dou)> that is, that the hexagonal terms

in the crystal-field expansion are dominant.

ECF B kC ( k ) = B 2C { 2 ) + B 4C ( 4 ) + B 6C ( 6 ) + B 6rC ( 6 ) + C { 6 )

W B 0 l 0 B0L0 + B0l0 B6lL6 C -6

The above interactions which constitute the model used in this investigation

are discussed in detail in Appendix I with reference to the similar treatment

of the more extensive data for Ln +:Lado-

For odd-f-electron systems the total Hamiltonian can be separated into

three submatrices and all three of them diagonal!zed simultaneously. The

methods of truncating the very large matrices that occur for ions in the mid-

dle of the series have been discussed previously, Carnall et al. (1976). The

results of the diagonalizations—which eventually included variation of most

of the parameters in the systems, are given in Appendix II.

Onopko (1968a,b) quoted his original results in the Stevens operator3+(g. ) normalization and subsequently extended the analysis to Er :LaF,,

• > -

-11-

Onopko (1969). The corresponding crystal-field parameters in the tensor opera-i,

tor normalization (B*) used in the present study, Wybourne (1965), are given

below:

3 2 0 =

3 6 Q =

666 =

Nd3+:

138 cm"1

176

100

645

LaF3

-8-BJ =

4-4-

276 cm"1

1408

1600

679

3 2 0 =

1*40 =

Er3+:

141 cm"1

145

48.3

430

LaF3

4-•4-

4-4-

282 cm"1

1160

773

453

The crystal-field parameters obtained from the Nd :LaF3 data in this investi-

gation are compared with those for Nd :LaCl3, Crosswhite et ai. (1976), where

the symmetry is hexagonal, below:

Nd3+:LaF3

(D3h Approximation)

BQ = 216 cm"1

BJ = 1225BQ = 1506

B5 = 7700

a = 1 7 cm"

139 levels fitted

Nd3+:LaCl3

(C3h Symmetry)

BQ = 163 cm"1

B« = -336

B0 = "713

B«=462

a = 8.1 cm"

101 levels fiti

It has been demonstrated that ab initio calculations of crystal-field

parameters based on an ionic model are not able to reproduce the values ob-

tained semi-empirically. However, serious efforts are being made to develop

suitable models for the LaF crystal, Newman and Curtis (1969), Stedman and

Newman (1971), and attempts have also been made to treat the low-symmetry LaF3

lattice case by actually using the appropriate number of terms in the poten-

tial, Matthies and Weisch (1975).

-12-

The experimental results of the present efforts should provide a useful

testing ground for further theoretical treatments. Systematic trends in the

values of the crystal field parameters for Ln3+:LaF3 are compared with those3+

for Ln :LaCl3 which are much better established experimentally, in Fig. 2.

i- . >

200-

100-

1000

500

1000-

500-

1

r2

0

i

1

o

1

1 1 1

1 1 1

1 1

_ 2o

1 1

1

o Lα«

• Lα!i

i i

.0 SL

1 I

1

I

I I 1 1 1 1

1

1

1

— — •

-flu

1

1

1

1

"TS—•

-flu

1

1

•

o

1

1 1

o

1 1

1

- 9 .

1

1 1

T-

"°—o-

i i

i

i

N2 3 4 5 6 7 8 9 10 I! 12Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm

Fig. 2. Crystal-f ie ld Parameters forLn3 +:LaCl3 and Ln3 +:LaF3.

-14-

IV. Energy Level Correlations - Survey of Experimental Data

The energy level structure in Pr :LaF, has been examined experimentally

in moderate to high resolution by several groups. Wong et al. (1963a), Yen

et al. (1964), Caspers et al. (1965a), Carnal! et al. (1969). Free-ion level

energies are recorded in Appendix III together with the corresponding computed

levels using parameters given in Appendix II. The weak point in the theoret-

ical analysis is the assumption of a center of gravity for the Ig and for the

3r transitions.

,3+.,Most of the possible crystal-field components in the spectrum of Tin :I-«»F-

have been observed, Carnall et al. (1970), and the centers of gravity of these

groups are compared to the calculated free-ion levels in Appendix XIII.

2. 4f3(f]1)

There are extensive published reports, Wong et al. (1963b), Caspers et

al. (1965b), of the structure observed in the low-temperature absorption and

3+fluorescence spectra of Nd :LaF^. These data have been extended by previously

unpublished work at ANL to provide as complete a set of crystal-field compo-

nents as possible. Of the 182 levels in the f configurations, 139 have been

assigned. The results are included in Appendix IV, and can be compared to

those obtained in the recent extensive investigation of the spectrum of3+

Nd :LaCI3, Crosswhite et al. (1976). Kumar et al. (1976) have examined the

absorption and fluorescence spectra of Nd +:LaF, at 77 K, the latter excitedo

using the 3371 A line of a Np-laser. They reported several transitions not

observed in previous investigations. Some of these are consistent with band

energies observed in the present study but there are discrepancies. In gen-

eral, there is a small shift in energy between observations at 77 K and those

?•••*

-15-

reported here which refer to 4 K. The assignments made to the fluorescence

spectrum serve to further establish the energies of the lower-lying states

which had been reported earlier. The components of the I-IR/O state reported

by Voron'ko et al. (1973) from observations made at 77 K are in good agreement

with the unpublished results recorded in Table 1, Appendix IV.

The present theory of intensities of f -»• f transitions treats the compos-

ite free-ion states rather than transitions between individual crystal-field

components (see Section V). A number of investigators are presently concerned

with extending the theory to the crystal-field case. In order to provide a

basis for testing the results of such calculations we include in Figs. 3-22,

Appendix IV, a set of absorption spectra of Nd3+:LaF3 taken at -\4 K covering

most of the levels observed in the f -configuration. No attempt was made to

preserve a constant resolution since two different instruments were used, and

several different crystals of varying concentrations and path lengths were em-

ployed. However, in any one group, the relative intensities of the components

are clearly evident.

The absorption and fluorescence spectra of Er :LaFg measured at 77 K and

including levels up to -v/39500 cm" were reported by Krupke and Gruber (1963,

1964, 1965). Several higher-energy transitions were also tentatively identi-

fied. A subsequent investigation, Carnall et al. (1972), included measurements

at %4 K in the range 6000-50000 c m . Additional spectroscopic measurements at

low temperature have been made, so that the levels recorded in Appendix XII

represent a composite and in a number of cases a revaluation of results ap-

pearing in the literature. In addition to a discrepancy in the calibration

standards applied to a number of groups originally reported by Carnal! et al.

(1972), the comparison of experimental energies with those computed based on

-16-

the crystal-field interpretation used here suggested a possible vibronic origin

for some of the states previously identified as crystal-field components.

3. 4f4( f1 0)

The absorption spectrum of Pm :LaF3 has not been reported, but an exten-

sive investigation of the absorption and fluorescence spectra of Pm :LaCl, has

been published, Carnail et al. (1976). We have therefore used the regularities3+in the energy level parameters for Ln :LaF- as the basis for interpolation and

3+

assignment of approximate parameters for Pm :LaFj. The corresponding computed

free-ion levels are given in Appendix V. The chemical shifts observed on com-

paring free-ion levels in Nd3+:LaF3 and Nd3+:LaCl3 are similar to those found

in comparing the computed results for Pm :LaF3 with the experimental states of

Pm3+:LaCl3.

An extensive investigation of the absorption and fluorescence spectra of

Ho :LaF3 has been reported by Caspers et al. (1970). Additional experiments

have been conducted at ANL, but only minor additions or modifications of the

published data were indicated. In many cases, the number of observed components

of free-ion groups is less than allowed theoretically based on C« site symmetry,

but the centers of gravity of these levels appear to provide the basis for cal-

culation of a consistent set of energy level parameters, as recorded in Appen-

dix XI.

4. 4f5(f9) », /<y

The observation and analysis of the absorption and fluorescence spectra \

of Sm3+:LaF3 in the range 0-11000 cm was reported by Rast et al. (1967), and . ';>• •^'•j

the line list was extended to 2000 cm in a tabulation given in Dieke (1968). ;

The number of observed lines was further extended in the present investigation,

and a composite tabulation based primarily on recent work at ANL is given in \- :

Appendix VI.

-17-

Absorption and fluorescence spectra of Dy3+:LaF- including levels up to

^32000 cm" have been reported in the literature by Fry et al. (1968). A num-

ber of new levels including groups at higher energies were recorded in the

course of the present investigation. The results are presented in Appendix X.

5- 4f6(f8)

Crystals of LaF3 doped with EuF. are found to contain some Eu2+ which

3+

makes it difficult to observe the Eu transitions in absorption in the near-

ultraviolet. Weber (1967a) observed fluorescence in Eu3+:LaF3 from the excited

states DQ, DJ, 5D 2. and D3 using pulsed selective excitation. The energy

level scheme for the low-lying D and F states that can be deduced from these

measurements shows the expected red shift with respect to the corresponding

levels observed in Eu :LaCl-, Dieke (1968), and is consistent with the results

given in Appendix VII. The latter were computed based on energy level param-

eters deduced from systematic trends over the series.

T*K; energy levels of Tb 3 + in single-crystal TbFj have been studied in

absorption and fluorescence by Krupka and Guggenheim (1960). From this data

the centers of gravity of the D- and the ground term F multiplet components

could be determined. The results are in agreement with the moderately exten-3+sive study of the low-temperature absorption spectrum of Tb :LaF, which was

3+part of the present investigation. The free-ion levels of Tb :LaF, are given

in Appendix IX.

6. 4flc c ox

The energy levels of the P and I groups in Gd :LaF3 were reported by

Schwiesow and Crosswhite (1969) who also performed a crystal-field analysis

assuming an approximate hexagonal site symmetry. The experimental results were

subsequently extended to include the 6D states in the 40000-50,000 cm range,

-18-

Carnall et al. (1971). The data recorded in Appendix VIII are a composite of

the indicated published results.

i>:

' : ' • • • • '

;3

&,

BLANK PAGE

-19-

V. Theoretical Interpretation of Excited State Relaxation

A. Theoretical Treatment of Absorption Spectra

1. General Concepts

The quantitative treatment of the intensities of trivalent lanthanide ab-

sorption bands relates an experimentally determined quantity, a normalized band

envelope, PEXpT, to a theoretical model based on the mechanisms by which radia-

tion can be absorbed, fhe terms oscillator strength or transition probability

are applied interchangeably to the symbol P. There is some magnetic dipole

character in a few transitions (P*. p ), but an induced electric-dipole mecha-

nism (Pc p ) must be invoked to account for the intensities of most lanthanide

absorption bands. The term induced or forced electric dipole is used to empha-

size that true electric dipole transitions require the initial and final states

to be of different parity, whereas no parity change is involved in transitions

within a configuration. In contrast, magnetic dipole transitions within a con-

figuration are (parity) allowed. The weak intra-f transitions are accounted

for by assuming that a small amount of the character of higher-lying opposite-

N

parity configurations is mixed into the f states via the odd terms in the

potential due to the ligand field, Wybourne (1965). We neglect higher multi-

pole mechanisms, (electric quadrupole, etc.), and write:

PEXPT = PE.D. + PM.D.

In expressing Pr n in terms of a theoretical model, Judd (1962) and Ofelt

(1962) summed over the intensities of the individual crystal-field components

of a given state. As a consequence, the model applies to spectra observed at •.'

room temperature or above since it is assumed that all of the crystal-field

-20-

components of the ground state are equally populated. Some attempts have been

made to avoid this summation and thus treat the intensities of transitions be-

tween the lowest crystal-field level of the ground state and excited crystal-

field states, Axe (1963). However, the intensity calculations reported in the

present summary deal only with composite levels. Thus the appropriate expres-

sion for I'exPT' which represents the number of classical oscillators in one ion,

more commonly referred to as the probability for absorption of radiant energy,

Hoogschagen (1946), is:

2P = 2303 mc /e.(a)da = 4.32 x 10"9 feAo)iotxP1 me* 1 n

where e. is the molar absorptivity of a band at the energy a. (cm" ), and the

other symbols have their usual meaning. P is here a dimensioniess quantity.

The molar absorptivity at a given energy is computed from the Beer-Lambert law:

E = l o g l o / I (l)

3where c is the concentration of the lanthanide ion in moles/1000 cm , S, is the

light path in the crystal (cm), and log IQ/I is the absorptivity or optical

density. The expression for Pc^pj is identical to that for f defined by Krupke

(1966) in his treatment of lanthanide spectra in LaF3-

In view of our interest in both absorption and fluorescence processes,

there is an advantage in pointing out the basic role of the Einstein coefficient

in expressing the transition probability due to dipole radiation:

2 (2)

where i and f signify the initial and final states, A is the (spontaneous)

transition probability per unit time, a(cm" ) is the energy difference between

-21-

the states, and D is the dipole operator, Condon and Shortley (1957).

In addressing the problem of the absorption of energy, Broer et al. (1945)

expressed eq. (2) in terms of oscillator strength using the relationship P =2 2 2

Amc/frr a e . The factor 2J + 1 was added since the matrix elements of D are

summed over all components of the initial state i. A refractive index correc-

tion x was also included giving:

(3)

n p

where F and M represent the matrix elements of the electric dipole and mag-

netic dipole operators, respectively, joining an initial state J to the final

fn + J>i

state J,, x - — g _ ' , and n is the refractive index of the medium.

2. Induced Electric-Dipole Transitions

Oudd (1962) and Ofelt (1962) independently derived expressions for theN

oscillator strength of induced electric dipole transitions within the f con-

figuration. Since their results are similar, and were published simultaneously,

the basic theory has become known as the Judd-Ofelt theory. However, Judd's

expression, eq. (4), was cast in a form that could be directly related to oscil-

lator strengths derived from lanthanide absorption spectra taken at 25°C or

above:

PE n " H Tv(^j|U

(X)||,J.'J')

2 (4)

t,u' X=2,4,6

A

where v(sec ) is the mean frequency of the transition ipj •* <|/'J', IΓ ' is a

unit tensor operator of rank X, the sum running over the three values X = 2,4,6,

and the T^ are three parameters which can be evaluated from experimental data.

These parameters involve the radial parts of the 4f wave functions, the wave

functions of perturbing configurations such as 4f 5d, and the interaction

Si*

-22-

between the central ion and the immediate environment.

Typically, several excited states are encompassed by a single complex

absorption envelope, and the matrix elements of u' ' are summed over these

states. The energy in this case becomes that of the center of gravity of

the envelope. Those investigators who have studied lanthanide intensities

in crystals have followed an alternate parametrization, Axe (1963), Krupke

(1966), which has clear advantages in describing both the absorption and

fluorescence processes in terms of a single set of adjustable parameters.

The expression for T given by Judd in eq. (4) was:A

(5)

Substituting v = cc? and eq. (5) into eq. (4) gives

9 n X=2,4,6E.D. 3h(2J+l (6)

where ft. = (2X+l)Z(2t+l)B+52(t,X), Axe (1963), and in terms of F2, eq. (3),

A x v

(7)

The matrix elements of eq. (6) are calculated in the SL basis using the

relation:

'S'L'J ,) = 6(S,S'J(-1)S+L '+J+Xt(2J+lJ(2J'+1(fNaSLJ

£,£'£} (fNaSL||U(A)||fNa'SL') (8)

Selection rules imposed by the nature of the mechanism assumed are discussed

by Ofalt (1962). The reduced matrix elements on the right side of eq. (8)

have been tabulated by Nielson and Koster (1963). The matrix elements as

-23-

computed must be transformed from the SL basis to intermediate coupling before

being squared and substituted into eq. (6).

The intermediate-coupling eigenvectors, |f i/>J>, are expressed in terms of

SL basis states, |fNaSLJ>, by:

|fN*J> = c(a,S,L)|fNaSLJ>

where c(a,S,L) are the numerical coefficients resulting from the simultaneous

diagonalization of the atomic parts of the Hamiltonian. The matrix elements

of U , eq. (8), have been calculated for transitions between various excited

states as well as between the ground and excited states of the whole series of

lanthanide ions using the energy level parameters given in Appendix II. The

results are tabulated in Appendices III-XII.

3. Magnetic Pipole Transitions

Following the results of Condon and Shortly (1957), the magnetic dipole

operator is given as M = -e/2mc £(L^+2S 4). The matrix elements of the opera-

(9)

tor FT in eq. (3) can then be wri t ten,

FT2 = e2/4m2c2(tf<J| |L+2S| |tfi'J' )2

The non-zero matrix elements w i l l be those diagonal in the quantum numbers a,

S, and L. The selection rule on J , &J = 0,± l , restr icts consideration to

three cases:

1) J'=J («SLJ||L+2S|jaSLJ,) = gfi [J(J+l)(2J+l)]1 /2 (10)

where a = 1 + J ( J + 1 ) + SiS+1? " L ( L + 1 )where g - l + 2J(J+1)

2) J'=J-1

(aSU||L+2S||aSU-l) = 1 i [

-24-

3) J'=J+1

(aSLJl |L+2S| laSLJ-t-IJ (12)

The matrix elements calculated in eqs. (10)-(12) must be transformed into

the intermediate coupling scheme before computation of the magnetic dipole con-

tribution represented by eq. (9).

Values of the quantity P, > 0.015 x 10"8 where PM D B P'n and n is the

refractive index of the medium, have been tabulated for transitions of the tri-

valent lanthanide ions between the ground states and all excited free-ion

states, Carnal 1 et al. (1968a).

4. Comparison of Calculated and Observed Transition Probabilities

A number of authors have determined the ft, intensity parameters from a

least squares fitting procedure using band envelopes for Ln :LaF, observed at

^25°C and available sets of the matrix elements of IP . Krupke (1966) was the

first to show that transition probabilities in good agreement with experiment

could be computed for Pr :LaF3 a"d Nd : L a l V A summary of parameter values,

3+Sly for Ln :LaF3 is presented in Table 1, Appendix XIV. The parameters for3+ 3+ 3+

Sm :LaF , Dy :LaF3, and Tm :LaF were checked against results obtained inthe present investigation, and those for Dy3+ and Tm were modified from the

values originally reported. While the values of the matrix elements of

given in Appendices III-XIII differ slightly from those in the literature, these

differences are not sufficient to affect the reported values of fi,.

B. Relaxation of Excited States

1. General Considerations

A great deal of progress has been made in analyzing the mechanisms of

excited state relaxation of lanthanides in crystal hosts. Two modes of

! • * - •

-25-

relaxation can be recognized: radiative and non-radiative processes. Axe (1963)

addressed the problem of expressing the radiative process in quantitative terms

using the Judd-Ofelt theory. Non-radiative relaxation was already being formu-

lated in terms of multiphonon processes in the early 1960's. Barasch and Dieke

(1965), Riseberg and Moos (1967,1968). Such processes become, less probable as

the energy gap between an excited state and the next lower energy state increases.

2. Radiative Relaxation

In treating the fluorescence process, the Einstein coefficient, eq. (2)

is used directly to express the rate of relaxation of an excited state (ifiJ) to a

particular final state (i|»'J'). Following Axe (1963), the counterpart of eq. (3)

becomesA Q

jl IX'F2 + n3M2] (13)

where a(cm ) represents the energy gap between states (IJIJ) and (i|>'J'), x, =2 22 2q > ana" n 1S tne refractive index of the medium. As in the absorptionq

process, there is an implicit assumption that all crystal-field components of

the initial state are equally populated. In principal, if fluorescence can be

detected, the lifetime of the state is long compared to the rate at which it is

populated in the excitation process, so thermal equilibrium at the temperature

of the system can be achieved prior to emission.

The matrix elements of the electric and magnetic dipole operators, r

and FT , are identical to those in eq. (7) and eq. (9), respectively. However,

the form of the refractive index correction in eq. (13) is not the same as for

the absorption process, eq. (3). Equation (13) can be evaluated using param-

eters & established from measurement of the absorption spectrum of the lan-

thanide ion in a crystal lattice identical to that studied in fluorescence.

' • $ '•• •

-26-

Since excited state relaxation generally involves transitions to several

lower-lying states, we define a total radiative relaxation rate, Ay(^J)

£ ,*,J,) (14)

where the sum runs over all states lower in energy than the fluorescing state.

It is useful to define in addition the radiative branching ratio, 3R,

from the relaxing state (ijjJ) to a particular final state (ij/'J,)

and the radiative lifetime of a state

1 (16)

The principal fluorescing states of the lanthanides in crystal hosts are

indicated in Fig. 3. However, fluorescence from many of these levels is only

observed at low temperatures since rapid relaxation of an excited state by non-

radiative processes competes strongly with the radiative mode unless the energy

gap to the next lower level is large, as discussed in the next section.

Since the parameters Q^ have been determined for a number of the lantha-

nides in LaF, host, Table 1, Appendix XIV, we can compute the radiative life-

time of any excited state using eqs. 13, 14 and 16. For those states with

large energy gaps to the next lower level, the observed and computed radiative

lifetimes would be expected to be in approximate agreement. Weber (1967b) has

pointed out that such agreement is observed for excited states in Er :LaF,

where the energy gaps are in excess of 3000 cm" :

i'?-'

4<

3

3

34

32

30

Sβ

26

24

22

20

Iβ

16

14

12

10

8

6

4

2

•lO'cm-i",

=i ,— — *^%

I » —

» %

»-^%

I^*

• '.

-\ —

, t

S!_ I—i'

-%

..-Ss- r y

is —

Ce Pr N-d Pm Sm Eu Gd Tb Dy Ho Er Tm Yb

Fig. 3. Energy Level Diagrams for Ln 3 + :LaCl 3 .

y

'r

/V*;-".:.i<";-

U.I t

1

-28-

Transition4 I - 4 I!13/2 M5/2

rn/2 *2PF3/2

3. Non-radiative

TR(msec)

10.9

11.6

0.43

Relaxation

Observed Lifetime(msec)

13

11

0.29

Following the excitation of a lanthanide ion in a crystal lattice, the

relaxation of excited states may occur by a purely radiative process, or more

generally, may occur by the transfer of some energy to lattice vibrations. It

was known experimentally for a number of years before any quantitative theory

of non-radiative processes was developed that fluorescence was not observed at

25°C from Ln :LaCl, if the energy gap between the excited state and that next

lower in energy was < 1000 cm" , Barasch and Dieke (1965). In a systematic

investigation of multiphonon orbit-lattice relaxation of lanthanide excited

states, Riseberg and Moos (1968) have given an explicit expression for the

temperature dependent transition rate in LaF,, LaCl, and LaBr,. The energy-gap

dependence of the multiphonon process is treated phenomenologically by assuming

that the appropriate phonon energy is that corresponding to the cut-off in the

phonon states. For LaF, this is 350 cm" , while for LaCl, it is 260 cm" .

In terms of the ^1000 cm energy gap cited earlier, it is apparent that a 3-4

phonon emission process is a relatively efficient mode of relaxation at 25°C.

However, as the gap increases, demanding the simultaneous emission of a large

number of phonons, the process rapidly decreases in probability such that radia-

tive decay can efficiently compete as a relaxation mechanism.

Since in the usual case both radiative and non-radiative processes operate

to relax an excited state, we can express the total fluorescence lifetime of the

-29-

state as

(17)

where AT is the radiative rate and WT(ij>J) is the sum of the rates of the various

non-radiative processes.

The dependence of the relaxation rate on energy gap alone, W(o) can be

expressed as a simple exponential, Moos (1970),

W(o) = Ce a A E

where C and a are parameters characteristic of the host material, not of the

lanthanide ion. For LaF3, C = 6.6 x 108 (sec-1) and a = -5.6 x 10"3, Riseberg

and Weber (1976).

Adding the temperature dependence, Riseberg and Moos (1967,1968), results

in the expression

= W(o) { [ e f ( V k T - I ] " 1 + l}AE/ f i a ) i

which can be rewritten

W(«J) = CeaAE[l - e " f i V k T r A E / f i a , i (18)

-1where Hia). is the maximum phonon energy, taken as 350 cm" for LaF,, Riseberg

and Weber (1976). Since k = 0.695, kT = 207 cm at room temperature and the

corresponding expression is:

= CeaAE(.8155)-AE/35°

For example, the radiative lifetime of the Ig/o state of Er :LaF, at

a/l?oon cm" has been computed to be 20.7 msec but observed to be M).15 msec,

Weber (1967b). Since AE between Ig/2 and the next lower I-j-j/g state 1S

'.'•%

-30-

1- 1 4 - 1 <

2000 cm , W(i|d) = -lO sec . Thus the non-radiative lifetime of 'vO.l msec

is rate determining.

4. Comparison of Computed Excited-State Lifetimes with Those Observed

Experimentally

Experimental measurements of excited-state lifetimes for a number of

lanthanides in LaF3 have been reported, and in many instances these values have

been compared to those computed using eq. (13), (17) and (18). Although the

results of the computations were reported, the availability of the relevant

matrix elements of U* ' interconnecting the excited states in the various con-

figurations is very limited. The only tabulation that includes all members of

the series is restricted to matrix elements that join excited states to the

ground state, Carnall et al. (1968b). As a consequence, the results presented

in Appendices III-XIII represent the first systematic effort to make intercon-

necting matrix elements of lr ' available for the whole series and thus enable

calculation of a wide range of lifetimes. Some minor corrections to values re-

ported in the earlier tables have also been made. Calculated radiative life-

times and observed lifetimes for some of the prominent fluorescing states in

Ln :LaF- are given in Table 2, Appendix XIV. An example of the complete cal-

culation of the lifetimes associated with the radiative relaxation of two

states in Tb , showing branching ratios to all lower-lying states, is given

in Table 3, Appendix XIV. The strong radiative coupling of the D4 to the D3

state is clearly indicated. Recently Page et al. (l>76) reported lifetimes in', 5 3 + '

v the 100 psec range for the D. state in Tb :LaF3 at 300 K, with little change,

!,> v, as expected, on cooling to 77 K. However, these values are a factor of ten,v . v shorter than would have been predicted, see Table 2, Appendix XIV, and must be'*' • 3+ 5

. i>. regarded as questionable. In Tb :LaCl, at 300 K the lifetimes of the D 3

:V ; 1 states were 570 and 1220 psec, respectively, in good agreement with the calcu-

< lated values for the LaF 3 host, Barasch and Dieke (1965).

-31-

•>£/

5. Comments on the Use of the Tables

(A) Atomic (free-ion) states

As discussed in the introduction, detailed crystal-field calculations

were only carried out for odd-f-electron systems. For the even-f-electron

systems a center of gravity was computed from the experimentally observed

crystal-field components of each state. These "free-ion" states are recorded

in the appendices and were used as the basis for computing the energy level

parameters. Similar tabulations of the free-ion state energies have been

included for the odd-f-electron systems in order to facilitate use of the

tables of U(K)*2. In these latter cases the computation was made using the

atomic parameter values given in Appendix I with the crystal-field parameters

set equal to zero. In all the tabulations of free-ion levels the state

designation corresponds to the largest component of the eigenvector.

(B) Tables of ( U ^ ) 2

The entries in these tables are arranged in order of increasing J-value

for the initial state. Entries are not repeated. For example, the matrix

element between an initial J = 9/2 and a final J = 3/2 state is identical

to the J = 3/2 -»• J = 9/2 entry. Only the latter is given. If the entry is

missing from the table, the matrix elements are zero. The following partial3+

tabulation of matrix elements of U(K)*2 for Nd :LaF3 joining the ground( I9/2) state with several excited states taken from Appendix IV serves as

3+

an illustration and may be compared with results given for Nd (aquo) in

Carnall et al. (1968b).

-32-

State

41

41

41

41

4F

4F

2H

M9

11

13

15

3

5

9

Eton"1)

235

2114

4098

6148

11621

12660

12768

.0194

0

0

0

.0006

.0095

.1072

.0135

0

.2283

.2337

.0082

1.1639

.4549

.0452

.0554

.3983

.1195

-33-

Acknowledgements

Several individuals contributed substantially to the experimental inves-

tigation and/or interpretation of important segments of the data presented in

this report, and their assistance is gratefully acknowledged:

Dr. Katheryn Rajnak, Kalamazoo College, Kalamazoo, Michigan

Prof. R. Sarup, College of the Holy Cross, Worcester, Massachusetts

Dr. H. Kramer (ne'e LSmmermann)

and the following senior thesis students:

E. A. Flom, St. Olaf College, Northfield, Minnesota

D. W. Mehaffy, Coe College, Cedar Rapids, Iowa

J. F. Pophanken, Houston Baptist College, Houston, Texas

G. A. Robbins, Stamford University, Birmingham, Alabama

BLANK PAGE

-34-

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Trees, R. E. (1951), Phys. Rev. 83, 756.

Trees, R. E. (1952), Phys. Rev. 85, 382.

Trees, R. E. (1964), J. Opt. Soc. Am. 54, 651.

Voron'ko, Y. K., V. V. Osiko, N. V. Savost'yanova, V. S. Fedorov and I. A.

Shcherbakov (1973), Soviet Phys. Solid State 1£, 2294.

Weber, M. J. (1967a), in Optical Properties of Ions in Crystals, H. M. Crosswhite

and H. W. Moos, eds., Wiley Interscience, New York, p. 467.

Weber, M. J. (1967b), Phys. Rev. 157, 262.

Weber, M. J. (1967c), Final Report to Research and Development Procurement

Office, U.S. Army Engineering R&D Laboratories, Ft. Belvoir, Virginia,

Contract DA44-009-AMC-1727(E).

Weber, M. J. (1968), J. Chem. Phys. 48, 4774.

-38-

Weber, M. J., B. H. Matsinger, V. L. Donlan and G. T. Surratt (1972), J. Chem.

Phys. 57, 562.

Wirich, M. P. (1966), App1. Optics 5_, 1966.

Wong, E. Y., 0. M. Stafsudd and D. R. Johnson (1963a), J. Chem. Phys. 39, 786.

Wong, E. Y., 0. M. Stafsudd and D. R. Johnson (1963b), Phys. Rev. 131, " ° -

Wybourne, B. G. (1965), Spectroscopic Properties of Rare Earths, Wiley, N. Y.

Yen, W. M., W. C. Scott and A. L. Schawlow (1964), Phys. Rev. 136, A271.

Zalkin, A. and D. H. Templeton (1953), J. Am. Chem. Soc. 75, 2453.

Zalkin, A., D. H. Templeton and J. E. Hopkins (1966), Inorg. Chem. 5_, 1466.

APPENDIX I

-1-

Appendix I

As a result of the correspondence between the energy levels of lantha-

nides in LaCl, and LaF,, it is convenient to summarize the present status of

the theory applied to the host LaClg in order to facilitate the LaF, discus-

sion. The basic experimental work on trivalent lanthanide spectra in LaCl,

crystals has been described by G. H. Dieke, Dieke (1968), who also gave a

comprehensive historical review and a brief discussion of early efforts at

theoretical analysis. Most of the subsequent extensions of the latter have

been based on the same data, and no attempt will be made to reproduce them

here.

The effect of the crystalline neighborhood on the electronic orbitals of

the rare earth ion is appreciable, but is nevertheless small compared with the

atomic electron interactions, and to a large extent can be treated in terms of

a model whose basis states are the free-ion orbitals themselves, without need

for specific structural detail of the electronic involvement with ligand ions.

Because of the dominance of the atomic forces it is important to have an atomic

Hamilton!an which is detailed enough to accurately describe the observed crystal

level groupings. In the process we have incidently learned much about the

structure of the atomic energy levels themselves.

In a pure 4f configuration the only interactions to be evaluated would

be the four Slater integrals F 0 , 2 ' 4 , 6 and the spin-orbit integral, s, plus rela-

tivistic correction terms representing spin-other-orbit and spin-spin inter-

actions. Ab initio evaluations for each of these can be carried out; however,

the latter values are not quite in agreement with experimental ones. This is

not because they are inaccurate in themselves but because there are additional

contributions due to ignored inter-configuration interactions which have the

-2-

same angular dependence and are therefore lumped with the former in any empirical

fitting. The experimental values are therefore only effective ones, although

we conventionally continue to give them the original names. These same inter-

actions will in addition produce completely new effective-Hamiltonian operators,

namely: ctL(L+l), Trees (1951, 1952, 1964); &G(G2) and Y G ( R ? ) , Racah (1949) and

Rajnak and Wybourne (1963); T^., the three-body electrostatic effective opera-

tors discussed by Rajnak and Wybourne (1963), Rajnak (1965), Judd (1966,1972)

and Crosswhite et al. (1968); and A-z., the generalized two-body double-vector

operators, Judd et al. (1968) and Crosswhite and Judd (1970).

Fortunately, not all of the theoretically possible operators are needed

in the analysis, and those that are (including the Fk and t, corrections) a-e

all either constant or slowly varying functions of the atomic number Z. For

instance, of the fourteen possible T^., only those six which have non-zero

matrix elements in second-order perturbation theory are retained. Furthermore,

these results are in good agreement with ab initio calculations, Newman and

Taylor (1971,1972), Balasubramanian et al. (1975). A review of the whole ques-

tion of crystal energy level parametrization was given by Newman (1971).

There are thirteen generalized two-body double-vector operators, eight

having rank one in each of the spin and orbital angular momentum spaces. (An

additional one has matrix elements exactly proportional to those of the spin-

orbit interaction and can be ignored). Five have rank two in each of the

spaces. The principal contribution to the latter comes from the spin-spin

interaction and can be estimated by ab initio calculations of the Marvin inte-

grals M 0 , 2' 4, Marvin (1947). The former appears to be dominated by spin-other-

orbit effects, parametrized by the same Marvin integrals, and another effect

arising from the fact that there are spin-orbit matrix elements connecting 4f

-3-

with configurations of the type 4f n'f. Rajnak and Wybourne (1964) have

called these "electrostatically-correlated spin-orbit" effects. Matrix ele-

ments have been given by Judd et al. (1968). Their essential role is to allow

for effective spin-orbit variations with spectroscopic term and are parametrized2 4 6

by the quantities P ' ' . Ab initio calculations have been given by Newman and

Taylor (1972).

A summary of the parameters derived from LaCl, crystal studies is given

in Table 1, Crosswhite (1977). As a rule of thumb for estimating atomic param-Keters appropriate for the LaF, case, the LaCl3 F and c. values reported in

Table 1 should be increased slightly: 1.8% for F2, 1.1* for F4, 0.8% for F6

and 0.5% for t,. More extensive details are given elsewhere; Crosswhite et al.

(1976), Carnal! et al. (1976), Crosswhite et al. (1977), Crosswhite and

Crosswhite (1977). For the major parameters we have found on comparison with

ab initio calculations that the required corrections are remarkably uniform.

Computations with a Hartree-Fock program containing an approximate relativistic

correction, Cowan and Griffin (1976), are given in Table 2, and differences ofit

these and experimental F and t, values are shown in Figs. 1 and 2. The two-

body electrostatic correction parameters a, 3 and y show similar slow varia-i k

tions across the series; the T are essentially constant; and the P can be

taken proportional to ?. The M (spin-other-orbit) are shown in Fig. 2.

The crystalline environment can in principle make contributions to each

of these terms in addition to new ones specific to the particular point-group

symmetry. However, experimentally we find that there is a great similarly be-

tween the parameters for the LaCK-doped spectra and those of the few free ion

cases for which experimental data are complete enough to permit full param-

etrization (La II, Ce III and Pr IV 4f2 and Pr III 4f 3). Systematic values can mV ~ * '

• « r'

APPENDIX I - TABLE 1

3+Parameters f o r Ln :LaCl

ave

F2

F4

F6

Alpha

Beta

Gamma

T2

T3

T4

T6

T7

T8

Zeta

M O b

p 2 cB?BJB|

Pr9928

68368

50008

32743

22.9

-674

[1520]—

—

—

- -

—

—

744

1.76

275

107

-342

-677

466

Nd24186

71866

52132

35473

22.1

-650

1386

377

40

63

-292

358

354

880

1.97

255

163

-336

-713

462

Pm36805

75808

54348

38824

21.0

-645

1425

302

45

34

-315

554

[400]

1022

2.1

319

143

-395

-666

448

Stn47190

78125

56809

40091

21.6

-724

[1700]

291

13

34

-193

288

330

1168

2.4

341

186

-270

-623

470

Eu64542

84399

60343

41600

16.8

[-640]

[1750]

[370]

[40]

[40]

[-330]

[380]

[370]

1331

[2.38]

245

189

-287

-801

525

Gd87538

85200

60399

44847

[19][-643]

1644

[315]

[44]

[40]

[-300]

[325]

[360]

[1513]

[2.82]

495

216

-.72

-688

474

Tb68200

90012

64327

42951

17.5

[-630]

[1880]

[340]

[40]

[40]

[-330]

[330]

[380]

1707

[3.00]

590

185

-291

-457

302

Dy

55894

92750

65699

45549

17.2

-622

1881

311

116

12

-474

413

315

1920

2.8

591

193

-328

-470

287

Ho48193

95466

67238

46724

17.2

-621

2092

300

37

98

-316

440

372

2137

3.0

523

216

-284

-448

294

Er35490

98203

69647

49087

15.9

-632

[2017]

300

48

18

-342

214 f449

2370

4.5

667

216

-271

-411

272

o>

sra.<a>

(t>

-nCO

o

03

2u>n

2(t>

STto

tn

aValues in brackets were not f reely varied.b0nly M° was varied; the ratios M2/M° = 0.56, M4/M° = 0.38 were maintained.c0nly P2 was varied; the ratios P4/P2 = 0.75, P6/P2 = 0.50 were maintained.

•>a

-5-

APPENDIX I - TABLE 2

,NRelat iv is t ic Hartree-Fock Integrals for 4f IV.

4f2

4f3

4f4

4f5

4f6

4f7

4f8

4f9

4 f 1 0

4 f "

4 f 1 2

4 f 1 3

Ce

Pr

Nd

Pm

Sm

Eu

Gd

Tb

Dy

Ho

Er

Tm

Yb

IV

IV

IV

IV

IV

IV

IV

IV

IV

IV

IV

IV

IV

F2

.

98723

102720

106520

110157

113663

117058

120366

123592

126751

129850

132897

-

F4

_

61937

64462

66856

69143

71373

73470

75541

77558

79530

81462

83361

-

F6

_

44564

46386

48111

49758

51342

52873

54361

55810

57227

58615

59978

-

696.

820.

950.

1091

1243

1407

1584

1774

1998

2197

2431

2680

2947

41

22

51

.46

.60

.71

.45

.46

.44

.06

.00

.97

.69

1.

2.

2.

2.

3.

3.

3.

3.

4.

4.

4.

M°

_

991

237

492

756

031

318

615

924

246

580

928

-

M2

-

1.110

1.248

1.391

1.540

1.694

1.855

2.022

2.195

2.376

2.563

2.758

-

M4

-

0.752

0.846

0.943

1.044

1.149

1.258

1.372

1.490

1.612

1.739

1 . i 72

-

Pr Nd Pm Sm Eu 6d Tb Dy Ho Er Tm

Fig. 1. Variation of the differences between the pseudo relativistic

Hartree-Fock (HFR) values of the Slater integrals i-"k and those determined

experimentally, Fk(HFR)-Fk(EXP) = AFk, with lanthanide atomic number.

C..

\J\J

80

60

4 0

20

o

C βi

—

—

i

Pri

c0

i

Ndi

Pm1

0

I

Smi

- 2 -

|

Eui

o

GdI

•' —

1

Tb1

o

i

Dy1

o

i

Hoi

\

o

1

Er1

1

TmI

X

l

Yb1

i 1

i

1

i

w —

—

i

1.0

0 . 8 -

0.6

/M° (SPIN OTHER ORBIT)EXP HrR

i

—

_

i

I

1

1

i

i i

o• " - " " - • ^ r

1 1

1

1

1

1

1

O

|

1 1

o

1 1

1

-

—

1

Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm

Fig. 2. Variation of the differences between the pseudo relativist1c

Hartree-Fock (HFR) values of the spin-orbit Slater Integral c> and those

determined experimentally, 5(HFR)-c(EXP) = Ac; and the ratios of the

corresponding spin-other orbit values M|x p/Mf)

F R with lanthanide atomic

number.

A V', I

-6-

i k k

be found for the T and a. (or alternately M and P ) which satisfy all known

spectra, whether free ion or crystal, in terms of only a few constants. It

follows therefore that the same model can be used for preliminary estimates for

other spectra such as LaF3-doped crystals.

As to the parametrization of the crystal-field itself, the general spec-

ification that the number of possible two-particle operators is equal to the

number of available independent cells in the Hamiltonian requires 366 additional

ones besides the ten single-particle •mes (of which only four are formally used).

Fortunately, the single-particle modeu, Judd (1963), Wybourne (1965), Dieke

(T968), works very well, although we must recognize that these parameters repre-

sent much more complicated effects than the simple Coulomb model visualized by

the early theories. Newman and Taylofr (1971) give a discussion of the physical

significance of these parameters.

APPENDIX I I

A'A

V '"if

BLANK PAGEcuaa•a

7 ' . ' ' •• '

APPENDIX I I - TABLE 1

Atomic Parameters for Ln3+:LaF,

EAV

F2

F4

F6

a

0

y

C

T2

T3

T4

T6

T7

T8

M0(b)

M2(b)

M4(b)

P2(c)

p4(c)

p6(c)

Pr

10163.

69305.

50675.

32813

(21)

-842

1625

750.8

-

-

-

-

-

-

(1.99)

0.11)(0.75)

(200)

(150)

(100)

Nd

24490.

73036

52624

35793

21.28

-583.

1443

884.9

306

41

59

-283

326

298

(2.237)

(1.248)

(0.84)

213

160

106.5

Pm

(37272)

(77000)

(55000)

(37500)

(21.00)

(-560)

(1400.)

(1022.)

(330.)

(41.5)

(62.)

(-295.)

(360)

(310)

(2.49)

(1.39)

(0.94)

(440)

(330)

(220)

Sm

47760.

79915

57256

40424

20.07

-563

1436

1177.2

288

36

56

-283

333

342

(2.76)

(1.54)

(1.04)

344

258

172

Eu

(64263)

(84000)

(60000)

(42500)

(20.)

(-570)

(1450)

(1327)

(330)

(41.5)

(62)

(-295)

(360)

(310)

(3.03)

(1.69)

(1.15)

(300)

(200)

(150)

Gd

87847.

85587

61361

45055

(20.)

(-590)

(1450)

1503.5

(330)

(+41.5)

(+62)

-(295)

(+360)

(+310)

(3.32)

(1.85)

(1.26)

611

458

306

Tb

68608.

91220

65798

43661

19.81

(-600.)

(1400)

1702

(+330)

(+41.5)

(+62)

-(295)

(+360)

(+310)

(3.61)

(2.02)

(1.37)

583

437

291

Dγ

56492.

94877

67470

45745

17.64

-608

1498

1912

+423

+50

+117

-334-

+432

+353

(3.92)

(2.19)

(1.49)

771

578

386

Ho

48453.

97025

68885

47744

18.98

-579

1570

2144

(+330)

(+41.5)

(+62)

-(295)

(+360)

(+310)

(4.25)

(2.38)

(1.61)

843

632

421

Er

35915.

100274

70555

49900

17.88

-599

1719

2381

+441

+42

+64

-314

+387

+363

(4.58)

(2.56)

(1.74)

852

639

426

Tm

18000..

102459

72424

51380

(17.)

-737

(1700)

2640

(4.93)

(2.72)

(1.37)

729.6

547

364

No. ofLevels f i ta 41

11 139

16.6

180

16.7

649

(26 )d36

201

22

(27 )d

32

117

12.1

Values In parenthesis were not freely varied.

assumed.: 0.75, P6/P2 = 0 . 5 were maintained.

Relativistic Hartree-Fock values werec0nly P was varied, the ratios P4/P2 !

Free-ion Hamiltqnian only

(12) c

76

-2-

APPENDIX I I - TABLE 2

Crystal-field Parameters for Ln3+:LaF3

Nd

216

1225

1506

770

Sm

209

1042

1415

659

Gd

(210)

(1050)

(1250)

(600)

Dy

218

1099

1129

553

Er

229

965

909

484

0n

~ r

APPENDIX III

0n

e

;>:•

PAGE

APPENDIJ

PR+3:LAF3

OBSEBVED

200

4487

521565687031

1

: in

TABLE 1CENTERS OF

CALC

19123034495

519665957009

o-c9

• • •

-7

19-26

22

GRAVITY

STATE

3H43H53H6

3F23F33F4

10001 10012 -10 1G«

17047 17052 -4 1D2

20927 20935 -7 3P021514 21555 -40 3P1

2174322746 22690

46986 46986

11656 3P2

0 ISO

M

00000

11111111

?222222

222222

33333

4444

444

55

LEVEL 1

2093120931209312093120931

2155221552215522155221552215522155221552

5194519451945194519451945194

170541705417054170541705417054

65956595659565956595

189189189189

700870087008

23052305

J2

22446

12234456

2234456

234456

34456

4456

456

56

PAGE 2APPENDIX III

TABLEU(K)*2

LEVEL 2

519417054189

70084499

215525194

170546595189

700823054499

5194170546595189

700823054499

170546595189

700823054499

6595189

700823054499

189700823054499

700823054499

23054499

2FOR PR+3

(02)*2

00000

0000,00,0,0,

00.0,0,0.0.0,

0,0.0.0.0.0.

0.0.0.0.0.

0.0.0.0.

0.0.0.

0.0.

.2954

.0152

.0

.0

.0

.1607

.2685

.0799

.5714

.0

.0

.0

.0

.0618

.0140,0209.5090.0014.0.0

.3745

.0319,0027,6015,0,0

06250653,02526285,0

7782018910950000

014602965668

91921080

(U4)*2

0.0.0.0.0.

0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.

0.0.0.0.0.0.

0.0.0.0.0.

0.0.0.0.

0.0.0.

0.0.

.0,0,17291079,0

,00.019641702263628570

0065086605094030001229770164

329501770174000000190686

00303465073134673182

4645050320120333

242731166095

36682327

(U6)*2

0.0.0.0.0.

0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.

0.0.0.0.0.0.

0.0.0.0.0.

0.0.0.0.

0.0.0.

0.0.

,00,000726

00000008921246

0001173090565903038

000534020100040066

06256982005408459

2642488961151392

035844 0746 23

12146420

f

':J •

4499 4499 1.2383 0.7108 0.7878

APPENDIX IV

JBSERVB

045136296500

197820 3720 68209121872223

3918397840384076411842084278

58165874598661416167632364546556

1159211634

125961261412622126761269412754128 4312902

135141359013671136761371113715

PAGE 1

APPENDIX IV

ID CALC

338142294500

196320 H :2075209822032227

3901398340434102412642054275

58205838599761716187629364206545

1159611626

1258512589126301267812704127631285412873

135141358313673136931369513711

TABLI! 1ND+3:LAF3

O-C

-27-520

15-4-6-6-15-3

17-4-4

-25-733

-336

-10-29-19303H11

-38

1125-7-1-9-8

-1029

07

-1-16164

STATE J

4141414141

414141414141

41414141414141

4141414141414141

4F4F

2H24F4F4F4F2H22H22H2

4F4F4Fas4S4F

9/29/29/29/29/2

11/211/211/211/211/211/2

13/213/213/213/213/213/213/2

15/215/215/215/215/215/215/215/2

3/23/2

9/25/25/25/25/29/29/29/2

7/27/27/23/23/27/2

MJ

-9/25/23/21/2

-7/2

-11/25/23/21/2

-7/2-9/2

13/25/23/21/2

-7/2-9/2-11/2

15/2-7/2-9/25/21/23/2

-11/213/2

1/23/2

-7/23/21/25/21/23/2

-9/25/2

3/2-7/21/21/23/25/2

»BSEFVE

1463114861148921492614959

159971603316060160461610016165

17316173061736317510175201757117605

19147192351925219324

19567196 15196511970419686• • •197411979919835• • •

• • «

19960

2115521176211982123221252

2133821353

PAGE 2

APPENDIX IV

!D CALC

1484714861148861492414957

160281604616059160601609516140

17308173111736017491175051756417611

19139192451927119324

195671963219645196871969319737197381979019845199171992719971

2115021183211992123521267

2133921352

TABLf! 1ND+3:LAF3

O-C

-120622

-30-12

1-13

525

8-4319157-5

8-9

-180

0-16

617-6

• • •

39

-9• • •• m •

-10

5-60-2-14

01

STATE J

4F4F4F4F4F

2H22H22H22H22H22H2

4G4G4G462G14G4G

4G4G4G4G

2K4G2K4G4G2KUG2K4G2K2K2K

2G12G12G12G12G1

2D12D1

9/29/29/29/29/2

11/211/211/211/211/211/2

5/25/25/27/27/25/25/2

7/27/27/27/2

13/29/213/29/29/213/29/213/29/213/213/213/2

9/29/29/29/29/2

3/23/2

HJ

1/23/23/25/2

-7/2

5/2-11/2

3/2-7/21/2

-9/2

3/21/25/25/23/25/21/2

5/21/23/2

-7/2

13/25/21/2

-7/2-9/2

-11/23/23/21/25/2

-9/2-7/2

-7/23/2

-7/21/2

-9/2

3/21/2

77

!'J . \:

S.

)BSEPV

• * •

• • •

2163321718• • •• • *• • •• • *• • •

21816• • •• • •• • «

21992

23473

• • •2399124080

2637826426

2834128374

« • •28525• • •

28676289622946329489295682964429773

30275• • •• • •

• • «

• • •

• • •

30576• • •

30631306823071930807

PAGE 3

APPENDIX IV

!

ED CALC

2153521620216212173121774217792179021824218272185721901219312194621995

23455

239962399924057

2639426416

2836128369

28495285282863428686289382945929475295652965929767

302713034 63041130451305333053430602306153064 6307013071230792

TABLE 1»D+3:LAF3

O-C

• • •• • •12

-12• • «* « •• • #• « •• • •

-10• • •• • •* • •-2

18

• • •

-723

-1510

-195

• • •

-2• • •-9244143

-146

4• • •• • •• • •

• • •

• • •

-25• • •-14-18715

STATE J

4G2K4G464G2K4G2K2K2K2K2K2K4G

2P

2D12D12D1

2P2P

4D4D

4D4D214D4D2121212121

2L2L2L2L212L4D2L4D2L4D4D

11/215/211/211/211/215/211/215/215/215/215/215/215/211/2

1/2

5/25/25/2

3/23/2

3/23/2

5/25/211/25/21/211/211/211/211/211/2

15/215/215/215/215/215/27/215/27/215/27/27/2

MJ

-7/215/25/2

-9/2-11/213/2-9/21/25/23/2

-11/2-9/2-7/21/2

1/2

3/21/25/2

1/23/2

1/23/2

5/21/2

-11/23/21/2

-9/2-7/25/23/21/2

13/215/21/23/2

-11/25/25/2

-9/2-7/2-7/23/21/2

V;,; V*'t".v

experimentally, FR(HFR)-FR(EXP) = AFK, with lanthanide atomic number.

',-;>,

?.'•••'- '•".',"

)BSERVE

• • •3089330933309943103031068• • •

3178131859• • •• • •• • •• * •• « •• • •• • *

3303033107331813322833255

3361933649

34292343803441934521

• • •

• • •

3467834706

• • •

386903875538841

4010340155

a • •

40288

PAGE 4

APPENDIX IV

B CALC

30850308953095531002310413107031079

317673183631926319683199032013320483209332126

3303533137331683322633258

3361233631

342743437434445345193455134573346863470934818

387233877838815

40113401264018740254

TABLE 1ND+3:LAF3

O-C

• • •-1

-21-7

-10-1

• • •

1423• • •• • •• m •

• • •

• • •

• * «

• • •

-4-29132

-2

718

186

-252

• • *• • •-7-2• • •

-32-4226

-929

• • •34

STATE J

21212121212121

2L2L2L2L2L2L2L2L2L

2H12H12H12H12H1

2D22D2

2H12H12D22H12H12H12H12D22H1

2F22F22F2

2F22F22F22F2

13/213/213/213/213/213/213/2

17/217/217/217/217/217/217/217/217/2

9/29/29/29/29/2

3/23/2

11/211/25/211/211/211/211/25/211/2

5/25/25/2

7/27/27/27/2

HJ

-11/2-9/2-7/213/25/23/2V2

15/217/21/23/2

13/25/2

-11/2-9/2-7/2

-7/21/2

-9/25/23/2

3/21/2

-9/21/25/2

-7/21/23/2

-11/23/25/2

5/21/23/2

-7/23/21/25/2

BSEBVE

4789447937479994 80 43

48839489084897749088

• • •• • •• • •

• • •

• • •

• • «

• • •

PAGE 5

APPENDIX IV

ID CALC

4787147888479644800648055

48861488694897949065

6654 8667056679366859

678576785868075

TABLE 1ND+3:LAF3

O-C

• • •6

-26-6

-11

-2139-123

• • •• • •• • •• • •

* • •

• • •

• • *

STATE

2G22G22G22G22G2

2G22G22G22G2

2F12F12F12F1

2F12F12F1

J

9/29/29/29/29/2

7/27/27/27/2

7/27/27/27/2

5/25/25/2

MJ

5/2-9/2

3/2-7/2

1/2

-7/23/25/2V2

5/2-7/2

3/21/2

5/23/2V2

•- A

!#l

PAGE 6

APPENDIX IV

TABLE: 1AND+3:LAF3 CENTERS OF GRAVITY

CALC CENTER

235211440986148

11621126601276813619136911489916105

1742817469192931970919785214252171421780234582400426424

STATE

41 9/24111/24113/24115/2

4F 3/24F 5/22H 9/24F 7/24S 3/24F 9/22H11/2

4G 5/24G 7/24G 7/24G 9/22K13/22D 3/24G11/22K15/22P 1/22D 5/22P 3/2

01

1/21/21/21/21/21/21/21/21/21/21/21/21/21/21/21/2

3 / 23 / 23 / 23 / 23 / 23 / 23 / 23 / 23 / 23 / 23 / 23 / 23 / 23 / 23 / 23 / 23 / 23 / 23 / 23 / 2

3 / 23 / 23 / 23 / 23 / 23 / 23 / 23 / 23 / 23 / 23 / 23 / 2

XEVEL

23U58234582345823458234582345823458234582345823458234582345823458234582345823458

1162111621116211162111621116211162111621116211162111621116211162111621116211162111621116211162111621

136911369113691136911369113691136911369113691136911369113691

1 J2

3 / 23 / 23/23 ,25 / 25 /25 /27 / 27 / 27 / 29 /29 / 29 / 29 /2

11/213/2

3 / 23 / 23 / 25 / 25 / 25 /27 / 27 / 27 / 29 /29 / 29 / 29 / 2

11/211/211/213/213/215/215/2

3 / 23 / 25 /25 / 27 / 27 /29 / 29 / 29 / 29 /2

11/211/2

PAGEAPPEKDIX

TABLEi 2U(K)*2 FOR

LEVEL 2

11621136912142526424126601742824004136191746919293

2351276814899197091610519785

116212142526424126601742824004136191746919293

2351276814899197092114

1610521714

4098197856148

21780

214252642417428240041746919293

23512/681489919709

211416105

7IV

ND+3

(U2)*2

0000000000000000

0000000000000,0,0,00.0.0,0,

0.0.0,0 .0 .0 .0 .0.0 .0 .0 .0 .

.0131

.0175

.0291

.0056

.0101.0346.0260. 0. 0. 0. 0. 0. 0. 0. 0. 0

.0612

.0050

.0024

.0773

.4856

.0009

.0063

.0735

. 1062

. 0

. 0

. 0

. 0

.0

.0

.0

.0

.0

.0

.0

.0073

.0060

.0007

.0071,0006.0021.0.0,0,0,0,0

(04)*2

0600000000000000.

0,0,0.0.0.0,0.0.0.0.0.0.0.0 .0 .0 .0 .0 .0 .0 .

0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .

. 0

. 0

. 0

. 0

. 0

. 0

. 0

.0200

.0097

.0026

.0396

.0871

.0033

.0010

. 0

.0

. 0

.0

.0

.0533

.0433

.0007

.0800

.0400

.0629

.2283,0149,0046,05701423

,00010015

,0.000

001775000007312023002500440023192200000563

(06) *2

0 . 00 . 00 . 00 . 00 . 00 . 00 . 00 . 00 . 00 . 00 . 00 . 00 . 00 . 00.16430.1746

0 . 00 . 00 . 00 . 00 . 00 . 00 . 00 . 00 . 00.05540.02230.11150.14510.40830.00810.09920.20930.00760.02800.0099

0 . 00 . 00 . 00 . 00 . 00 . 00.23470.00010.00110.00090.20990.0016

J1

3/23/23/23/2

3/23/23/23/23/23/23/23/23/23/23/23/23/23/23/23/23/23/2

3/23/23/23/23/23/23/23/23/23/23/23/23/23/23/23/23/2

5/25/25/25/25/25/25/25/2

LEVEL

13691136911369113691

21425214252142521i»252142521425214252142521425214252142521425214252142521425214252142521425

2642426424264242642426424264242642426424264242642426424264242642426424264242642426424

1266012660126601266012660126601266012660

1 J2

11/213/215/215/2

3/23/25/25/25/27/27/27/29/29/29/29/211/211/211/213/215/215/2

3/25/25/25/27/27/29/29/29/29/211/211/211/213/213/215/215/2

5/25/25/27/27/27/29/29/2

PAGEAPPENDIX

TABLE: 2U(K) *2 FOR

LEVEL 2

2171440986148

21780

2142526424126601742824004136191746919293235

1276814899197092114161052171419785614821780

264241266017428240041361919293235

12768148991970921141610521714-' 4098197856148

21780

126601742824004136191746919293235

12768

8IV

ND+3

(U2)*2

0000

000000000000000000

000.0,0,00,0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.

.0

.0

.0

.0

.0161

.0052

.0038

.0002

.1744

.0025

.0104

.0206

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0838

.0022

.0058

.0074

.0003

.0063

.0

.0

.0

.0

.0

.0,0,0,0,0,0

04622671,000506552504256900060062

(U4)*2

0000

000000000000000,0,0.0

0.0,0.0.0.0-0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.

.3245

.0

.0

.0

.0

.0

.0000

.0039

.0011

.0001

.0839

.0418

.0202

.0259

.0003

.0023

.0016

.1078

.0300

.0

.0

.0

.0

.0033

.0000

.0001

.0007

.0052,0010,01000527,0601,0159,019400430000

02181301000605400075000923370308

(06) *2

0000

000000000000,0,0,000.0,

0,0.0.0,0.0.0.0,0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.

.0004

.3295

.3306

.0030

.0

.0

.0

.0

.0

.0

.0

.0

.0001

.0872

.0139

.0325

.0326

. 1807

.0003

.0860

.0083

.3482

.0

.0,0.0,0,0,0005.0813,05780647,0005,013600000098231900290076

00008720750119539830052

t e « >- O U-< j - a

J1

5/25/25/25/25/25/25/25/25/2

5/25/25/25/25/25/25/25/25/25/25/25/25/25/25/25/2

5/25/25/25/25/25/25/25/25/25/25/25/25/25/2

7/27/27/27/27/27/27/27/2

LEVEL

126601266012660126601266012660126601266012660

17428174281742817428174281742817428174281742817428174281742817428174281742817428

2400424004240042400424004240042400424004240042400424004240042400424004

1361913619136191361913619136191361913619

1 J2

9/29/2

11/211/211/213/213/215/215/2

5/25/27/27/27/29/29/29/29/211/211/211/213/213/215/215/2

5/27/27/27/29/29/29/29/2

11/211/211/213/213/215/2

7/27/27/29/29/29/29/2

11/2

PAGEAPPENDIX

TABLE: 20(K)*2 FOR

LEVEL 2

1489919709211416105217144098197856148

21780

17428240041361917469192 93235

127681489919709211416105217144098197856148

21780

24004136191746919293235

1276814899197092114161052171440981978521780

136191746919293235

1276814899197092114

9IV

ND+3

(02)*2

000000000

000000000000000.0,

0.0,0.0.0.0.0.0.0.0.0.0.0.0.

0,0.0.0.G.0.0.0.

.0105

.1912

.0

.0

.0

.0

.0

.0

.0

.0024

.0014

.0382

.0002

.0000

.8975

.0012

.0026

.0000

.0

.0

.0

.0

.0

.0

.0

.2977

.0005

.0064

.0003

.0000

.0078

.0003

.0000,0,0.0.0,0,0

,15251267174700110056093455480009

(04)*2

000000000

00,000,00,0,0,00,0,0.0,0,0.

0.0.0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.

.0508

.0995

.1698

.0030

.0611

. 1817

.0026

.0

.0

.1883

.0008

.1047

.1321

.2391

.4126

.0134

.0070

.1035

.2867

.0002

.0094

.0342

.0018

.0,0

,0045,0171.0688,0481,00021994,01100077000125230314003700330

00820589073204060344091200012335

(U6)*2

0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.0.0.0.

o.0.,0.0.0.0.0.0.

,1091,002203690239,19764010004823000051

00,16260845057103460018130324770961014509140485007700460051

00064175605580017079101320064002901840006016918284889

1033,0104002342720040078308~253076

J1

7/27/27/27/27/27/2

7/27/27/27/27/27/27/27/27/27/27/27/27/2

7/27/27/27/27/27/27/27/27/27/27/27/2

9/29/29/29/29/29/29/29/29/29/29/2

9/29/29/29/2

LEVEL

136191361913619136191361913619

17469174691746917469174691746917469174691746917469174691746917469

192931929319293192931929319293192931929319293192931929319293

235235235235235235235235235235235

12768127681276812768

1 32

11/211/213/213/215/215/2

7/27/29/29/29/29/211/211/211/213/213/215/215/2

7/29/29/29/29/211/211/211/213/213/215/215/2

9/29/29/29/211/211/211/213/213/215/215/2

9/29/29/211/2

PAGE 10APPENDIX

TABLII 2U (K)*2 FOR

LEVEL 2

16105217144098

197856148

21780

1746919293235

12768148991970921141610521714409819785614821780

19293235

127681489919709211416105217144098197856148

21780

235127681489919709211416105217144098197856148

21780

1276814899197092114

IV

SD+3

(02)*2

000000

0000000000000

0000,0.0,0.0,0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.

.0336

.1729-0.0.0.0

.0111

.0633

.0707

.0088

.0261

.0730

.3996

.0068

.0119

.0

.0

.0

.0

.0937

.0596

.0508

.0006

.0375

.6684

.0011

.0023

.0

.0

.0,0

1195,0095,0009,0044,0194,0000,00000000007100

1156048703900028

(U4)*2

000000

0,00,0,0,00,0,0,0,0,0.0.

0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.

.0154

.1623

.3314

.0664

.1553

.0000

.0002

.0008

.1720

.0292

.0504

.1395

.1764

.0000

.1233

.0875

.7062

.0010

.0383

.0433, 1709,0543,0112,144910750197,03412407517902730186

17270082009205841072002700520135000200000052

0016002904780004

(U6)*2

000000

00000,0000,0,00,0,

0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.1.0.0.0.0.0.0.

0.0.0.0.

. 1287

.1447

.0001

.0003

.6166

.0077

.0189

.0359

.0274

. 1989

.2665

.0034

.0522

.3593

.0015

.0345

.0012

.1064

.0122

.0772

.0566

.3685,0099.1417, 0099,1020,3811,0613,001400450018

68921195040603831639010400794549033004520149

2728001809820254

6

J1

9/29/29/29/29/29/2

9/29/29/29/29/29/29/29/29/2

9/29/29/29/29/29/29/2.9/2

11/211/211/211/211/211/211/2

11/211/211/211/211/211/2

11/211/211/211/211/2

13/215/213/2

LEVEL

127681276812768127681276812768

148991489914899148991489914899148991489914899

1970919709197091970919709197091970919709

2114211421142114211421142114

161051610516105161051610516105

2171421714217142171421714

409840984098

0

1 J2

11/211/213/213/215/215/2

9/29/211/211/211/213/213/215/215/2

9/211/211/211/213/213/215/215/2

11/211/211/213/213/215/215/2

11/211/213/213/215/215/2

11/213/213/215/215/2

13/213/215/2

PAGE 1APPENDIX

TABLI: 2(K)*2 FOR

LEVEL 2

16105217144098197856148

21780

1489919709211416105217144098197856148

21780

1970921141610521714409819785614821780

21141610521714409819785614821780

1610521714409819785614821780

217144098197856148

21780

4098197856148

1IV

ND+3

(02) *2

000000

000000000

00000000

0,00.0.0,0,0,

0.0.0.0.0.0.

0.0.0.1.0.

0.0.0.

.0687

.1796

.0389

.1211

.0

.0

.1407

. 1181

.0001

.0873

.9423

.0029

.0462

.0

.0

.0042

.1403

.0032

.0521

.9552

.0210

.0

.0

.1321

.0043

.0044

.0256

.0002

.0000

.0020

.0107

.0009

.0043,0014, 1293,1556

,00151283000153010099

169300320195

(U4)*2

000000

00,0,00,0,0,0,0,

0,0.0.0.0.0.0.0.

0.0.0.0.0.0.0.

0.0.0.0.0.0.

0.0.0.0.0.

0.0.0.

.0037

.0001

.0064

.0063

.2155

.4675

.0960

.1593

.0328

.0239

.2060

.2148

.0042

.5000

.0003

.0063

.3495

.0308

.5102,3843.0440, 1426, 1408

,1159,00940645,1352,000001090003

,000908090168004406870017

63443514007789150162

172900011187

(U6)*2

0.0.0,1.0.0.

0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.

0.0.0.1.0.0.0.

0.0.0.0.0.1.

0.0.0.0.0.

0.0.1.

.2755,0037.1217, 1292,0775,4145

,000302073702017204115102293146282037

01220505231012060157113123980246

0673006205632376016841800039

028401090029479500005224

18581609023315900912

233100244522

'.1

7 '•'

• 'f,' c' -' '~\••* „ • i

8

1 08CD

CO

ro

gABSORBANCE UNITS

-4278

— 4208

— 4076

>=—4038

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-3978

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c 3918

',. » '

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.'.•;.-• £4

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ABSORBANCE UNITSP P— C\J

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-61676141

5986

5874

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5816 £

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APPENDIX; V

PAGE 1

APPENDIX V

TABLE 1PM+3:LAF3 CENTERS OF GRAVITY

OBSERVED CALC

1201612323919516714

126381308013933

. . . 144861488716223

1693918053180751825518565198622030720554219352247522807231402377224216247022484024907258112589525907

O-C STAT

. . . 514

. . . 515

. . . 516

. . . 517

. . . 518

. . . 5F1

. . . 5F2

. . . 5i>3

. . . 5S2

. . . 5F4

. . . 5F5

3K6. . . 562. . . 3H4. . . 3K7

5G 33K8

. . . 3H5

. . . 5G4

. . . 3G 3

. . . 5G5. . . 5G6. . . 3D2. . . 3L7. . . 3P1

3H63G4

. . . 3L 8

. . . 3P0

. . . 3D3

. . . 319

BLANK PAGE

/*<?

M

000000

11111111111111111111

111111111111111

222222

LEVEL 1

258102581025810258102581025810

1265812656126581265812658126581265812658126581265812658126581265812658126581265812658126581265812658

242212422124221242212422124221242212422124221242212422124221242212422124221

130941309413094130941309413094

J2

244666

12223334444555566777

222334455566677

222333

PAGE 3APPENDIX V

TABLEU(K)*2

LEVEL 2

231421488218083

32471695722787

12658130941807023142139391857721946

161148821808320565

1639162082030322476

324722787

49371825823796

13094180702314218577219461808320565

16392030322476

32471695722787

493718258

130941807023142139391857721946

2FOR PM+3

(02)*2

000000

00000000,00,0,0,00,0,0,0,0,0,0.

0.0.0.0.0 .0.0.0.0 .0 .0 .0 .0 .0 .0 .

0 .0 .0 .0.0.0.

.0054

.0

.0

.0

.0

.0

.0268

.0529

.2682

.0032

.0177

.1965

.0225

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0,0.0

.0013

.0077,0082.0100,0539,0,0,00000000

020228600001089914860339

(04) *2

0.0.0.0.0.0.

0.0 .0 .0.0.0 .0.0.0.0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .

0.0.0.0 .c.0.0 .0.0 .0 .0.0.0 .0 .0 .

0.0 .0 .0.0.0 .

,0,0019,0142,00

,0

,0.0,00

,0641046901051405032202770604153200160090006600000

000010105370137023600470402034000000

079407220011000303700127

(U6) *2

0.00.00.00.00370.08200.0168

0 . 00 . 00 . 00 . 00 . 00 . 00 . 00 . 00 . 00 . 00 . 00.15440.13030.04620.08560.29860.03030.06800.00460.0016

0.00.00.00 . 00 . 00 . 00 . 00.01320.01210.00540.00490.00190.06540.00190.2964

0.00.00.00.00.00.0

•4 .,'

I - y--*'

J1

22222222222222

22222222222222

22222222222222222222

LEVEL 1

1309413094130941309413094130941309413094130941309413094130941309413094

1448614486144861446614486144861448614486144861448614486144861448614486

1807018070180701807018070180701807018070180701807018070i30701807018070180701807018070180701807018070

J2

44445555666788

23344455b56678

22333444455556677788

PAGE 4APPENDIX V

TABLE0(K)*2

LEVEL 2

1611488218083205651639

1620820303224763247

169572278749376674

19845

180701857721946

16118083205651639

1620820303224763247

2278749376674

1807023142139391857721946161

1488218083205651639

1620820303224763247

227874937

18258237966674

19845

2FOR PB+3

(U2)*2

00000000000000

000000,0,0,0,0,0,0.0.0.

0.0.0.0.0.0.0.0.0.0.0.0.0»0.0.0.0.0.0.0.

.0016

.0385

.0916

.2071

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0030

.0033

.0000

.0000

.0003

.0007

.0

.0

.0

.0

.0

.0

.0,0

,0011,0035,0610.0013,0013729300240006002700000000000

(U4)*2

00000000000000

00,00,0,0,0,0.0.0.0,0.0.0.

0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.

.2042

.0705

.0097

.0209

.0594

.0172

.0733

.0634

.2200

.0032

.0032

.0

.0

.0

.1411

.2032

.0308

.0011

.0794

.2059

.0000

.0035

.1422

.1509

.0023

.3099

.0,0

,03450013,11192434,0203241202121209140927020003036502350372000800000

<U6) *2

0000000000,0000

0,0,0,0.0,0,0,Is.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.

.1258

.0537

.0174

.0929

.2878

. 1467

.0135

.0125

.0825

.00 33

.1147

.3057

.0743

.0130

.0

.0

.0

.2296

.0003

.0022

.1908

.00 04

.0014

.0023

.23 94,00 37,36 833463

,00000004920000081113304070988080209230781020302030097015800130111

11°

PAGE 5APPENDIX V

TABLE 20{K)*2 FOB PM+3

J1 LEVEL 1 J2 LEVEL 2 (02)*2 (04) *2 (06)*2

I'0

222222222222222222

3333333333333333333

3333333333

231422314223142231422314223142231422314223142231422314223142231422314223142231422314223142

13939139391393913939139391393913939139391393913939139391393913939139391393913939139391393913939

18577185771857718577185771857718577185771857718577

233344445555666778

3334444555566677789

3344445555

23142139391857721946

161148821808320565

16391620820303224763247

1695722787182582379619845

139391857721946

161148821808320565

1639162082030322476

32471695722787

49371825823796

667425888

1857721946

161146821808320565

1639162082030322476

00000000000,00,0,0,00.0,

0.0.0.0,0.0.0.0.0.0.0 .0.0 .0.0 .0.0 .0 .0 .

0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .

.0521

.0104

.0161

.0002

.0044

.0010

.0878

.0067

.0

. 0

.0

.0

.0

.0

.0

.0

.0

.0

.0221

.3740

.0344

.0001

.1295

.0407

.2248

.0000,0285,18191560

,000

,0,0000

0000007015380623018400487098001100000020

0.08300.00000.00780.00660.00200.00450.07910.04120.00030.00030.02010.0S700.01970.00810.03310 . 00 . 00 . 0

0.05890.04150.00070.10790.03490.00070.03790.24290.06730.09280.05950.07770.00560.07270.24880.00460.00080 . 00 . 0

0.04710.00000.28550.07920.11970.09220.02760.00320.19070.0568

0 . 00 . 00 . 00 . 00.00250.00240.01270.00000.03420.00090.13290.09270.01840.07230.06470.01260.01370.4641

0.04090.12230.03440.42260.11350.00400.03160.02600.08100.02850.01100.20990.00120.17610.25510.00320.00080.33260.0094

0.08760.05790.05120.01560.00020.05700.01730.22120.09100.0397

K' i .-'-*• -A

' , ' , ' ' ' . ' •}•

J1

333333333

33i333333333333333

44444444444444444

444

f\

LEVEL 1

185771857718577185771857718577185771857718577

219462194621946219462194621946219462194621946219462194621946219462194621946219462194621946

161161161161161161161161161161161161161161161161161

148821488214882

J2

666777889

344445555666777889

44445555666777889

444

PAGE 6APPENDIX V

TABLEU(K) *2

LEVEL 2

324716957227874937

182582379666741984525888

21946161

1488218083205651639

162082030322476324716957227874937

182582379666741984525888

1611488218083205651639

1620620303224763247

1695722787493718258237966674

1984525888

148821808320565

2FOB PM+3

(02)*2

000000000

00000,0,0,0.0,0,0,0.0,0,0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.

.0

.0

.0

.0

.0

.0

.0

.0

.0

.1057

.0137

.0108

.0298

.0495

.1623

.0004

.0042

.0224

.0

.0

.0

.0

.0,0.0.0.0

,1156,0004.007900810247000000010002001700210000000000

018022262695

(U4)*2

000000000

00000000,00.00,00.0,0.0.0.

0,0.0,0.0.0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.

.3298

.0008

.0238

.0533

.0245

.0606

.0

.0

.0

.0228

.0428

.0269

.0264

. 1601

.0314

.0100

.0005

. 1341

.0422

.0189

.0022

.0048

.0806

.2660

.0

.0

.0

.1393

.0290

.0313

.0883

.1172,0020,00790082,030000230003002400180014000000020

000011790467

(06) *2

000000000

00,00,0,0,0,0.0.0.0,0.0.0.0,0.0.0.

0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.

.0388

.0073

. 1178

.0611

.0070

.0088

.00 48

.0105

.0362

.0094

.0056

.0000

.1162

.0046

.0201

.0106

.0163

.0825

.0003

.04 98,00 97.0174,0310.1614,00 86.0026,0110

,34 952400,027807649702034101020330689101010016157301910095010100800017

069304 530319

//a-

11

44444444444444

4444444444444444

444444444444444

55

LEVEL 1

1488214882148821488214882148821468214882148821488214882148821488214882

180631808 31808318083160831808318083180831808318083180831808318083180831608318083

20565205652056520565205652056520565205652056520565205652056 5205652056520565

16391639

J2

5555666777889

10

445555666777889

10

45555666777889

10

55

PAGE 7APPENDIX V

TABLE 2U(K)*2

LEVEL 2

163916208203 122476

32471695722787

49371825823796

6674198452588830230

1808320565

1639162082030322«76

3 *4 71695722787

49371825823796

6674198452586830230

205651639

162082030322476

32471695722787

49371825823796

6674198452588830230

163916208

FOR PM+3

( 0 2 ) * 2

0.00250.13600.25520.33710.00560.00090.20400 .00 . 00 . 00 . 00 . 00 .00 . 0

0.07710.12870.05150.02450.00170.03020.21660.02650.01460 . 00 . 00 . 00 . 00 . 00 . 00 . 0

0.01290.17730.02630.00720.00110.76270.02560.00000 .00 . 00 . 00 . 00 .00 .00 .0

0.10780.0003

(04)*2

0.14680.14090.02130.00000.29310.00030.22080.15890.02540.00120.20250.01180 . 00 . 0

0.28550.09250.04490.00250.01220.07440.00010.04000.01330.19030.06170.07830.02490.06520 . 00 . 0

0.07440.27200.03560.26390.08040.05060.02570.12900.31060.02a70.01060.02520.00010 . 00 . 0

0.04980.0229

(0 6) *2

0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .

0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .

0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .

0 .0.

3679014313510587"S3001£8091502390257013772 3200 5001860041

039603 03097909460196066900003893160604 93775119010004402400950141

05200052167900650116015926 291574035334 7506620325109004 980097

05141551

\

1

J1

555555555555

5555555555555

555555555555

5555555555

LEVEL 1

163916391639163916391639163916391639163916391639

16208162081620816208162081620816208162081620816208162081620816206

203032030320303203032030 32030320303203032030 3203032030 320303

22476224762247622476224762247622476224762247622476

J2

5566677788910

55566677788910

55666777889

10

5666777089

PAGE 8APPENDIX V

TABLEU(K)*2

LEVEL 2

2030322476324716957227874937

18258237966674198452588830230

162082030322476324716957227874937

18258237966674198452588830230

20303224763247

1695722787493718258237966674

198452588830230

22476324 7

16957227874937

182582379666741984525688

2FOR PM+3

(U2)*2

000000000000

00,0,0,0,1,00,0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.

.0120

.0072

.0352

.0000

.0001

.0023

.0003

.0014

.0

.0

.0

.0

.1448

.2912

.1431

.0027

.0000

.0815

.0100

.0003

.0000

.0

.0

.0

.0

,0199,13681014,0009,02765669,00920000,0000

0557137700240019735203880005000

(U4)*2

000000000000

0000,00,00,0,0.0.0,0,

0,0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.

.0673

.0792

.1378

.0016

.0096

.0372

.0003

.0002

.0018

.0004

.0014

.0

.1799

. 1071

.0674

.1118

.0000

.2777

.3247

.0026

.0003

.5368

.0305

.0152

.0

.0479,2224.1560,0044.1058,0540,0097,0311,34150226,14050

0445255200783339153502160230186604180243

(U6) *2

00C000000000

00,00,00,00,0,0.0.0.0,

0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.

.0867

.0376

.7160

.0219

.0181

.7862

.0024

.0088

. 1248

.0034

.0093

.0010

.0011

.06 34

.0828

.3966

.0123

.0181

.6748

.0069

.0135,59 27,0032.0013.0516

.0891,06 46.1462,2903,2984,0185,0397304103 9456 2623780220

0226006034940775002907802824043149742139

?, : .If

PAGE

J 1

5

666666666

666666666

66666666

7777777

777777

7777

LEVEL 1

22476

324732473247324732473247324732473247

169571695716957169571695716957169571695716957

2278722787227872278722787227872278722787

4937493749374937493749374937

182581825818258182581825818258

23796237962379623796

J 2

10

66677788

10

66777889

10

6777889

10

777889

10

77889

10

7869

PAGE 9APPENDIX V

TABLEU(K)*2

LEVEL 2

30230

32471695722787

49371825823796

66741984530230

1695722787

49371825623796

6674198452588830230

227874937

1825823796

6674198452588830230

49371825823796

6674198452588830230

1825823796

6674198452588830230

237966674

1984525888

2FOR PM+3

(U2)*2

0 .

0 .0 .0 .0.0.0 .0 .0 .0 .

0 .0 .0 .0 .0 .0 .0 .0 .0 .

0 .0 .0 .0 .1 .0 .0 .0 .

0 .0 .0 .0 .0.0 .0 .

0 .0 .0 .0 .0.0 .

0 .0 .0.0 .

0

12160017

,0099036500010013001400000

013900000000040419360000000100

01441320000000003628000300

1535007200000266000400090

079308400000052100000

3401000000010010

(U4)*2

0 . 0

0.05420.00060.08510.15280.00430.00010.02430.00010.0033

0.00640.00000.00140.02270. 11510.00000.01820.00460.0000

0.24780.36480.00000.00060.76290.00000.04590.0617

0 .12250.00260.00050.13630.00850.00300.0005

0.00540.03510.00360.08060.03880.0168

0.73100.00000.04760.1302

(06) *2

0.0109

0.05620.00050.08461.02110.03420.00000.62240.01090.0024

0.00000.02990.00720.09531.15230.00460.14700.25820.0159

0. 19070.18180.10990.05510. 14950.12120.15450.1374

0.03310.00000.01161.55290.04880.03250.0044

0.35510.53250.01810.00001.29920.3257

0.00330.00870.06450.0867

J1

7

CO

CD

CO

00

00 C

D 0

0

99

LEVEL 1

23796

6674667466746674

198451984519845

2588825888

J 2

10

889

10

89

10

910

PAGE 10APPENDIX V

TABLE 20(K) *2 FOR PM+3

LEVEL 2

30230

6674198452588830230

198452588830230

2588830230

(U2)*2

0 . 0

0.20o50.01740.00«20.0000

0.14020. 19420.0000

1.32400.3074

(04)*2

0.0215

0.33660.00940.01560.0354

0.00560.58840.5142

0 . 1 5 5 71 .2875

(06) *2

0.0057

1.67410.02510.03210.0577

0.34640.67291.5495

0.48921.3587

10 30230 10 30230 3 .3000 0 . 0 0 0 4 1.5336

PAGE 10

r"

APPENDIX VI

PAGE 11

BLANK PAGE

ill

BSEKVE

04 8

1 1 5

1000104411851280

22102245234324092473

352035683651367637 2737 91

497249835007504650 5651235160

6309634264066450646165676567• • •• • •66916707

717671847223

PAGE 1

APPENDIX V]

D CALC

- 15 2

126

1000101712031258

21912236233524082461

352935313651365837313794

49714995500 65014503851165183

6299633564176464649 3656565806588666067106736

716871797228

TABLE 1SM+3:LAF3

O-C

2- 3

- 1 0

027

- 1 722

19971

12

- 837

018- 3- 2

1- 1 1

13218

7- 2 2

107

- 1 0- 1 3- 3 1

2- 1 2• • •• • •- 1 8- 2 8

85

- 4

C

STATE J

6H6H6H

6H6H6H6H

6H6H6H6H6H

6H6H6H6H6H6H

6H6H6H6H6H6H6H

6H6H6F6H6H6H6F6H6H6F6F

6F6F6F

5 / 25 / 2V 2

7 / 27 / 27 / 27 / 2

9 / 29 / 29 / 29 / 29 / 2

11/211/211/211/211/211/2

13/213/213/213/213/213/213/2

15/215/2

1 / 215/215/215/2

3 / 215/215/23 / 23 / 2

5 / 25 / 25 / 2

HJ

3 / 21 / 25 / 2

1 / 25 / 2

-7/23 / 2

1 / 2-7/2-9/2

3 / 25 / 2

1 / 2-9/2-7/2

3/2-11/2

5 / 2

-11/23 / 21 / 25 / 2

••9/2-7/213/2

-7/2-9/2

1 / 25 / 2

-11/23 / 21 / 2

15/2-11/2

3 / 21 / 2

1/25/.?3/2

. <•

)BSERVI

799280U180608092

91709178922892529268

10561105841059310603106 1310644

178581794918045

1892418942

200372009 32011220164

20416204732049920526

•

•

•

•

••

•

PAGE 2

APPENDIX V]

!D CALC

79958020804 8

' 8096

91709171920992409268

10560105771058110616106 1810640

178741796918077

1892118934

20050200942012020159

204132048 32051720528205412065320790207932087020874209092091620941209872110321124211482124921272

TABLE 1SM+3:LAF3

O-C

- 22112-3

07

1912

0

17

11- 1 2

- 44

- 1 5- 1 9- 3 1

3S

- 1 20

- 75

3- 9

- 1 7- 1

•

•

m

•

r

STATE J

6F6F6F6F

6F6F6F6F6F

6F6F6F6F6F6F

4 64G4S

6F6F

4G4G464G

4H4 1414 1414M4H4M4H4M4H4H4 14H41414 14 14 1

7 / 27 / 27 / 27 / 2

9 / 29 / 29 / 29 / 29 / 2

11/211/211/211/211/211/2

5 / 25 / 25 / 2

3 / 23 / 2

7/27 / 27 / 27 / 2

15/29 / 29 / 29 / 29 / 2

15/215/215/215/215/215/215/211/215/211/211/211/211/211/2

MJ

3 / 2-7/2

V 25 / 2

1/2-7/2-9/2

3 / 25 /2

-7/2-9/2

5 /2-11/2

3 / 21/2

1/25 / 23 / 2

3 / 21/2

1/2-7/2

3 / 25 / 2

-9/21/25 / 23/2

-7/2-11/2

-7/213/25 / 2

-9/21/23 / 25 / 2

15/2-11/2

3 / 2-7/2

1/2-9/2

PAGE

PAGE 3

APPENDIX VI

TABLE 1SH+3:LAF3

OBSEEVED CALC O-C STATE J MJ

21539 41 13/2 -7/2a a a

mm*

21663216742170621736

221642220722240

a • a

• * a

a a •

a a •

• « a

a • a

a a a

a a a

a a a

a a a

a a a

a a a

a a a

a a a

a a a

a a a

a • ')

a a a

• • •

a a a

• a a

a a a

a • a

a a a

a a a

J4084a a •

241 19a a a

• a a

* a a

24153* a a

• a a

a * a

216072162321638216592166621681

221712222322242

224862253922546225592257022631226782272722734

2279422816228542290222943229812301823025230352304 5230772311123146

23973240322407424079241002411524118241402414724160241652417224178

a a a

• mm

25154055

-6-15-1

a a •

a a a

a a a

a a a

• a a

• a a

a a a

a a a

a a a

m m »

a a a

a a a

a a a

a a •

• a «

a a a

a a •

a a a

a • •

a a a

a a a

a a •

m m m

a a a

a a •

5a a a

4a a a

a a a

a a a

-6a a a

a a a

a a a

414141414141

4F4G4F

4H4M4M4M4H4M4H4H4H

4G464G414G4141414141414141

4H4H4M4M4M4M6P6P4H4M6P4M4H

13/213/213/213/213/213/2

5/25/25/2

17/217/217/217/217/217/217/217/217/2

9/29/29/215/29/215/215/215/215/215/215/215/215/2

19/219/219/219/219/219/25/25/219/219/25/219/219/2

13/2-9/25/2

-11/21/23/2

3/25/21/2

13/215/2

-11/2-9/2-7/25/23/21/2

17/2

-9/25/23/2

-11/2-7/2

-11/2-7/2-9/213/25/23/21/2

15/2

15/213/217/2

-11/2-9/2-7/21/23/21/23/25/2

-19/25/2

PAGE 4

APPENDIX V]

OBSERVED CALC

24608246292463124644246782466224710

2491124993250072506425081

...2516625182•. .252042521625248• • •25282.........• • •

• • •

. . .

. . .

. . .

• * •

• « m

m • •

• • •

. . .

• • •

. . .

. . .

* • •

• • •

• * •

. . .

. . .

• • •

246202464 02464124659246852469324724

249132497424997250552506 225093

251532515925198252022520425238252552527525312253352540425420254442552225555255822560 32563625641256892569125692256982576425765257782581225812258492586625896

TABLE 1SM+3:LAF3

O-C

-11-10-9

-14-6-10-13

-11910919

• •.7

-15...0

-21-6• * •-29* * •• • *• • •• • •

• • •

• • •

. . .

. . .

• • •

• * •

. . .

. . .

. . .

• • •

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

STATE J

4L4L4L4L4L4L4L

4G4F4G6P6P4F

4H4K4K4K4K4K4H4K4H4H4H4M4N4H4H4H4L4L4L4H4L4L4L4L4G4L4G4G4G4G4G

13/213/213/213/213/213/213/2

7/27/27/23/23/27/2

21/211/211/211/211/211/221/211/221/221/221/221/221/221/221/221/215/215/215/221/215/215/215/215/211/215/211/211/211/211/211/2

HJ

1/23/213/2

-11/2-7/25/2

-9/2

5/23/2-7/21/23/21/2

17/21/23/25/2

-9/2-11/215/2-7/2-19/21/23/25/213/2-11/2-9/2-7/21/23/213/2

-21/2-11/2

5/215/2-9/25/2-7/23/2-7/2-11/21/2

-9/2

26492 4D 1/2 1/2

I*-

v . V JJ3 u. u

JDSEEVI

• • •* • •• • •a • a

• • •

• • •

• • •

• • •

• a •

• • •

• a •

• • *

a • •

• • •

• • •

• • •

• • •

• • •

• • •

• a •

2736327417274322744827508

2764627658

276912773127758

28248282622834328409

287152872628753

a • a

2877828790

• • a

28810

PAGE 5

APPENDIX VI

3D CALC

26691266932670726735267472677126792267992680726809268392684 526852

26926269532698326990270112707027110

2736127432274682748427533

2765527664

277192776527773

28250282532834928403

2873 828742287532875428781287942880628811

TABLE 1SH+3:LAF3

O-C

• • •• • •« • •• • a

a a a

a a •

a • •

• • m

mem

• a a

• a •

• a a

a a a

a a •

• a •

• mm

a a a

a a a

a a a

a a a

2-14-35-35-24

-6-5

-27-30-14

-19-56

-22-150

a • a

-2-3

• • a

0

STATE J

4K2K4L4K6P2K4L6P4K6P6P4LUK

4K4K4K4K4K4K4K

4F4F4F4F4F

4D4D

6P6P6P

6P4H4H6P

4K4K4K4K4K4K4K4K

17/217/217/217/27/217/217/27/217/27/27/217/217/2

13/213/213/213/213/213/213/2

9/29/29/29/29/2

3/23/2

5/25/25/2

7/27/27/27/2

15/215/215/215/215/215/215/215/2

MJ

1/23/25/213/2-7/215/217/25/2

-11/23/21/2

-7/2-9/2

1/2-9/23/2

-11/25/2

-7/213/2

-7/25/23/21/2

-9/2

. 1/23/2

1/25/23/2

1/25/2

-7/23/2

5/21/23/2

-11/213/215/2-9/2-7/2

II i

//<=

BSEBVE

28938• • •

28981290 37290552908629094

a • •

« • •

• * •

• • a

• • •

• • a

• • •

• • «

• • •

• • •

* • •

• > •

• • •

* • *

• • •

• • a

• « •

• • •

• • a

• • •

« * •

• • •

• a •

a • •

• • •

• • •

• • •

• • •

• • •

• • •

• • •

• • •

• • •

• • •

PAGE 6

APPENDIX VI

:D CALC

28935289562900 7290632907629103291032910729117291362913729143291382915129168291842920529223

2929829307293122933129347293562936129365294122944829456294762950329572295822958729590296322964029683297082971229761

TABLE! 1SM+3:LAF3

O-C

3• • a

-25-25-20-16-8

• • •

a • «

a « •

• • a

• « a

• • •

• • •

• • *

• • a

• a •

• • a

• a a

» * m

• • a

• • •

• • •

• * •

* m •

• a *

a • •

• a •

• a •

m • •

• • a

• a •

a • •

• • •

* * m

• • •

• • a

• a •

• • a

a a •

• • •

STATE J

4H4H4H6P4H6P6P4K4K4K4K4K6P4K4K4H4K4K

4H4M4L4H4L4H4H4H4H4M4L4M4H4H4H4L4H4H4H4H4H4H4H

9/29/29/27/29/27/27/217/217/217/217/217/27/217/217/29/217/217/2

19/219/219/211/219/211/211/211/211/219/219/219/211/219/213/219/219/213/213/213/213/213/213/2

MJ

-7/21/2

-9/25/23/23/21/25/2-7/2-9/2-11/217/2-7/213/23/25/21/2

15/2

1/23/25/2-9/217/2

-11/21/2

-7/23/2

15/2-19/213/25/2

-11/2-11/2-7/2-9/23/21/25/2

-9/213/2-7/2

u.vv^u U.UDOO

PAGE 7

APPEHDIX VI

OBSERVED CALC

300273012530141

• m m

• a •

30219302353028630329

* a •

• • •

. . .

a • •

• a •

• a •

314203144231473

• a a

a a a

a a a

« • *

a a a

31627a • a

• mm

. . .

3171631761

328003282232853

336083368133765

a a a

m m •

a • •

• mm

• a a

• mm

a • •

a • •

• a •

a • •

a a a

a • a

300253013930142301913020730217302623027530346304443048930539

31222

31341313583141231454314743148831515315183152531552316083161531628316763171031735

328083282932861

335833365833742337953382433891339033394233961339663399634033340483405634090

TABLESM+3:L

O-C

2-13

0......2

-2611

-16• m •

a a a

• • a

a a •

a • •

a • •

8-11

0• • a

• • •

a • •

• • *

. . .

19a * a

• * a

• a a

626

-7-6-7

252323

a • a

• • •

• • a

• • a

a • a

• • a

• • •

• a a

a • •

a * a

« a •

1AF3

STATE J

4G4G4G4G4G4G4G4G4G4G4G4G

4P

2K2K2L2L2L2K4G4G2L4P2K4G4G2L4G4G

4P4P4P

2F2F2K2K2F2K2K4F2K4F4F4F2K4F2K

7/27/27/29/29/25/29/29/27/25/25/25/2

1/2

15/215/215/215/215/215/211/211/215/23/215/211/211/215/211/211/2

5/25/25/2

5/25/213/213/25/2

13/213/29/213/29/29/29/213/29/213/2

HJ

5/2-7/21/23/2

-9/25/2

-7/21/23/21/25/23/2

1/2

13/2-11/2-9/25/23/21/2

-11/25/2

-7/23/21/2

-7/215/2-9/21/2

1/25/23/2

1/25/2

-11/2-9/23/21/2

-7/2-7/23/25/2

-9/21/25/23/2

13/2

II)

PAGE 8

APPENDIX VI

TABLE 1SH+3:LAF3

OBSEFVEP CALC O-C STATE J

a • •

• • •

• • *

• • •

• • •

• a a

• • *

• • •

• • •

• • •

• • •

• • •

• • •

• * •

* a a

• a •

• • •

• a a

a • a

• • •

a • •

• • •

• • •

• • •

• • *

• • •

• • •

• • a

• • •

358903590535954359963600736055

3433134347343973440234407344533445534474344873453434557345883459934630

355753565135666356783569935701357183572835737357593576235762357943586435874

359023592035955359833600936052

• • •• • •• • •* • •• • •• • •a * •

a • •

• • a

• a *

• • •

• • •

• a •

• • •

• a •

• a •

• • •

a a a

a • •

• • •

• • a

a • a

• • •

• • •

• * •

a a a

• • a

a a *

• • •

-11-14

013-13

2L2L2L2L2L2L2L2L412L41414141

2N4F2N4F2N2N2N2N2N2N2N2N4F2P4F

414141414141

17/217/217/217/217/217/217/217/29/217/29/29/29/29/2

19/27/219/27/219/219/219/219/219/219/219/219/27/21/27/2

11/211/211/211/211/211/2

13/215/2

-11/2-7/23/25/2

-11/2-9/25/217/25/23/2-9/21/2

-19/25/217/21/2

-9/2-11/2-7/217/213/25/23/21/2

-7/21/23/2

-7/2-9/25/2

-11/23/21/2

PAGE 9

APPENDIX VI

TABLE 1SM+3:LAF3

OBSEBVED CALC O-C STATE J HJ

• a •

• a •

• a a

• • a

a • a

• a *

a a a

• • a

36567a a •

• • •

a a •

• • a

• • a

• • a

• • •

a • •

366 51a a •

• a •

• • a

• a a

• • a

* a a

a a •

36755a • •

a • •

• a •

a * •

a • •

9 9a

• a a

• a a

9 a a

• • a

• a a

9 a a

a • •

• • a

376233763^376343765737679

3631036339364043646136496365203652636526365503657136572366023663236643366453664 83665136659366803670036702367093672636735367383675 23678136839368393684036845

369033692236960370373705137072371313721637268

375993761U376193763837661

• a a

9 9a

a • 9

9 9 a

a a a

a a 9

a • a

a a a

17a a a

• a •

• 9 •

a • a

• a a

9 • 9

a a a

a a *

-7a a a

* * m

9 9*

a a a

a a a

• a a

9 a •

39 9 9

9 a a

a a a

9 9*

9 9 •

9 9 9

9 a «

a a a

9 9 9

9 • m

9 9 9

* 9 a

• 9 9

9 9a

2420151918

41412K414F2K41414F2K41412N2N2N4F414F2N2N4141-41412N4F2N2N2N2N2N

2M2M2M2M2H2H2M2M2H

2H2H2H2H2H

15/215/215/215/25/215/215/215/25/215/213/213/221/221/221/23/213/25/221/221/213/213/213/217/221/23/221/221/221/221/221/2

17/217/217/217/217/217/217/217/217/2

9/29/29/29/29/2

13/2-11/2-9/2-7/21/2

. 3/21/25/25/215/2

-11/2-9/2

-19/2-21/217/23/2

-7/23/21/23/25/21/23/213/25/21/215/2-7/213/2-9/2-11/2

17/217/2-9/21/25/23/2

-11/215/213/2

-7/21/2

-9/23/25/2

PAGE 10

APPENDIX VI

TABLE 1SH+3:LAF3

OBSERVED CRLC O-C STATE HJ

381843825638280

38467 3846738492 38484

38499

389023897139000391173914239171392143924539316393613940039446394553946839475395063954139581

403164048640505405554069640698407194076240781408064084 9408834089540909409724098141061410874113941178412504125241359'41382

... 2F

... 2F

. .. 2F0 2P9 2P

... 2F

... 2K

... 2K26

. .. 2K2G2G

... 2K

... 2K

... 2G

... 2K2H2H

... 2H

... 2K

... 2H

... 2H2G

... 2K

... 2M2M

... 2H

... 2M

... 2H2.12M2D

... 2D

... 2D2D21

... 2M

... 21

. .. 2121

... 2H

... 212K21

... 2K

... 2K

... 2K

... 2K

7/27/27/23/23/27/2

15/215/27/215/27/27/215/215/27/215/211/211/211/215/211/211/27/215/2

19/219/219/219/219/219/219/25/25/25/25/211/219/211/211/211/219/211/213/211/213/213/23/2

Id/2

3/2-7/21/23/21/25/2

13/2-11/2

5/23/21/2

-7/21/25/23/2

-9/2-7/2-9/2

-11/215/25/21/23/2-7/2

-19/2-7/2-9/2

-11/21/25/23/21/21/25/23/2

-11/217/23/21/2

-9/215/2-7/2-11/2

5/2-9/21/25/23/2 r

PAGE 11

APPENDIX VI

TABLE 1SM+3:LAF3

OBSEPVED CALC O-C STATE J HJ

4139741534

42066

421354217642227

423784246242466

42616

4265842711

429594299043040

430 74

43258

43324

4173741756

4205442102421124215842199

423904246542481

42616426254264242700

427154287542923429384296342973429934302343025430454304543079430884311843144431464316743169431964321543226432284323743266432664327243276432944330243368

1611

-13-217

• • •

29

-7

22

2K 13/2 13/22K 13/2 -7/2

... 2D2D

12 2G22 2G23 2G1828

2G2G

-11 4G-2 4G5 4G

4G4G4G4G

202K2K4H4H4H4H4H204H2N2K202K2K2K4H2K20414H2020204H4H4H2K2020

3/23/2

9/29/29/29/29/2

5/25/25/2

7/27/27/27/2

21/215/215/29/29/29/29/29/221/29/221/215/221/215/215/215/211/215/221/211/211/221/221/221/211/211/211/215/221/221/2

1/23/2

-9/25/23/21/2

-7/2

1/25/23/2

-7/21/23/25/2

-21/213/2-11/23/25/2-9/21/2

-7/2-9/2-7/2-9/21/2

-11/25/215/2-7/21/2

-9/213/2-11/23/2

-19/23/21/2-7/2-9/25/2-7/217/215/2

r 1 •

*3Bt A*'

PAGE 10

APPENDIX VI

TABLE 1SH+3:LAF3

OBSERVED CALC O-C STATE J MJ

X"K' • % ' • • • •

fro ,•1':. °. . ,

*" - *4/t;'. /'<'^\

381843825638280

38467 3846738492 38484

38499

38902389713900039117

.. . . 391423917139214

.... 3924539316393613940039446394553946839475395063954139581

40316... 40486

405054055540696406984071940762407814080640849408834089540909

'.'... 40972... 40981... 41061

41087.. 41139.. 41178...J: ~41250. . % 41252

'••a. •".•, • »«rv 4:1382

... 2F

... '2F

. .. 2F0 2P9 2P

... 2F

2K... 2K

26. .. 2K

26262K2K

... 2G

... 2K

... 2H

... 2H

... 2H

... 2K

... 2H

... 2H

... 26

... 2K

... 2H

... 2M

... 2M

... 2H

... 2H2H2M2D

. .. 2D

... 2D2D21

... 2H

... 21

... 2121

... 2H

... 21

... 2K

... 21

... 2K

... 2K

... 2K

... 2K

7/27/27/23/23/27/2

15/215/27/215/27/27/215/215/27/215/211/211/21V215/211/211/27/215/2

19/219/219/219/219/219/219/25/25/25/25/211/219/211/211/211/219/211/213/211/213/213/213/213/2

3/2-7/21/23/21/25/2

13/2-11/2

5/23/21/2

-7/21/25/23/2

-9/2-7/2-9/2

-11/215/25/21/23/2-7/2

-19/2-7/2-9/2

-11/21/25/23/21/21/25/23/2

-11/217/23/21/2

-9/215/2-7/2-11/2

5/2-9/21/25/23/2

='f—.-

r

IBSEFVI

• • •• • •

• • •

• • •

4206642124421354217642227

423784246242466

42616• • •

4265842711

• • •• • •• • *• • *• • •

429594299043040• • •

43074• • •• • m

• • •

• • •

• • •

• • •

• • •

• • *

• • •

• • •

• • •

• • •

• • •

43258• • •• • a

• • •

43324• • *

PAGE 11

APPENDIX V3

iD CALC

4139741534

4173741756

4205442102421124215842199

423904246542481

4261642625426 24270u

427154287542923429384296342973429934302343025430454304543079430884311843144431464316743169431964321543226432284323743266432664327243276432944330243368

TABLE! 1SM+3:LAF3

O-C

• • •• • •

• • *

• * •

1222231828

-11-25

0• • •1611

• • •• • *« • •• « a

• • •

-13-217

• • •29• • •• • •a • «

• • •

• • •

• • *

• • a

• • •

• • •

• • •

a a a

a • a

• • •

• • a

-7• a a

• • •

• • a

22• a •

STATE J

2K2K

2D2D

2G2G2G2G2G

4G4G4G

4G4G4G4G

202K2K4H4H4H4H4H204H2N2K202K2K2K4H2K20414H2020204H4H4H2K2020

13/213/2

3/23/2

9/29/29/29/29/2

5/25/25/2

7/27/27/27/2

21/215/215/29/29/29/29/29/221/29/221/215/221/215/215/215/211/215/221/211/211/221/221/221/211/211/211/215/221/221/2

MJ

13/2-7/2

1/23/2

-9/25/23/21/2

-7/2

1/25/23/2

-7/21/23/25/2

-21/213/2

-11/23/25/2

-9/21/2

-7/2-9/2-7/2-9/21/2

-11/25/215/2-7/21/2

-9/213/2

-11/23/2

-19/23/21/2

-7/2-9/25/2

-7/217/215/2

PAGE 12

RPPENDIX VI

TABLE 1SH+3:LAF3

OBSERVED CALC 0-C STATE 3 MJ

43446 ...43542 ...43545 ...43545 ...43565 ...43576 ...43590 ...43703 ...

43728 ...43780 ...43789 ...43829 ...

... 43888 ...

43953 ...44003 . ..

... 44005 ...

... 44016 ...

... 44481 ...44559 ...

44597 44622 -2444692 ...44710 ...

45031 ...... 45065

45071 ...45122 45146 -23

45262 ...45320 ...45324 ...

45366 45379 -12... 45440 ...

4566845732 ...45770 ...

... • 45812 ...45817 ...4582845837 ...45845 ...45861 . .4586945891 ...45917 ...45930 ...

4H4H4H4H4H4H2H21

2121212121

4H4H4H4H

2G2G2G2G2G

4G4G4G4G

4G4G4G4G4G

2121214G214G464H4G4G214H4G

13/213/213/213/213/213/213/211/2

11/211/211/211/211/2

7/27/27/27/2

9/29/29/29/29/2

7/27/27/27/2

9/29/29/29/29/2

13/213/213/211/213/211/211/213/211/211/213/213/211/2

13/23/2-7/2-11/2

1/25/2

-9/25/2

-11/23/2-7/21/2

-9/2

-7/23/21/25/2

-7/21/2

-9/25/23/2

• 1/2-7/23/25/2

1/2-7/2-9/23/25/2

13/21/23/25/2

-11/23/21/25/2

-11/2-7/2-9/2-7/2-9/2

•tl

ill

IBSEBVE

• a •

• a •

a « m

a • m

• a •

46284• • •• * V

" • • * •

• • a

• • a

m * •

46402• • •• • •• a •

• • •

• • a

a • a

• a a

• • a

• • a

46603• m 9

a a a

a • •

a a •

• • •

4733647374• • •• • a

PAGE 13

APPENDIX VI

!D CALC

4620446222462674626 94629846300J»63304633446341463494639346412464224642246435464454644846473464924651246531465504658746592469624697247057472664732 7473974747147620

TABLE 1SM+3:LAF3

O-C

* • m

• • •

m • •

a a •

* m »

-15• • •4 a •

* a •

* • a

• • •

• • •

-19a • •

• • •

mm*

• • *

• • •

• • a

* • •

• a •

16• a •

• • a

• a •

a • •

a a a

9-22a a •

mm*

STATE J

2H2H4H2L2L2H2L2L2L2L2H4H4H4H2L2L2L4H4H4H4H4P4P2H2D2D2D2H2H2H2H2H

11/211/213/217/217/211/217/217/217/217/211/213/213/213/217/217/217/213/213/213/213/23/23/211/25/25/25/211/211/211/211/211/2

MJ

1/2-9/213/217/2-7/2-11/2

3/21/2

15/25/23/21/25/23/2

-11/2-9/213/2-7/2-7/2-11/2-9/23/21/2

-7/25/23/21/2

-11/25/23/2

-7/2-9/2

PAGE 12

APPENDIX VI

TABLE 1SH+3:LAF3

OBSEBVED CALC O-C STATE J MJ

43446 ...43542 ...43545 ...43545 ...

... 4356543576 ...43590 ...43703 ...

43728 ...43780 ...43789 ...43829 ...43888

43953 ...... 44003 ...

44005... 44016 ...

... 44481 ...44559 ...

44597 44622 -2444692 ...44710 ...

45031 ...4506545071 ...

45122 45146 -23

45262 ...45320 ...45324 ...

45366 45379 -1245440 ...

4566845732 ...45770 ...45812 ...45817 ...

... 45828 ...45837 ...45845 ...45861 ...

... 4586 9 ...45891 ...45917 ...45930 ...

4H4H4H4H4H4H2H21

2121212121

4H4H4H4H

262G2G2G2G

4G4G4G4G

4G4G4G4G4G

2121214G214G4G4H4G4G214H4G

13/213/213/213/213/213/213/211/2

11/211/211/211/211/2

7/27/27/27/2

9/29/29/29/29/2

7/27/27/27/2

9/29/29/29/29/2

13/213/213/211/213/211/211/213/211/211/213/213/211/2

13/23/2-7/2-11/2

1/25/2

-9/25/2

-11/23/2

-7/21/2

-9/2

-7/23/21/25/2

-7/21/2

-9/25/23/2

' 1/2-7/23/25/2

1/2-7/2-9/23/25/2

13/21/23/25/2

-11/23/21/25/2

-11/2-7/2-9/2-7/2-9/2

tl

12-°

IBSERVE

'• • •• • •• • m

• • a

m • *

46284• • •• • •• • •• • •• • m

• • •

4 6 4 0 2• • •• • •• • •« • •• « •a • •

• • a

• • •

a a •

46603• • •

• • •

• • »

• • •

• • •

4733647374• • *• • •

PAGE 13

APPENDIX VI

ID CALC

4620446222462674626946298463004633046334463414634946393464124642246422464354644546448464734649246512465314655046587465924696246972470574726647327473974747147620

TABLE: 1SM+3:LAF3

d-c

« • •• • •• * •• • •a • •

-15• • •a • •

• • •

* • *

• a a

• • •

-19a • •

• • •

* • •

a • a

* • •

• a a

• * *

• • •

16* • •• • •

• • •

• • •

• • •

9-22• • •a a a

STATE J

2H2H4H2L2L2H2L2L2L212H4H4H4H2L2h2L4H4H4H4H4P4P2H2D2D2D2H2H2H2H2H

11/211/213/217/217/211/217/217/217/217/211/213/213/213/217/217/217/213/213/213/213/23/23/211/25/25/25/211/211/211/211/211/2

HJ

1/2-9/213/217/2-7/2-11/2

3/21/2

15/25/23/21/25/23/2

-11/2-9/213/2-7/2-7/2-11/2-9/23/21/2

-7/25/23/21/2

-11/25/23/2

-7/2-9/2

7 /i

PAGE 14

APPENDIX VI

TABLEI 1 ASM+3:LAF3 CENTERS OF GRAVITY

CALC CENTER

10111352341366750726 3876520663771418009918910583

180311898220161206602082521147216442230122612228732304824132241382467624 9952506425201254342566725829264462676226786

STATE

6H 5/26H 7/26H 9/26H11/26H13/26F 1/261515/26F 3/26F 5/26F 7/26F 9/26F11/2

4G 5/24F 3/24G 7/241 9/24M15/24111/24113/24F 5/24M17/24G 9/24115/26P 5/24M19/24L13/24F 7/26P 3/24K11/24M21/24L15/24G11/24D 1/24L17/26P 7/2

J1

1/21/21/21/21/21/21/21/21/21/21/21/2V21/21/21/21/21/2

1/21/21/21/21/21/21/21/21/21/21/21/21/21/21/21/2

3/23/23/23/23/23/23/23/23/23/23/23/23/23/2

IEVEL

638763876387638763876387638763876387638763876387638763876387638763876387

26406264462644626446264462644626446264462644626446264462644626446264462644626446

66376637663766376637663766376637663766376637663766376637

1 J2

3/23/25/25/25/25/27/27/27/27/29/29/29/2

11/211/211/213/213/2

3/23/25/25/25/27/27/27/29/29/211/211/211/211/213/213/2

3/23/23/25/25/25/25/25/27/27/27/27/27/29/2

PAGE 15APPENDIX

TitBLI! 20(K) *2 FOR

LEVEL 2

663725064

1017141

223012413211358009

249952678623419189

20660366710583

' 258295072

24676

189822506418031223012413220161249952678620660228733667

2114725201258292164424676

66371898225064101

714118031223012413211358009

2016124995267862341

VI

SM+3

(02)*2

000000000000000000

00000000000000,0,0,

0.0.0,0.0.0.0.0.0.0.0.0.0.0.

.0174

.1920

.1938

.0140

.0011

.0106

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0079

.0061

.0180

.0532

.0106

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0029

.0011

.2922

.1444

.0222,0010,0036,0711243401830023,001000240

(04)*2

00000000000000000,0,

0.00,0.0.0,0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.0.0.0.

.0

.0

.0

.0

.0

.0

.1386

.0306

.0030

.0966

. 1521

.0071

.0012

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0226

.0789

.0028,0805,0294,00,0,000

,00013650282000000030237117400800009006315921183

(06) *2

00000000000000000,0.

0.000,0,0,0,0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.0.0.0.

.0

.0

.0

.0

.0

.0

.0,0.0.0.0.0.0.3365.0287.0015. 1026.0026

.0

.0

.0

.0

.0

.0

.0

.0,0,0.002909920527081602971446

00000000000003793

J1

3/23/23/23/23/23/23/23/23/23/23/23/2

3/23/23/23/23/23/23/23/23/23/23/23/23/23/23/23/23/23/23/23/23/23/2

3/23/23/23/23/23/23/23/23/23/23/23/23/23/2

LEVEL

663766376637663766 376637663766376637663766376637

18982189821898218982189821898218982189821898218982189821898218982189821898218982189821898218982189821898218982

2506 4250642506425064250642506425064250 64250642506425064250642506425064

1 J2

9/29/2

11/211/211/211/211/213/215/215/215/215/2

3/23/25/25/25/27/27/27/27/27/29/29/29/2

11/211/211/213/213/213/215/215/215/2

3/25/25/25/25/25/27/27/27/27/27/29/29/29/2

PAGE 16APPENDIX

TABLE 20(K)*2 FOB

LEVEL 2

91892287336671058321147252012582950726520208252304825667

189822506418031223012413211358009

2016124995267862341

206602287321147252 01258295072

2164424676208252304825667

250641C1

714118031223012413211358009

20161249952678623419189

20660

VI

SH + 3

(U2)*2

000000000000

000000,0,0,0,0,0,0,0,0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.c.0.0.0.0.0.

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0023

.0037

.0763

.0609

.0015

.0083

.0001

.0289

.0149

.0013

.0

.0

.0

.0

.0

.0

.0,0,0.0,0,0

,00960000263800080012122000001450001803264736000

(04)*2

0000000,0,0,0,0.0.

0,0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.0.0.0.

.0301

.0000

.2119

.0041

.0062

.0013

.0000

.0

.0

.0

.0

.0

.0

.0,0440,0018.0771,000000131525,00010158002910750401299014830016000000

01630009400010310001315890469008700700000112514480101

(06) *2

0,0,0,0,0.0.0,0.0.0,0.0.

0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.0.0.0.

.0098

.0026

.0287

.0489

.0001

.0001

.0013

.4036,0615.0099,0028,0021

,0,0,000,00000004 90204372909850066239600140556075435771386001 c>

00000000000001100000023

34090 2K 13/2 13/2

J1

3/23/23/23/23/23/23/23/23/23/2

5/25/25/25/25/25/25/25/25/25/25/25/25/25/25/25/25/25/25/25/25/25/25/25/2

5/25/25/25/25/25/25/25/25/25/25/25/25/25/2

IEVEL

25064250642506425064250642506425064250642506425064

101101101101101101101101101101101101101101101101101101101101101101101101

71417141714171417141714171417141714171417141714171417141

1 J2

9/211/211/211/211/211/213/213/215/215/2

5/25/25/27/27/27/27/27/29/29/2V29/2

11/211/211/211/211/213/213/213/215/215/215/217/2

5/25/25/25/27/27/27/27/27/29/29/29/29/211/2

PAGE 17APPENDIX

TAB LI: 20(K)*2 FOR

LEVEL 2

228733667105832114725201258295072

216446520

25667

1017141

2413211358009

20161249952678623419189

20660228733667105832114725201258295072

21644246766520

208252566722612

714118031223012413211358009

20161249952678623419189

20660228733667

VI

SM + 3

(U2)*2

0000000000

000000000000000000000,0.0,0,

0,0.0.0.0.0.c.0.0.0.0.0.0.0.

-.0.0.0.0.0.0.0.0-0.0

.3881

.0331

.0000

.2062

.0020

.0003

.0002

.0000

.0257

.0000

.0022

.0000

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0007

.0062

.0072,1864.^118.0397.0004.0014024333740140000000230

(U4)*2

000000000,0,

00,0,0,0,0,0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.0.0.0.

.0388

.0465

.3702

.0040

.0039

.0049

.0

.0

.0

.0

.0567

.2844

.0244

.1963

.1429

.0017

.0011

.0015

. 1397

.0205

.0005

.0009,0240,0006,00000004,0001,000600320080,0000

01170014004206740507003700080074180210130298001100042305

(06) *2

0000000000

000.0000,0,0.0,0,0,0,0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.0.0.0.

.0016

.0118

.0000

.0470

.0000

.0118

.0570

.0574

. 1418

.0316

.0

.0

.0

.0952

.4301

.0023

.0005

.0663

.3262

.3416

.0014

.0027

.2649

.0516

.0111,0024.0010,0662,0237,00920043,031900560054

00004192004 500190003000004750356001900042087

J 1

5 / 25/25 / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 2

5 / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 2

5 / 25 / 25 / 25/25 / 25 / 25 / 25 / 25/25 / 25 / 25 / 25 / 25 / 2

LEVE1

7141714171417141714171417141714171417141

180311803118031180311803118031180311803118031180311803118031180311803118031180311803118031180311803118031180311803118031

2230122301223012230122301223012230122301223012230122301223012230122301

1 J2

11/211/211/211/213/213/213/215/215/217/2

5 /25 / 25 /27 / 27 / 27/27 / 27 / 29 / 29 / 29 /29 /2

11/211/211/211/213/213/213/215/215/215/217/217/2

5 / 25 /27 /27/27 / 27 /27 / 29 / 29 /29 /29 /2

11/211/211/2

PAGE 18APPENDIX

TABLE: 2U (K) *2 FOB

LEVEL 2

10583211472520125829

50722164424676

65202082522612

180312230124132

11358009

201612499526786

23419189

2066022873

3667211472520125829

507221644246762082523048256672261226762

2230124132

11358009

201612499526786

23419189

2066022873

36671058321147

V I

SM + 3

( 0 2 ) * 2

0000000000

0000000000000000000000,0,0,

0.0 .0 .0.0.0.0 .0 .0 .0 .0 .0 .0 .0 .

. 0

. 0

. 0

.0. 0. 0.0. 0. 0. 0

. 3 4 2 4

. 0 0 9 8

. 0 1 0 6

. 0 0 0 0

. 0 0 0 0

. 0 0 0 0

. 0 0 2 2

. 0 0 1 8

. 0 0 9 6

. 0 0 1 6

. 0 3 6 9

. 0 0 3 2

. 0

. 0

.0

. 0

. 0

. 0

.0

.0

.0

.0

.0

.0

,0003,0444,0004,0123, 1850,0203.0125,0064009902290222000

(U4)*2

0000000000

00000000,00,0,0,0,0,0,0,0.0.0.0.0.0.0.0 .

0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .

.0225

.0027

.0016

.0000

.2116

.0094

.0000

. 0

. 0

. 0

.2483

.0369

.0391

.0078

.0015

.0083

.0057

.0250

.0061

.0002

.1101

.0187

.0045

.0009

.0074

.0013

.0000

.3028

.1459,0,0.0,0,0

.03450016005900870808031901280008003700911156014100440054

(U6)*2

0.05110.00000.00040.00750.28670.00010.00180.34000.01790.0193

0 . 00 . 00 . 00.00750.00010.40940.02810.00080.00190.00020.01880.03090.00180.23500.02890.13140.00140.72180.07670.83540.04350.00570.02030.0092

0 . 00 . 00.00080.00000.03730.11240.00000.00000.00000.11220.07210.00800.00010.3369

J1

5/25/25/25/25/25/25/25/25/2

5/25/25/25/25/25/25/25/25/25/25/25/25/25/25/25/25/25/25/25/25/25/25/2

7/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/2

LEVEL

223012230122301223012230122301223012230122301

2413224132241322413224132241322413224132241322413224132241322413224132241322413224132241322413224132241322413224132

1135113511351135113511351135113511351135113511351135113511351135

U

1 J2

11/211/213/213/213/215/215/215/217/2

5/27/27/27/27/27/29/29/29/29/211/211/211/211/211/213/213/213/215/215/215/217/217/2

7/27/27/27/27/29/29/29/211/211/211/211/211/213/213/215/2

PAGE 19APPENDIX

TABLE! 2(K) *2 FOR

LEVEL 2

25201258295072

216442467620825230482566722612

241321135800920161249952678623419189

20660228733667105832114725201258295072

2164424676652020825230482261226762

11358009

20161249952678623419189

20660366710583211472520125S2S5072

246766520

VI

SM + 3

(U2)*2

000000000

00000000000000000000000

000,0.0,0,0,0,0.0,0,0.G.0.0.0.

.0

.0

.0

.0

.0

.0

.0

.0

.0

.2386

.0000

.3046

.0062

.0651

.2737

.0004

.3246

.0007

.0577

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.2831

.0420

.0000

.0000

.0000

.2938

.0017

.0002

.0382

.0000

.0002

.0016COOO000

(U4) *2

000000000

00000000000000000000000

0000000000,0,0.0.0.0.0.

.1495

.0056

.0035

. 1186

.1341

.0

.0

.0

.0

.0005

.0706

. 1199

.0319

.0110

.0077

.1302

.1715

.0185

.0195

.1527

.1616

.0205

.0265

.1119

.1224

.0002

.0047

.0

.0

.0

.0

.0

.0143

.2955

.0024

.0000

.0088

. 1652

.1328

.0007

. 1792

.0104

.0000

.0000

.0005

.0245,0000,0003

(06) *2

0.01160.20320.00700. 11110.06390.00820.01720.19340.6557

0.00.00500.00000.00170.00050.00010.01780.00000.13260.00520.04670.00000.00090.02170.06270.08240.04760.00150.07400.02490.20110.01860.1009

0.29510.00040.00480.00260.08620.00800.45550.00660.25420.22810.010aC.C06 10.00On0.28110.00950.0467

176

J1

7/27/27/27/27/2

7/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/2

7/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/2

LEVEL

11351135113511351135

800980098009800980098009800980098009800980098009800980098009800980098009800980098009

201612016120161201612016120161201612016120161201612016120161201612016120161201612016120161201612016120161

U

1 J2

15/215/217/217/219/2

7/27/27/27/29/29/29/29/2

11/211/211/211/211/213/213/215/215/215/215/217/219/2

7/27/27/29/29/29/29/211/211/211/211/211/213/213/213/215/215/215/217/217/219/2

PAGE 20APPENDIX

TABLE! 2(K) *2 FOR

LEVEL 2

2304825667226122676224138

800920161249952678623419189

20660228733667105832114725201258295072

2164465202082523048256672261224138

20161249952678623419189

20660228733667105832114725201258295072

2164424676208252304825667226122676224138

VI

SM + 3

(U2)*2

00000

000000000000000000,0,0,0,

0.0,0,0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.

.0

.0

.0

.0

.0

.0034

.0070

.0035

.1128

.2493

.0550

.0000

.0000

.4881

.0065

.0000

.0000

.0012

.0

.0

.0

.0

.0

.0

.0

.0

.3327

.0066

.0003

.0000

.0004

.0099

.0006,0099,0010,0240,0000,00790,0,0000000

<U4)*2

00000

00000000000000,0,0.0,0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.

.0019

.0076

.0

.0

.0

.0217

.0000

.0041

. 1713

.1320

.0051

.0023

.0007

.0308

.0497

.0006

.0018

.0000

.4372

.0049

. 1306

.0012

.0038

.0019

.0

.0

.1197

.0556

.0436

.0090,0000,0768,0005,0014,0000074100810022005901330685144112232806000

(06) *2

00000

0000,0,0,0,0,0,000,0,0.0,0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.

.0104

.0071

.0220

.0033

.0043

.0290

.0004

.0000

.0000

.2625

.0586

.0009

.0031

.3276

.0357

.0013

.0013

.0017

.0002

.0017,7121,0043,0015,0031,02300215

,0001,02660062,0038,00061086190400000001166214390660000001693055000097511634502207690330

43368 20 21/2 15/2

J1

7/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/2

7/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/2

9/29/29/29/29/29/29/29/29/2

LEVEL

2499524995249952499524995249952499524995249952499524995249952499524995249952499524995249952499524995

26786267862678626786267862678626786267862678626786267862678626786267862678626786267862678626786

234123412341234123412341234123412341

1 J2

7/27/29/29/29/29/211/211/211/211/211/213/213/213/215/215/215/215/217/219/2

7/29/29/29/29/211/211/211/211/211/213/213/213/215/215/215/215/217/219/2

9/29/29/29/2

11/211/211/211/211/2

PAGE 21APPENDIX

TABLE: 2U(K)*2 FOR

LEVEL 2

249952678623419189

20660228733667

105832114725201258295072

216442467665202082523048256672676224138

2678623419189

20660228733667

105832114725201258295072

21644246766520

2082523048256672676224138

23419189

2066022873366710583211472520125829

VI

SM+3

(02)*2

00000000000000000000

000,0,0,00.0,0,0,0.0,0,0,0.0.0.0.0.

0.0.0.0.0.0.0.0.0.

.0048

.0000

.0009

.0137

.0092

.2300

.0074

.0230

.0122

.0003

.0137

.0

.0

.0

.0

.0

.0

.0

.0

.0

.1550

.0000

.3402

.0002

.0000

.0004

.8957

.0002

.0000

.0765

.0

.0

.0

.0

.0,0,0,0,0

,3286,0336,0002000034320007,000000100001

(04)*2

00000

o,0.000,0,0.0.0.0,0,0.0,0.0.

0,0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.

.0668

.0030

.0011

.0010

.0009

.1546

.0002

.0010

.0098

.0576

.0245

.0121

.0230

.0061

.0185

.0001

.1892

.0196

.0

.0

.0042

.0361, 1343,0002,0714, 10800658,0072,00751692229501220082430900020000004900

021033400001002623170691000600000001

(U6)*2

00000000000,0,0.00.0,0,0,0,0.

0.0.0,0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.

.0135

.0106

.0103

.0000

.2028

.004 9

.0121

.0001

.0373

.1335

.0991

.0016

. 1164

. 1391

.0007

.0074

.0009

.1390

. 1659

.7863

.0005

.0968

.0000

.1008

.0240,0933,0000,0975,06900281070607210481030500590594029503980394

263218090034002800005206001500430011

m

-'.™^^-iAJ..\_.^^_ -J^- , " ~ ~ ' '

• • >

J1

9/29/29/29/29/29/29/29/29/29/2

9/29/29/29/29/29/29/29/29/29/29/29/29/29/29/29/29/29/2

9/29/29/29/29/29/29/29/29/29/29/29/29/29/29/29/2

9/29/29/2

IEVEL

23m234123412341234123412341234123412341

918991899189918991899189918991899189918991899189918991899189918991899189

20660206602066020660206602066020660206 6 02066020660206602066020660206602066020660

228732287322873

1 32

13/213/213/215/215/215/217/217/219/221/2

9/29/29/2

11/211/211/211/211/213/213/213/215/215/215/217/217/219/221/2

9/29/2

11/211/211/211/213/213/213/215/215/215/215/217/217/219/2

9/211/211/2

PAGE 22APPENDIX

TABLI! 2U(K) *2 FOR

LEVEL 2

507221644246766520208252566722612267622413825434

918920660228733667105832114725201258295072

21644246766520208252304822612267622413825434

2066022873105832114725201258295072

216442467665202082523C4825667226122676224138

228733667

21147

VI

SM+3

(U2:*2

0000000000

000000000000000000,

0.0,0.0.0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.

.0337

.0000

.0002

.0

.0

.0

.0

.0

.0• 0

.0368

.0000

.0072

.2417

.0503

.0000

.0000

.0002

.7085

.0005

.0001

.0

.0

.0

.0

.0

.0

.0

.2267

.0029

.0000

.1471

.0316

.0007

.0000

.0306,0181,0.0,00000

314300000176

(04)*2

0000000000

0000,0.0,00,0,0,0.0,0.0,0,0.0.0.

0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.

. 1744

.0001

.0014

.0117

.0008

.0000

.0002

.0066

.0

.0

.0094

.0009

.0001

.3531

.0652

.0035

.0010

.0008

.0332

.0013

.0018

.5743

.0010

.0037

.0002

.0023

.0,0

,1580,0356,0000,1009055401380000122519040000022202880630001100290

022400950879

(06) *2

0000000000

00000,0,00,0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.1.0.0.0.0.0.

0.0.0.

.3905

.0129

.0002

.2043

.0056

.0069

.0018

.0095

.0125

.0016

.0482

.0003

.0003

.0092

.0149

.0000

.0000

.0004

.4312,0020.0000.7457.0002.0090.0048.0061,0231,0160

,004 8140000090782225606870017271045060010005502652417463600270253

129100160067

••it

43368 20 21/2 15/2

J1

9/29/29/29/29/29/29/29/29/29/29/29/29/2

11/211/211/211/211/211/211/211/211/211/211/211/211/211/211/2

11/211/211/211/211/211/211/211/211/211/211/211/211/211/2

11/211/211/211/211/2

LEVEL

22873228732287322873228732287322873228732287322873228732287322873

366736673667366736673667366736673667366736673667366736 673667

1058310583105831058310583105831058310583105831058310583105831058310583

21147211U7211472114721147

1 J2

11/211/213/213/213/215/215/215/215/217/217/219/221/2

11/211/211/211/213/213/213/215/215/215/215/217/217/219/221/2

11/211/211/211/213/213/213/215/215/215/215/217/219/221/2

11/211/211/213/213/2

PAGE 23APPENDIX

TABLI! 2U(K)*2 FOR

LEVEL 2

25201258295072

21644246766520

20825230482566722612267622413825434

36671058321147258295072

2164424676652020825230482566722612267622413825434

105832114725201258295072

21644246766520208252304825667267622413825434

2114725201258292164424676

VI

SM + 3

(U2)*2

0000000000000

0000000000000,0.0,

0.0,0,0,0.0.0.1.0.0.0.0.0.0.

0.0.0.0.0.

.0015

.0100

.0044

.0120

.0002

.0

.0

.0

.0

.0

.0

.0

.0

.4871

.0158

.0017

.0002

.3428

.0000

.0005

.0171

.0000

.0000

.0002

.0

.0

.0

.0

.1382

.0000

.0000

.0066

.1668

.0002

.0000

.0103,0003,0018.0002.0,0,0

11810141009326400437

<U4)*2

0000000000000.

00,0,0.0,0.0,0,0,0,0,0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.

.0041

.0015

.0005

.0497

.0319

.0016

.0161

.0007

.0793

.2156

.4347

.0

.0

.0004

.2559

.0000

.0008

.3560

.0016

.0002

.1085

.0016

.0001

.0031

.0018

.0001

.0018,0

,0483.0008,0001,0001,5949,0038,00157789001200790034001200010

04950374073904811422

(U6)*2

0,20430.00050.00000.14060.02720.00020.07060.16300.28810.03571.10740.28490.0467

0.28370.76100.00500.00680. 10860.00110.01010.49780.00000.02090.00250.01370.00290.00320.0051

0.00260.00330.00120.00050.71120.00420.00350.34200.00040.00290.00470.00410.00270.0200

0.32970.33880.16360. 14490.1556

J1

11/211/211/211/211/211/211/211/2

11/211/211/211/211/211/211/211/211/211/211/211/211/2

11/211/211/211/211/211/211/211/211/211/211/211/2

13/213/213/213/213/213/213/213/213/213/213/2

IBVEL

2114721147211472114721147211472114721147

25201252012520125201252012520125201252012520125201252012520125201

258292582925829258292582925829258292582925829258292582925829

50725072507250725072507250725072507250725072

1 J2

15/215/215/215/217/217/219/221/2

11/211/213/213/213/215/215/215/215/217/217/219/221/2

11/213/213/213/215/215/215/215/217/217/219/221/2

13/213/213/215/215/215/215/217/217/219/221/2

PAGE 24APPENDIX

TABLI! 20(K) *2 FOR

LEVEL 2

652020825230482566722612267622413825434

252012582950 72

2164424676652020825230482566722612267622413825434

258295072

2164424676652 020825230482566722612267622413825434

50722164424676652020825230482566722612267622413825434

VI

SM + 3

(U2)*2

00000000

0000000000000

00000.0,0,0,0.0,0.0.

0,0.0.0.0.0.0.0.0.0.0.

.0000

.0278

.0129

.0316

.0

.0

.0

.0

.1673

.0005

.0000

.0251

.4310

.0000

.0052

.0048

.0001

.0

.0

.0

.0

.1454

.0017

.0409

.0120

.0000

.0004

.0010

.0298

.0

.0

.0

.0

.7978,0048,000725040001000000150000000000

(U4)*2

00000000

0000000,0,0,0,0,00.

0.0,0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.

.0000

.5935

.0092

.0593

.0122

.0386

.0078

.0

.0033

.0051

.0000

.0020

.2064

.0000

.5504

.1994

.0549

.2208

.0801

.0063

.0

.0061

.0032

.1123

.0224

.0011

.0070,056900860415,003936230

074C0000000041480021001000090057003600240039

<U6)*2

000

.0028

.0427

.09500.31420000

0000000.0.00.0.0,0,

0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.

.8906

.1126

.4568

.0141

.0060

.0909

.0048

.2442

.0427

.0029

.1659

.3966

.1969

. 0289

.0920

.0648

.0038

.0652,0063.0487.0820.0012,0126.000109730828093507590548

10340022001469920039007401790038031003140028

tl

J1

13/213/213/213/213/213/213/213/213/213/2

13/213/213/213/213/213/213/213/213/2

15/215/215/215/215/215/215/215/2

15/215/215/215/215/215/215/2

15/215/215/215/215/215/2

15/215/215/215/215/2

LEVEL

2164U216442164421644216442164421644216442164421644

246762467624676246762467624676246762467624676

65206520652065206520652065206520

20825208252082520825208252082520825

230482304823048230482304823048

2566725667256672566725667

1 J2

13/213/215/215/215/215/217/217/219/221/2

13/215/215/215/215/217/217/219/221/2

15/215/215/215/217/217/219/221/2

15/215/215/217/217/219/221/2

15/215/217/217/219/221/2

15/217/217/219/221/2

PAGE 25APPENDIX

TABLI! 2U(K)*2 FOR

LEVEL 2

21644246766520

20825230482566722612267622413825434

246766520

20825230482566722612267622413825434

652020825230482566 722612267622413825434

20825230482566722612267622413825434

230482566722612267622413825434

2566722612267622413825434

VI

SM + 3

(U2)*2

0000000000

000000000

100,000.0,0.

0,

c,0.0,0.0.0.

Q.0.0.0.0.0.

0.0.0.0.0.

.0493

.0727

.0001

.3284

.0388

.0649

.0529

.0346

.0

.0

.0081

.0000

.5111

.2441

.0007

.0113

.0258

.0

.0

.3358

.0022

.0103

.0009

.0004

.0034

.0003

.0

.3461

.1093

.0334

.0501

.0071

.0154

.0

.0608,0336,1358.0855.0469,0

,00387604000102760

(U4)*2

00000,000,0,0,

0,0,0,0,0.0.0.0.0.

0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.

0.0.0.0.0.0.

0.0.0.0.0.

.0529

.1363

.0001

.1409

. 1682

.0926

.5293

.0208

.0228

.0055

.0818

.0000

. 1021

.0014

.0717

.0124,0452.0245.0000

,6497.0000.0001,0000,0019,0026.0095,0030

9739012207230137015616310009

4222160037010082444000C3

08582200143721821058

(06) *2

000000001

.0871

.0550

.0041

.0720

.2002

. 1637

.0138

.2962

.07420.3034

00.0,0,00,0.0,0,

0.0,0.0.0.0.0.0.

0.0.0.0.0.0.0.

0.0.0.0.0.1.

0.0.0.0.0.

.0001

.0034

.4209

.1029

.0032

.8855

.6603

.0316

.0681

.4629

.0001

.0038,0037,0015.0003.0056, 0C19

0240,204027133581259815813139

013909330002001301381875

07670417048499320364

45930 4G 11/2 -9/2

PAGE 26APPENDIX VI

TABLE 2U(K) *2 FOR SH+3

J1 IEVEL 1 J2 LEVEL 2 (U2)*2 (U4)*2 (U6)*2

17/217/217/217/2

17/217/217/2

19/219/2

22612226122261222612

267622676226762

2413824138

17/217/219/221/2

17/219/221/2

19/221/2

22612267622413825434

267622413825434

2413825434

0.60200.00070.04990.0056

0.00070.93570.0674

0.67710.0437

0.84420.06290.06760.0853

0.13500.55520.5015

0.90870.0943

0.00080.41900.49430.3317

0.04590.06700.7585

0.02750.8814

21/2 25434 21/2 25434 0.6674 1.2562 0.9348

/¥*"

APPENDIX VII

PAGE 1

APPENDIX VII

TABLE 1EU+3:LAF3 CENTERS OF GRAVITY

OBSERVED CALC

... 037210261666

... 282338494907

172931902721483243552532526357263922662226735267522676327244275862796028427

O-C STATE

... 7F0

... 7F1

... 7F2

... 7F3

... 7F4

... 7F5

... 7F6

... 5D0

... 5D1

... 5D2

... 5D35L 6

... 5L7

... 5G2

... 5G3

... 5G4

... 5G6

... 5G 5

... 5L85D4

... 5L9

... 5L10

It?

3 /2 6637 9 / 2 2341 0 . 0 U. l l B j U. 31-33

J1

000000

00000000

1111111111111

111111111111

2222222

LEVEL 1

000000

1729317293172931729317293172931729317293

372372372372372372372372372372372372372

190271902719027190271902719027190271902719027190271902719027

1026102610261026102610261026

J2

244666

2224U466

1123334556667

122333445667

2233445

PAGE 3APPENDIX VII

TABLEU(K)*2

LEVEL 2

10262823

275864907

2532526752

102621483263922823

26735275862532526752

3721902710261866

243552662228233849

267634907

253252675226357

1902721483263921866

24355266222823

275862676325325 "2675226357

1026214831866

243552823

267353849

2FOR EU+3

(U2)*2

000000

00000000

0,0,0.0,0,0,0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.

.1374

.0

.0

.0

.0

.0

.0032

.0142

.0146

.0

.0

.0

.0

.0

.1541

.0025

.0518

.2092

.0004

.0002

.0

.0

.0,0.0.0,0

,0133,0122,0209003801830164000000

1000001818630002222600000

(U4)*2

000000

00000,00,0,

0,0,0.0,0.0,0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.

.0

. 1402

.0011

.0

.0

.0

.0

.0

.0

.0023

.0359

.0134

.0

.0

.0

.0

.0

.1281

.0012

.0012, 1741.1192,0004.0,0,00

.00,0001900590594002800780484000

1219001521240020006200073153

(06)*2

000000

0000000,0,

0,00.0,0.0,0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.

.0

.0

.0

.1450

.0153

.0037

.0

.0

.0

.0

.0

.0

.2384

.2212

.0

.0

.0

.0

.0

.0

.0

.0544

.0097

.3774,0091,0049,0181

,0,0,00000023321479571720 20

0000032900782089

->/ *•

J1

22222

22222222222222

22222222222

333333333333

3333

LEVEL 1

10261026102610261026

2148321483214832148321483214832148321483214832148321483214832148321483

2639226392263922639226392263922639226392263922639226392

186618661866186618661866186618661866186618661866

24355243552435524355

J2

56678

22333444556678

23344456678

333445566689

3344

PAGE 4APPENDIX VII

TABLEU(K) *2

LEVEL 2

267634907

267522635727244

21483263921866

2435526622282326735275863849

2676325325267522635727244

263922435526622282326735275862676325325267522635727244

186624355266222823267353849

26763490725325267522724427960

24355266222823

26735

2FOR EU+3

<U2)*2

00000

00000000000000

0,0,0,0.0,0.0,0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.

.0

.0

.0

.0

.0

.0011

.0086

.0023

.0351

.0305

.0020

.0267

.0042

.0

.0

.0

.0

.0

.0

.0784

.0017

.1097

.0000

.0225

.0005

.0

.0

.0

.0

.0

02750010,00003880,00021754000000000

0149011500390215

((J4) *2

00000

00000000000000,

00,00,0,0.0,0.0,0.0.

0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.

.0003

.0477

.0000

.0

.0

.0069

.0482

.0026

.0126

.0031

.0003

.0320

.0003

.0016

.0008

.0041

.0343

.0

.0

.0032

.0373

.0215

.0000

.0279,0040.0067,0480.0004.0.0

,0260,0005,00041352,00012527,001123100000000400

0023022900020005

(U6) *2

00000

0000000000,00.00.

0,0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.

.0046

.4696

.0019

.0110

.0193

.0

.0

.0

.0

.0

.0000

.2210

.0040

.0000

. 38 29

.1586

. 1586

.2479

.2481

.0

.0

.0

.0019

.0057,4282.1056,4599,01925130,0853

028100000048158800303836000541350013010200920168

003126 56000036 33

fl

5 / 2 71K1 Jbbt 0 . 0 0.2305 0.2087

J1

33333333

33333333333

444444444444

44444444444

4444

LEVEL 1

2435524355243552435524355243552435524355

2662226622266222662226622266222662226622266222662226622

282328232823282328232823282328232823282328232823

2673526735267352673526735267352673526735267352673 526735

27586275862758627586

J2

45566789

34455666789

4445566678910

445566678910

4556

PAGE 5APPENDIX VII

TABLEU(K)*2

LEVEL 2

275863849

267632532526752263572724427960

2662226735275863849

267634907

2532526752263572724427960

2823267352758o3849

267634907

25325 •2675226357272442796028427

2673527586384 9

267634907

253252675226357272442796028427

275863849

267634907

2FOR EO+3

(U2)*2

00000000

0,0,0.0,0,0,0.0,0.0,0.

0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.

.0592

.0001

.0328

.0

.0

.0

.0

.0

.0227

.1414

.0021

.0000

.0292

.0

.0

.0

.0

.0

.0

.0117,0002,0005,5684,0001,085600000001,0000

04070156000909820000009402790000

0817003408250012

(U4)*2

00000000

00000,00,0000,

0.0.0,0,0,0.0,0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.

V. .

0.0.0.

.0063

.0014

.0174

.0000

.0097

.0067

.0

.0

.0017

.0745

.0129

.0000

.0508

.0000

.0155

.0019

. 1106

.0

.0

.2841

.0009

.0006

.0128

.0000,5145.0002,0020.00000000,0,0

,00000381,00001241,0003029705380070189700

0022000403220000

(U6) *2

00000000

000,0000,0,0,00,

0,0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.

.0030

.0000

.2023

.0164

.0500

.1349

.3256

.34 77

.0644

.1508

.2131

.0010

.0086

.0020

.3677

.1249

. 1248

.5665

. 1166

.3528

.0005

.0002,4412.0059,2691,0046,0048,008000 4000520093

011611080036050500201569000126 62123282110161

0068000303840000

\f £. £. I I *f F

J1

444444

55555555

55555555

666666

666666

66666

7777

LEVEL 1

275862758627586275862758627586

38493849384938493849384938493849

267632676 3267632676326763267632676326763

490749074907490749074907

253252532525325253252532 525325

2675226752267522675226752

26357263572635726357

J2

66789

10

556678910

5666789

10

66789

10

6678910

678910

78910

PAGE 6APPENDIX VII

TABLEU(K)*2

LEVEL 2

253252675226357272442796028427

3849267634907

2675226357272442796028427

267634907

253252675226357272442796028427

490726752263572724 42796028427

253252675226357272442796028427

2675226357272442796028427

26357272442796028427

2FOB E0+3

(U2)*2

000000

000,00,0,0,0,

0.0,0.0.0.0.0.0.

1.0.0.0.0.0.

0.0.0.0.0.0.

0.0.0.0.0.

0.0.0.0.

.0005

.0363

.0

.0

.0

.0

.2762

.0020

.5410

.0001

.0000

.0

.0

.0

.0511

.0010

.0070

.0743

.0163

.00,0

,20290085,00000000.00

005000190147007600

10470004017700

0152024900830

(U4)*2

000000

00000000

0,00,0,0,0.0.0,

0,0.0.0.0.0.

0.0.0.0.0.0.

0.0.0.0.0.

0.0.0.0.

.0020

.0028

.0023

.0001

.0

.0

.2063

.0002

.6451

.0016

.0002

.0000

.0002

.0

.0008

.0011

.0403

.1716

.0692

.0134

.2596

.0

.3940,0022.0001,0003.0000,0020

,9355,03283310,072500000067

05780612048003842938

6740485608040000

(U6) *2

000000

00000,00,0

0,0,0,0,0,0.0.0.

0.0.0.0.0.0.

0.0.0.0.0.0.

0.0.0.0.1.

0.0.0.0.

.0166

.0000

.06 08

. 1575

.1547

.6379

.3225

.0047

. 1213

.0026

.0073

.0176

.0176

.0015

.0186

.0012

.0405

.0025

.1518

.3016

.4888

.6377

.02 94,0003.0013,0074.02420524

175800091468102000460563

00940509060130094460

0269167110320313

1%

7 / 2 1 1 3 5 1 5 / 2 6 5 2 0 0 . 0 0.0003 0.0467

PAGE 7APPENDIX VII

TABLE 20(K)*2 FOR EO+3

J1 LEVEL 1 J2 LEVEL 2 (U2)*2 (U4)*2 (06) *2

888

o> o>

272442724427244

2796027960

8910

910

272442796028427

2796028427

0.01760.03450.0055

0.01100.0379

0.71790.53120.0466

1.05740.4237

0.01750.19170.1105

0.05130.2855

10 28427 10 26427 0.0002 1.8415 0.4018

•I - , I - • •/

;• '-. 'if?

e l f

if? .;-/*

m

APPENDIX VIII

9/2 2341 11/2 25829 0.0001 0.0001 0.0011

OBSERVED

0.00.00.00.0

32177.1132185.6232199.6132228.57

32771.7532791.9632809.29

33352.0033370.00

35923.0035945.2435969.0335996.14

36275.2536286.0836306.2436314.2636333.45

36340.8136343.0336 347.1836351.6936354.8036364.5136371.713637 7.8636384.90

36551.433656 3.3336573.1836586.1436594.8636613.04

36661.8136670.9936679.9836690.1736700.50

PAGE 1APPENDIX VIII

TABLE 1GD+3

CALC

1111

32183321893220932232

327873278832799

3335133366

35929359393596235979

3626836276362973630536316

363423634436344363463034836350363553635836359

365563656736575365933659336611

3667436686366903670636707

I:LAF3

O-C

0000

-5-3-8-3

-14410

14

-56717

81091017

-1035715172026

-4-3-1-622

-11-14-9-14-5

STATE J

8S8S8S8S

6P6P6P6P

6P6P6P

6P6P

61616161

6161616161

616161616161616161

616161616161

6161616161

7/27/27/27/2

7/27/27/27/2

5/25/25/2

3/23/2

7/27/27/27/2

9/29/29/29/29/2

17/217/217/217/217/217/217/217/217/2

11/211/211/211/211/211/2

15/215/215/215/215/2

HJ

-7/25/23/21/2

-7/25/23/21/2

3/25/21/2

1/23/2

5/23/2

-7/21/2

5/2-7/23/2

-9/21/2

-9/2-11/2-7/213/215/25/23/2

17/21/2

-7/2-9/25/23/2

-11/21/2

-9/2-11/2-7/25/2

13/2

• • • " . • ! ' . ' • /

li .'V

- • %

OBSEBVED

36703367133671536720367243673436738367523676336772

3966739686397193974239758

• • •

40734407404074440751

• • •• • •

• • •

• • •

• • *

49170• « •

4922149240

• • •i « •

» • *

• •

• • •

• • •

• •

• •

• • •

• •

.65

.00

.52

.08

.82

.46

.99

.82

.02

.50

.00

.00

.00

.00

.00

.00

.00

.00

.00

.00

.00

.00

PAGE 2APPENDIX VIII

TABLE 1GD + 3

CALC

36714367223672236725367323673736737367593676936770

3966039694397293974139763

40644

40732407374074340754

4089540909

410044104941061

49159492324923349248

49533495394960849633496434967049674496954973249735497414981549849

:LAF3

O-C

-10-8-6-3-6-22-5-52

7-7-91

-4

• • •

231

-2

• • •• a •

• • •

• • •

• • •

11• • •-11-7

• * •• • •

• • •

• • •

• * •

• • •

• • •

• • «

• • •

• • •

• as

• • •

• • •

STATE J

61616161616161616161

6D6D6D6D6D

6D

6D6D6D6D

6D6D

6D6D6D

6G6G6G6G

6G6G6G6G6G6G6G6G6G6G6G6G6G

15/213/215/215/215/213/213/213/213/213/2

9/29/29/29/29/2

1/2

7/27/27/27/2

3/23/2

5/25/25/2

7/27/27/27/2

11/29/29/29/25/29/29/29/211/211/211/211/211/2

MJ

15/2-7/23/215/21/2

-11/25/213/23/21/2

-9/21/23/2-7/25/2

1/2

5/23/21/2

-7/2

3/21/2

3/25/21/2

-7/23/25/21/2

-11/2-9/2-7/21/25/23/2-7/23/21/23/25/2

-7/2-9/2

11/2 21147 13/2 24676 0.0437 C.1422 0.1556

.'¥'

PAGE

APPENDIX

3

VIII

TABLE 1AGD+3:LAF3 CENTERS OF GRAVITY

CALC CENTER

2

322323282733398

359193629136345365823670436742

39723406544090141037

STATE

8S 7/2

6P 7/26P 5/26P 3/2

61 7/261 9/26117/26111/26115/26113/2

6D 7/26D 1/26F 3/26D 5/2

r

"NJi- ' - • }

' •*, **'*

BLANK PAGE

u

U. 1/JO4

J1

1/21/21/21/21/21/21/2

3/23/23/23/23/23/23/.?3/23/23/2

3/23/23/2-V2V23/23/23/23/2

5/25/25/25/25/25/25/25/25/25/2

5/25/25/25/25/25/25/25/25/25/2

LEVEL

40654406544065440654406544065440654

33398333983339833398333983339833398333983339833398

409014090140901409014090140901409014090140901

32827328273282732827328273282732827328273282732827

41037410374103741037410374103741037410374103741037

1 J2

3/23/25/25/29/29/211/2

3/23/25/25/27/29/29/211/213/215/2

3/25/25/27/27/29/211/213/215/2

5/25/27/27/29/29/2

11/213/215/217/2

5/27/27/27/29/29/211/213/215/217/2

PAGEAPPENDIX

TABLE

5VIII

2U(K) *2 FOR

LEVEL 2

33398409013282741037362913972336582

33398409013282741037322J23629139723365823674236704

409013282741037322323594936291365823674236704

32827410373223235949362913972336582367423670436345

410372

3223235949362913972336582367423670436345

GD + 3

<U2) *2

0000000

0000000000

00,0,0.0,0,0,0,0,

0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.

.0028

.0090

.0572

.0301

.0

.0

.0

.0109

.0222

.0430

.0725

.0090

.0

.0

.0

.0

.0

.0323

.0742

.0130

.0276

.0000

.0

.0

.0

.0

.0292

.0424

.0180

.0000,0001,20030,0,0,0

0005002608680002000100350000

(04)*2

0000000

00000.00.0,0.0,

0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.

.0

.0

.0

.0

.0031

.0088

.0

.0

.0

.0002

.0013

.0004

.0002

.0022

.0016

.0

.0

.0

.0018,0061.0022,0045.0005,0116,00

0013,007300010023001500140000005200

0247000000050123008801200000024500

(U6)*2

0000000

000,00,00,0,0,0

0.0,0.0,0.0,0.0.0.

0.0.0.0.0.0.0.0.0.1.

0.0.0.0.0.0.0.0.0.0.

.0

.0

.0

.0

.0

.0

.003 3

. 0

.0

.0

.0

.0

.2310

.0000

.4382

.5719

.5483

.0

.0

.0

.0

.0

.0011,0362.0837.0355

.0,000017074410900021428002614351037

00000000004«V5094500020660001507151368

II

PAGE 6APPENDIX VIII

TABLE 20{K)*2 FOR GD+3

J1 LEVEL 1 J2 LEVEL 2 (U2)*2 (U<J)*2 (O6)*2

, <JU

7/27/27/27/27/27/27/27/21/27/27/27/27/27/27/27/27/2

7/27/27/27/27/2

9/29/29/29/29/2

9/29/29/29/29/2

11/211/211/211/2

13/213/213/2

15/215/2

222222220

3223232232322323223232232322323223232232

3594935949359493594935949

3629136 291362913629136291

3972339723397233972339723

36582365823658236582

367423674236742

3670436704

7/27/29/29/2

11/213/215/217/21/27/27/29/29/211/213/215/217/2

7/29/29/211/215/2

9/29/2

11/213/215/2

9/211/213/215/217/2

11/213/215/217/2

13/215/217/2

15/217/2

3223235949362913972336582367423670436345

03223235949362913972336582367423670436345

3594936291397233658236704

3629139723365823674236704

3972336582367423670436345

36582367423670436345

36742367043634 5

3670436345

00000000

0000000,0,

0,0.0.0.0.

0.0.0.0.0.

0.0.0.0.0.

0.0.0.0.

0.0.0.

0.0.

.0011

.0000

.0000

.0060

.0000

.0

.0

.0

.1202

.0000

.0003

.1879

.0000

.0

.0

.0

.0047

.0008

.0002

.0008,0

.0099

.00080021.00160

08540011000200

0129004500190

012200820013

00670115

00000000

00000000,

00.0.0,0,

0.0.0.0.0-

0.0.0.0.0.

0.0.0.0.

0.0.0.

0.0.

.0000

.0000

.0000

.0001

.0000

.0000

.0000

.0

.0017

.0018

.0048

.0210

.0051

.0019

.0037

.0

.0087

.0013

.0011

.0005

.0001

.0141

.0060

.00190013.0019

,0722,0191032603180140

0191000900330018

023500010055

01890088

00000000

00.0000,0,0,

0,0.0.0.0.

0.0.0.0.0.

0.0.0.0.0.

0.0.0.0.

0.0.0.

0.0.

.0000

.0044

.0110

.0000

.0188

.0257

.0287

.0228

.0001

. 1763

.3759

.0000

.5639

.7186

.8186

.7818

.0007

.0025,0046.0000,0009

0005,0099001800010002

00170075000200950409

0007001600000011

001500100012

00400008

ft?

APPENDIX IX

PAGE 1

APPENDIX IX

TABLE 1TB+3:LAF3 CENTERS OF GRAVITY

OBSERVED CALC O-C STATE

• • •

• • *

• • •

4423507455605814

205662631726529271112791928247• • •

28489290692934329595• • •

• • •

30750a a a

3149232998339423446635063• • •35344• • •• • •

3665737275• • •• • *• • •• a •

39287a • a

• • •

4091341447a • •

• • a

124217234394418510655615784

205682636026547270952789128231284112853229101293142958129655297343073431348

315033301533891344633505835060352553549836674367133726037606377223773238110

39297395154030940939414584147341817

• • •• • •• • •5

-310

30

-1-42-17162816

• • •-42-312914

• • a

• • •

16a • •

-10-165135

« • •89

a • •

a • a

-5515

• a •

a • •

• • a

• • •

-9a • •

• a a

-25-10• a •

• • •

7F67F57F47F37F27F17F0

5D45D35G65L105G55D25G45L95G35L85L75G25L65D15D0

5H75H65H55H45F55H35185F45F35175F25F1516514515

5K95D25G65K85K55G65K7

67

2 10262 1026

45

26735 0.0000 0.0007 0.00783849 0.0 0.3153 0.2089

J1

00000

111111111

222222222222

22222222222

333333333

LEVEL 1

57845784578 457845784

556155615561556155615561556155615561

510651065106510651065106510651065106510651065106

2823128231282312823128231282312823128231282312823128231

441944194419441944194419441944194419

J2

22446

123344567

223344455678

23344455678

334445568

PAGE 3APPENDIX IX

TABLEU(K)*2

LEVEL 2

5106282313439

20569125

556151064419

263603439

205692173125

29582

5106282314419

263603439

2056 9284122173

27892125

2958229315

282314419

263603439

20569284122173

27892265482958229315

4419263603439

20569284122173

27892125

29315

2FOR TB+3

(U2)*2

00000

0000,00,0,0,0,

0,0,0,0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.

.1391

.0010

.0

.0

.0

.1562

.0513

.2102

.0011

.0

.0

.0

.0

.0

.1002

.0010

.1829

.0014

.2224

.0011

.0016

.0

.0,0.0,0

,0168,0028,026900090362,060200000

027200073782002200251767001900

(U4)*2

0.0.0.0.0.

0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.

.0,0.1389,0017.0

,0,0,1273001317190025118800

121100102101002600600004000031350001048100

00800024005600050048000800270166025500

025300091343000500002504000123230

(06) *2

00000

00,00,00,0,0,0,

00.0,0.0,0,0,0.0,0.0.0.

0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.

.0

.0

.0

.0

.1441

.0

.0

.0

.0

.0

.0

.0537

.3761

.00 93

.0

.0

.0

.0

.0324

.0001

.0005,2071.0014,4695,0157,0199

00,0,00000059021700061466351035792572

02780000157500 060026381600 2041290152

J 24355 4 26735 0.0215 0.0005 0.3633

11

3

33333333333

44444444444

4444444444

444444444

LEVEL 1

4419

2636026360263602636026360263602636026360263602636026360

34393439343934393439343934393439343934393439

2056920569205692056920569205692056920569205692056 9

284122841228412284122841228412284122841228412

J2

9

34445566789

444556678910

445566789

10

45566789

10

PAGE 4APPENDIX IX

TABLEU(K)*2

LEVEL 2

28532

263603439

20569284122173

27892125

26548295822931528532

343920569284122173

27892125

2654829582293152853227096

20569284122173

27892125

2654829582293152853227096

284122173

27892125

2654829582293152853227096

2FOR TB+3

(U2)*2

0

00000000000

0,0,0,00,0,0.0,0.0.0.

0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.

.0

.0000

.0065

.0535

.0058

.0005

.0837

.0

.0

.0

.0

.0

.0120

.0002

.0000

.5541

.0042

.0888

.0023

.0

.0

.0

.0

.0463,0004,0142,0046,0009113100,00

068200050285000101130000

(U4)*2

0

00000000000

0,0,0,00,00,0,0,0.0.

0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.

.0

.0021

.0001

.0291

.0228

.0028

.0303

.0002

.0341

.0035

.0

.0

.2792

.0022

.0006

.0120

.0009

.5159

.0000

.0029

.0014

.0,0

.0310,0051,0013,0631.00082067,03330104,00

01480000156 4000309032416001600

(U6) *2

0

00,0,0,0,0,0,0.0,0.0.

0.0,0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.

.0255

.0027

.00 02

.0085

. 1398

.0016

.2981

.0014

.2412

.0221

.2546

.4161

,3500.0014,0068.43 74,0012.26 58,00 25,0069000401500322

00385115002239640013145703 36072327588669

00620021066500870677392000 3627360540

5 2173 5 21735 2173 5 278925 2173 6 125

0.2764 0.2071 0.317.90.0001 0.0002 0.00650.5377 0.6420 0.1178

Iff

44

2758627586

56

Jtujy26763

4907

U.0 .0 .

UU3408250012

0 .0 .0 .

000403220000

0 .0 .0 .

000303840000

11

55555

5555555

666666

66666

7777

LEVEL 1

21732173217321732173

27892278922789227892278922789227892

125125125125125125

2654826548265482654826548

29582295822958229582

J2

6789

10

566789

10

66789

10

6789

10

789

10

PAGE 5APPENDIX IX

TABLEU(K) * 2

LEVEL 2

2654829582293152853227096

27892125

2654829582293152853227096

1252654829582293152853227096

2654829582293152853227096

29582293152853227096

FOI2

I TB+3

( 0 2 ) * 2

0.0 .0 .0 .0 .

0 .0 .0 .0 .0 .0 .0 .

1 .0 .0.0 .0 .0 .

0 .0 .0 .0 .0 .

0 .0 .0 .0 .

00400002000

2578001202030115000

212500160006000000

58020464005900

0832082900030

(U4) *2

0.00280.00030.00190.00070 . 0

0.00010.00180.14660.10910.28770.00010 . 0

0.38810.00440.00010.00010.00190.0003

0.02880.00020.02560.25200.0068

0.44930.40470.03420.1037

(U6)*2

0 .0 .0 .0 .0 .

0 .0 .0 .0 .0 .0 .0 .

0 .0 .0 .0 .0 .0 .

0 .0 .0 .0 .0 .

0 .0 .0 .0 .

00 930066021001360015

05400131064830 75339605324457

02 7501160121022804550580

34 993264560771239143

2158087711390029

8 29315 8 293158 29315 9 285328 29315 10 27096

9 28532 9 285329 28532 10 27096

0.0509 0.6174 0.17990.0771 0.4809 0.12040.0000 0.0698 0.0803

0.0236 0.9206 0.17660.0727 0.4668 0.1548

10 27096 10 27096 0.0002 1.8580 0.3777

taX-stf

Iff

7 26357 10 28427 0.0 0.0000 0.0313

BLANK PAGE

•f: • • . •

APPENDIX X

•T/

' •''-<;.• 'A-.

(BSEEVE

0176912a184208307

• • •

3502• • •35763618363036453695

588259085924594459756020

76337665772877587801781478387842793379988077899290879074914491819235928293439435

102221028510345

:D CALC

222679106195216323335

3493357936163636363736713679

5873591059135931596 86021

761376547719mi78097839784 0785279388009809489749069907291399176924092779330944 7

102111026510336

PAGE 1

APPENDIX X

TABLI5 1DY+3:LAF3

O-C

-21-8-918

-10-7-15• • •

9• • •-39-17-6

-2516

9-1111370

20119

-18-7

-24-1-9-4

-10-161818255

-4513

-11

11209

STATE J

6H6H6H6H6H6H6H6H

6H6H6H6H6H6H6H

6H6H6H6H6H6H

6H6H6H6F6H6F6F6F6H6F6F6F6H6F6F6F6F6H6H6H

6H6H6H

15/215/215/215/215/215/215/215/2

13/213/213/213/213/213/213/2

11/211/211/211/211/211/2

9/29/29/211/29/211/211/211/29/211/211/^9/27/29/29/29/29/27/27/27/2

5/25/25/2

MJ

1/215/213/23/25/2

-11/2-9/2-7/2

13/2-7/23/25/21/2

-9/2-11/2

-7/2-11/2-9/25/23/21/2

5/2-9/23/21/2

-7/21/25/23/21/2

-7/2-9/25/23/2

-7/23/21/2

-9/2-7/21/25/2

5/21/23/2

36690.17 36706 -14 61 15/2 5/236700.50 36707 -5 61 15/2 13/2

BLANK PAGE

J

i _»

49849 6G 11/2 -9/2

)BSERVI

11037111091114011153

124561250412520

1327113285

• • •

2105721142211592120521395

2202222132221752218922213222922234222379

2346823497235132353723551* « •

• • •• • •

249902500825073• • •

250 98• • •

25195• • •

25303

!D CALC

11028111011114111143

124551249312512

1327713286

13827

2107121137211632120521393

2195622111221552218422209222722233222357

234572351223531235542357023616

2486524955249692498625097250972510225145252272522925272

PAGE 2

APPENDIX 3

TABLE 1DY+3:LAF3

O-C

98010

1118

-50

• • •

-135-302

66212054201022

11-14-17-16-18• • •

« • •• • •2122

-239 • •

-3• • • '-31• • «31

C

STATE J

6F6F6F6F

6F6F6F

6F6F

6F

4F4F4F414F

414141414F414141

4G4G4G4F4G4G

4H4H4M4M4H4H4M4H4N4H4M

7/27/27/27/2

5/25/25/2

3/23/2

1/2

9/29/29/29/29/2

15/215/215/215/215/215/215/215/2

11/211/211/211/211/211/2

21/^!21/221/221/221/221/221/221/221/221/221/2

HJ

5/21/2

-7/23/2

3/25/21/2

3/21/2

1/2

-9/25/23/2V2

-7/2

15/25/213/21/2

-7/2-9/2-11/213/2

-9/2-7/2

-11/25/23/21/2

-21/2-7/23/21/2

-9/2-11/2

5/213/215/2

-19/217/2

• 71

" 7 : - * > " ' V £ r "'••"•'?'

IBSEBVE

a • *

256612569125740257 4825778• • •

25824• • •

258492586'• • •• • •• • r

2590325918• • *

259402595325990

• • •

• • •

• • •

26260263582642926448265092657126583

2748227536

2758127624276 65

• • •279 19• * •

279882803628074

!D CALC

2558825647257132571625748258112581425819258312585925899259002590725910259202592925958259682597425986

26178261882619426228263482639626421264812651726527

2750827556

275862762627659

278412794427959280012800628035

PAGE 3

APPENDIX J

TABLH! 1DY+3:LAF3

O-C

• a •

14-21240

-32• • •5

• • •-9-31• • •• • *• • •-16-10• • •

-27-20

4

• • •• • •• • *32103327285456

-25-19

-4-16

• • •-24• • •-123039

STATE J

414141414F4K41414K414K414F4F4K4K4F4K4141

4M4M4H4H4M4H4H4M4M4H

4P6P

6P6P6P

414141414141

13/213/213/213/27/217/213/213/217/213/217/213/27/27/217/217/27/217/217/217/2

19/219/219/219/219/219/219/219/219/219/2

3/23/2

5/25/25/2

11/211/211/211/211/211/2

MJ

13/25/23/2

-7/21/2

17/2-9/2

-11/2-7/21/25/2

-9/2-7/23/21/23/25/2

15/2-11/213/2

-19/2-9/2-7/2

-11/213/25/23/21/2

17/215/2

1/23/2

5/23/21/2

-11/25/23/21/2

-7/2-9/2 •?"<•„ ' • " ' *

il

IBSERVE

2834728381

• • •

2853628577286132863628658286742871528734

• • «

• • •29535296382966729684297522978729855

29890• • *• * •• • •

• # •

29982• • •• • •

3007530141

• • •30243

* • •30302

3088730924

;D CALC

284092844828515285742860028632286532866228667287072876928797

2946729574296202962229688297322982529855

2991729945299492998429986299883003730047300663013130193302203026930293

3086830897

PAGE 4

APPENDIX X

TABLE: 1DY+3:LAF3

O-C

- 6 1-66• • •- 3 7- 2 2- 1 8-16

- 378

- 3 4• • •

• • •- 3 8

1845- 320

-370

-26• • •• • •• • •• • *

-5• • •• • •

910

• • •

23• • *

9

1927

STATE J

4K4K4H4H4H6P6P6P6P6P4H4M

4F41414F4F414141

464H4M4H4H4K4114K4K4M4G4G4G4G

6P6P

15/215/215/215/215/27 / 27 / 27 / 27 / 27 / 2

15/215/2

5 /29 / 29 /25 / 25 /29 / 29 / 29 / 2

9 / 217/217/217/217/217/217/217/217/217/2

9 /29 / 29 / 29 /2

3 /23 /2

HJ

15/25/23 /21/2

-7/23 /21/23 / 25 /2

-7/2-11/2

13/2

3 / 21 / 2

-9/25/21/2

-7/23 / 25/2

-7/25 /23 /2

17/2-9/2

1/215/2

-11/213/2-7/2

1/23 / 25/23 /2

1/23 /2

• s •••

5/2 41037 17/2 363450.00.0

0.00.0

tl

0.07150.1368

)BSEBVI

31055• • •

3113431169311943121131225• • •

312593128231294* • •

31328• • •• • •

3137931452• • •

3158031660• • •

31716

• • •• • •

• • •

• • •

33146• • •

33202• • •

332183323633256

• • •

3352733527335 27335273362333558

3366633652

!D CRLC

310613110131137311*23117131219312323123431250312823131531319313293134431348313823143131434

31570316553171231717

32060320893216932182

33149331793318633196332073321233225

33492335153351933520335233357833579

3364533646

PAGE 5

APPENDIX X

TABLE! 1DY+3:LAF3

O-C

-5• • •-21723-7-6• • •90

-20• • •

0• • •• • •-221

• • •

105

• « •0

• • •

• • •

• • •

• • •

-2• • •16

• • •

112431

• • •12674

45-20

216

STATE J

4K4K4K4L4K4K4L4H4M2L4L4H4H4K4L2L2L4K

4G4G4G4G

4D4D4D4D

4K4K4K4K4K4K4K

4H4H4H4H4H4K4H

4F4F

15/215/215/219/215/215/219/219/219/219/219/219/219/215/219/219/219/215/2

7/27/27/27/2

5/25/21/25/2

13/213/213/213/213/213/213/2

13/213/213/213/213/213/21V2

3/23/2

HJ

1/213/23/215/2

-11/25/2

-9/217/217/21/2

-9/25/2

-19/2-7/215/213/2

-11/2-9/2

5/23/21/2

-7/2

1/25/21/23/2

-11/2-7/213/23/21/2

-9/25/2

-9/213/25/23/213/2-7/21/2

1/23/2

)BSERVE

34029340403405234080

• • •

• # •

• • •

3424734250• • •• • m

m m •

3429834313

• • •

• • •

• • •

• * •

• • •

3436634393344 18344263447734466• • •

34525

348543487334904349143492534973

• • •• • •• * •

35940359663599436006360553605536080

iD CALC

34021340223403634058

3423634237342673427234284342843429334317343223432734328343453435434361343673438434418344373443934470344703448234502

348513487434902349063492934998

3578035781359103595 2359633598836008360543609536162

PAGE 6

APPENDIX X

TABLII 1DY+3:LAF3

O-C

8181622

• • •• • •• • a

-24-33• • #• • •• • m

-23-13• • •

• • •

a • •

• * *

• • •

-17-24-18-12

7-3

• • m

23

30286

-24

• • •• • *• m m

-1136-11

-39-81

STATE J

4D4D4D4D

4H4H4H4L4L4H4F4H4L4L4L4L4L4H4L4L4H4H4H4H4H4F4H

4G4H4H4G4G4G

4K4K4K4K4K4G4G4G4K4G

7/27/27/27/2

11/211/211/217/217/211/25/211/217/217/217/217/217/211/217/217/29/29/29/211/29/25/29/2

11/211/211/211/211/211/2

11/211/211/211/211/27/27/27/211/27/2

HJ

1/23/2-7/25/2

-9/2-7/2-11/2

3/21/2

-7/23/21/25/215/213/23/2

-11/2-7/2-9/217/2-9/21/2

-7/25/23/21/25/2

-9/2-7/25/21/23/2

-11/2

-9/21/2

-11/2-7/23/23/2

-7/21/2

-7/25/2

OBSERVED CALC

• • •• • •• • •

364943651236536

•#

#366 34• • •

366663665336686

3675236780* • •• • •• * •

• • •• • •• • •• • •• • •

37944• • •

37978

389 373899639090

3915239176

364673646936469365023652636543365443656436564365653658236586366043661036622366393664036677

367503678 5368123664036854

3763837672376813777737794

37948379773801138021381123821438223382963841638476

389083899439080

3916939192

PAGE 7

APPENDIX X

TABLE 1DY+3:LAF3

O-C STATE J

•••

-

•

m

•

•

•

•

•

•

• 4

m «

- ,

.. 4L

.. 4G

.. 4L-7 4L13 4L-6 4L.. 4L.. 4L.. 41.. 4L.. 4L.. 41.. 4G24 4G.. 4L29 4L13 4L9 4L

2 4G-4 4G.. 4G

4G4G

.. 4G

.. 4P4L

.. 4L. 4G

•3 2L. 4F32 2L.. 4F. 2L. 2L. 2L. 2L. 2L. 2L

29 4P

1

-1-1

2 4P0 4P

16 4P15 4P

13/25/215/215/213/215/213/215/215/213/213/213/25/25/213/215/215/213/2

9/29/29/29/29/2

7/21/27/27/27/2

15/23/215/23/215/215/215/215/215/215/2

5/25/25/2

3/23/2

HJ

5/21/23/21/2

-7/213/2-9/215/25/21/2

13/23/25/23/2

-11/2-7/2-9/21/2

-7/23/2

-9/2-7/21/2

3/21/25/2

-7/21/2

15/21/2

-7/23/2

-9/25/21/2

-9/2-11/213/2

3/25/21/2

3/21/2

PAGE 8

APPENDIX X

TABLE 1ADY+3:LAF3 CENTERS OF GRAVITY

CALC CENTER STATE

1753626595278067853916692231027311070124711326713814

212282222223563251092579425 85625890263342754327624

6H15/26H13/26H11/26H 9/26F11/26F 9/26H 7/26H 5/26F 7/26F 5/26F 3/26F 1/2

4F 9/24H15/24G11/24B21/24113/24F 7/24K17/24H19/26P 3/26P 5/2

333

441944194419

568

27892125

29315

0.0.0.

001900

0.0.0.

000123230

0.0.0.

002041290152

• ' • • * ( •

J1

1/21/21/21/21/21/2V21/21/21/21/21/21/21/21/2

3/23/23/23/23/23/23/23/23/23/23/23/23/23/23/2

3/23/23/23/23/23/23/23/23/23/23/23/23/23/23/23/23/2

LEVEL

138141381413814138141381413814138141381413814138141381413814138141381413814

132671326713267132671326713267132671326713267132671326713267132671326713267

2754327543275432754327543275432754327543275432754327543275432754327543275432754327543

1 32

3/23/25/25/25/27/27/27/29/29/211/211/211/213/213/2

3/25/25/25/2V27/27/29/29/2

11/211/213/213/215/215/2

3/25/25/25/27/27/27/29/29/29/211/211/211/213/213/215/215/2

PAGEAPPENDIX

TABLE 2U(K)*2 FOE

LEVEL 2

132672754310273124712762492231107025856780691665952785323563362625794

275431027312471276249223

11070258567806916659527853362625794

17522222

2754310273124712762492231107025856780691662122859527853 .

235633626

25794175

22222

9X

DY+3

(U2)*2

000000000000000

0000,00,00.0,0,0,0,0.0.0.

0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.

.0175

.0665

.1918

.0100

.0147

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.1391

.1396

.0222

.0964

.2421

.0134

.0000

.0

.0

.0

.0

.0

.0

.0

.0

,0572,0007,1151,0185,0004,042019070,0,00000000

(U4)*2

0000000000,00,0,0,0,

0,0.0,0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.

.0

.0

.0

.0

.0

.1394

.0294

.0156

. 1512

.0060

.0

.0

.0

.0

.0

.0

. 1346

.0260,0227.1179,0104.0212, 1224,03111935,0166, C,000

00743002300000494017904790393075710310072173104170000

(U6)*2

000000000000,0,0.0,

0,0.0.0.0,0.0.0.0.0.0.0.0.0.0.

c.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.3478

.0050

.0020

. 1001

.0013

.0,0.0,0.0,0.0, 3636,01120390,03533950.007606110014

00000000089000901140070000002960016153105080051

5 2173 5 27892 0.0001 0.0002 0.00655 2173 6 125 0.5377 0.6420 0.1178

J1

5/25/25/25/25/25/25/25/25/25/25/25/25/25/25/2

5/25/25/25/25/25/25/25/25/25/25/25/25/2

5/25/25/25/25/25/25/25/25/25/25/25/25/25/2

7/27/27/27/27/2

LEVEL

102731027310273102731027310273102731027310273102731027310273102731027310273

12471124711247112471124711247112471124711247112471124711247112471

276242762427624276 2427624276 242762427624276242762427624276242762427624

92239223922392239223

U

1 J2

5/25/25/27/27/27/29/29/29/211/211/211/213/215/217/2

5/25/27/27/27/29/29/29/2

11/211/213/213/215/2

5/27/27/27/29/29/29/211/211/211/213/213/215/217/2

7/27/27/29/29/2

PAGE 10APPENDIX

TABLE 2(K) *2 FOB

LEVEL 2

1027312471276249223110702585678069166

2122859527853235633626175

2S890

12471276249223110702585678069166

2122859527853362625794

175

276249223110702585678069166

2122859527853

235633626

25794175

25890

9223110702585678069166

X

DY+3

(U2)*2

000000000000000

000,0,0,0.0.0,0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.

.3736

.0379

.0000

.2143

.0044

.0007

.0237

.0000

.0000

.0

.0

.0

.0

.0

.0

.0007

.2868

.1943

.0439

.0059

.3358

.0095

.0062

.0

.0

.0

.0,0

,2570,00004684,09100011,498100870000000

26180511003130350039

(U4)*2

00000000000,00,00.

0,0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.

.0659

.2727

.0302

.1919

.1315

.0059

. 1300

.0182

.0035

.0236

.0031

.0007

.0012

.0

.0

.0171

.0890

.0583

.0033

.0188

.1045,0333.0008,1971,0503,2103,0008,0

00040997186601461621255100463230163801991722009800

00872930004515341255

(U6)*2

000000000000000

000.0,0.0,0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.

.0

.0

.0

.0758

.4393

.0113

.3127

.3551

.0011

.2993

.0177

.0014

.0590

.0026

.0024

.0

.0

.4192

.0087

.0005

.0390

.0301

.0004, 1557.0898,2852,0007,3446

0,01440000,00050279,000001100564002902830820001007210633

28590000023101324498

J1

7/27/27/27/27/27/27/27/27/27/2

7/27/27/27/27/27/27/27/27/27/27/27/27/2

7/27/27/27/27/27/27/27/27/27/27/27/27/2

9/29/29/29/29/29/29/29/29/29/29/2

LEVEL

9223922392239223922392239223922392239223

11070110701107011070110701107011070110701107011070110701107011070

25856258562585625856258562585625856258562585625856258562585625856

78067806780678067806780678067806780678067806

1 J2

9/211/211/211/213/213/215/215/?17/219/2

7/27/29/29/29/211/211/211/213/213/215/217/219/2

7/29/29/29/2

11/211/211/213/213/215/215/217/219/2

9/29/29/211/211/211/213/213/215/215/217/2

PAGE 1APPENDIX

TABLE: 2U(K) *2 FOR

LEVEL 2

2122859527853

235633626

25794175

222222589026334

110702585678069166

2122859527853

235633626

25794175

2589026334

2585678069166

2122859527853

235633626

25794175

222222589026334

78069166

212285952785323563362<>

25794175

2222225890

1X

DY+3

(U2) *2

0000000000

0000000,0,0.0,0,0,0,

0,0,0.0,0,0.0.0.0.0.0-0.0.

0.0.0.0.0.0.0.0.0.0.0.

.0008

.0348

.0004

.0001

.0

.0

.0

.0

.0

.0

.0016

.0102

.2267

.0630

.0002

.4449

.0344

.0107

.0

.0

.0

.0

.0

.0512

.0027

.0544

.0465

.0405

. 1014

.0872

.0,0.0,0.0,0

,3081,0424,0021,34460037,000203380057000

(U4)*2

0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.

,0079, 1465.03060044,03090034,00060016,00

027402431387,00520043,05030344000042170015135200

0275007402660838031801981410011137560695038900

0160J327002416621159007417120000016600770202

(U6)*2

0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.

0067342614380013276300010393000300210082

0267000425080435002925210843000000000076713800730156

0123011200083307002000012588032100070260004503932900

26841716003201374969000039210040201700000000

J1

9/2

9/29/29/29/29/29/29/29/29/29/29/29/2

9/29/29/29/29/2V29/29/29/29/29/2

11/211/211/211/211/211/211/211/211/211/2

11/211/211/211/211/211/211/211/211/2

11/211/2

LEVEL

7806

916691669166916691669166916691669166916691669166

2122821228212282122821228212282122821228212282122821228

5952595259525952595259525952595259525952

785378537853785378537853785378537853

2356323563

1 J2

21/2

9/29/211/211/211/213/213/215/215/217/219/221/2

9/211/211/211/213/213/215/215/217/219/221/2

11/211/211/213/213/215/215/217/219/221/2

11/211/213/213/215/215/217/219/221/2

11/213/2

PAGE 1APPENDIX

TABLI! 2U(K)*2 FOE

LEVEL 2

25109

91662122859527853235633626

25791*175

22222258902633425109

2122859527853

235633626

25794175

22222258902633425109

59527853

235633626

25794175

22222258902633425109

7853235633626

25794175

22222258902633425109

235633626

2X

DY+3

(U2)*2

0

000000000000

000000000.0.0,

0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.

0.0.

.0

.0313

.0007

.2561

.0239

.0061

.6670

.0012

.0

.0

.0

.0

.0

.0226

.0093

.0032

.4708

.0490

.0068

.0

.0

.0

.0

.0

.4989

.0021

.0001

.2547,0032.0912,0049,00,0

1428015b2518000493940020000

35770012

(U4)*2

0

000000000000

000,0000.0,0.0,0.

0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.

0.0.

.0

.0106

.0055

.3942

.0190

.0001

.0236

.0167

.5746

.0126

.0321

.0

.0

.2572

.0018

.0032

. 1686

.0164

.0418

.0046

.5584

.4557

.0

.0

.0328,19190001,49330031,03690026004202130

138500014^48006882990270003700010

05550299

(06) *2

0

000000000000

00000,00,0,0.0.0.

0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.

0.0.

.0226

.0428

.0004

.0114

.0154

.0085

.3778

.0082

.7186

.0063

.0132

.0425

.0919

.3827

.0033

.0024

. 1511

.0545

.3971

.0292

.0182

.0315

. 1410,9115

,0498.8336001903000221,63920006C11303300376

062400837751003820610022003602080318

01270065

J1

11/211/211/211/211/211/2

13/213/213/213/213/213/213/2

13/213/213/213/213/213/2

15/215/215/215/215/2

15/215/215/215/2

17/217/217/2

19/219/2

21/2

IEVEL

235632356323563235632356323563

3626362636263626362636 263626

257942579425794257942579425794

175175175175175

22222222222222222222

258902589025890

2633426334

25109

1 J2

13/215/215/217/219/221/2

13/213/215/215/217/219/221/2

13/215/215/217/219/221/2

15/215/217/219/221/2

15/217/219/221/2

17/219/221/2

19/221/2

21/2

PAGE 1APPENDIX

TABLf: 2U(K)*2 FOE

LEVEL 2

25794175

22222258902633425109

362625794

17522222258902633425109

25794175

22222258902633425109

17522222258902633425109

22222258902633425109

258902633425109

2633425109

25109

3X

DY+3

(U2)*2

000000

0000000

000,0,0,0,

1.0,0,0.0.

0.0.0.0.

0.0.0.

0.

c.0.

.0000

.0004

.1356

.0

.0

.0

.7945

.0014

.2454

.0049

.0022

.0

.0

.5060

.0039

.0220

.0009

.0

.0

.3310

.0071

.0101

.0002

.0

.4738,2741,0014,0

12638045,0018

04287683

6719

(04)*2

0000.00,

0,0.0.00,0,0.

0.0,0.0.0.0.

0.0.0.0.0.

0.0.p.0.

0.0.1.

0.0.

1.

.0053

.0141

.0812

.0981

.4117

.0

.0738

.0003

.4136

.0041

.0044

.0049

.0034

.2108

.0012

.0103

.1791,2761,0878

,64520003,00420139,0101

4363054 849092399

073303612616

06123865

2335

(U6)*2

0.0.0.0.0.0.

0.0.0.0.0.0.0.

0.0.0.0.0.0.

0.0.0.0.0.

0.1.1.0.

0.0.0.

1.0.

0.

5958000 39026769453936624

1064000468340107000100260037

1877024 90886008100294522

42660659090509680808

5634288902518452

134602650075

68291317

8622

APPENDIX XI

PAGE 1

APPENDIX XI

TABLE 1HO+3:LAF3 CENTERS OF GRAVITY

iSERVED

05146856811123• • •

15420183971852H20596210562127922187• • •

2394225872260872767227672• • •

28878288782994329943307S5• • •• • *

34100341003481135206

• • •

• • •

• • •

« • •

36724• • •• • •

38378• • •

' CALC

950648578

1114513212

15456183811853820594210392126722179222552398725859260582765227678282342887528895299412994730799330633324734072341563481235203360083600936294363143672037794379003833938515

0-C

82-9

-21• • •

-3516

-13217128

• • •-44132920-5

• • •

3-16

2-3-3• • •• • •28

-5503

• # •• m •

• • •

« * •

4• • •* • •39

a • •

STATE

518517516515514

5F55S25F45F35F23K85G65F15G55G43K75G53H65F25G33L93K6.3F45G23D 33P13M103L85G43G33P05D43F21L83H53P23L73173F4,

25303 25272 31 4M 21/2 17/2

{•, . " .

M

000000

111111111111111

2222222222222222

2222222222

LEVEL 1

360083600836008360083600836008

222552225522255222552225522255222552225522255222552225522255222552225522255

18381183811838118381183811838118381183811838118381183811838118381183811838118381

21040210402104021040210402104021040210402104021040

32

244666

122344455556677

2234445555666778

2344455556

PAGE 3APPENDIX XI

TABLEU(K) *2

LEVEL 2

2104013212185388579

2218027679

2225518381210402059513212185382585911146154572398827653857 9

221805065

26059

183812104020595132121853825859111461545723988276538579

22180276795065

260599

2104020595132121853825859111461545723988276538579

2FOR HO+3

(U2)*2

000000

000000000000,00,0,

0,0.0,0.0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.

.0027

.0

.0

.0

.0

.0

.0302

.0109

.0539

.0084

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0000

.0016

.0065

.0014,0000.0328.0.0,0,0,000000

0077052100050085260800000

(U4) *2

000000

000000000000,0,0,0,

0.0.0,0.0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.

.0

.0089

.0013

.0

.0

.0

.0

.0

.0

.0586

. 1442

.0468

.0564

. 1396

.0000

.0070

.0074

.0

.0

.0

.0

.0016

.0035

.0000

.0302

.0159

.2811,0052.0123,1062,0570,024031280437000

0271000020110805001204730052142312331365

(06) *2

000000

000000000000,0,0,0.

0,0,0.0.0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.

.0

.0

.0

.0175

.0351

.0805

.0

.0

.0

.0

.0

.0

.0

. 1704

.1.147

.0537

.0548

.2383

.0528

.0568

.0020

.0

.0

.0

.2839,0033,0216.0968,005000040006145800470065419505532145

0002 930317120430241466011500121604

BLANK PAGE

• • > > " ;

J1

222222

3333333333333333

444444444444444

4444444444

LEVEL 1

210402104021040210402104021040

20595205952059520595205952059520595205952059520595205952059520595205952059520595

132121321213212132121321213212132121321213212132121321213212132121321213212

18538185381853818538185381853818538185381853818538

J2

667788

3444555566677889

44455556667788

10

4455556667

PAGE 4APPENDIX XI

TABLEU(K)*2

LEVEL 2

22180276795065

260599

21268

20595132121853825859111461545723988276538579

22180276795065

260599

2126828896

132121853825859111461545723988276538579

22180276795065

260599

2126834072

1853825859111461545723988276538579

22180276795065

2FOR HO+3

(U2)*2

000000

0000000000000000

0,0,0.0,0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.

.0

.0

.0

.0

.0

.0

.0358

.0002

.0973

.2147

.0000

.0396

.1800

.1544

.0

.0

.0

.0

.0

.0

.0

.0

.1222

.0002

.0152

.0310

.0001

.0000

.0036

.0023,00050000,00,0.0,0

0770396200161980275129740011252601030

(U4)*2

000000

0000000000000,00,0,

0,0.0,0,0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.

.0225

.0068

.0

.0

.0

.0

.0637

.0982

.0298

.0176

.2173

.0816

.1005

.0474

.0897

.0655

.0112

.2463

.0068

.0

.0

.0

.1308

.0241

. 1072,1237.0061.0091.0097,0282,0013,000000340006,000000460

0085105213340920023800252574238002101965

(U6) *2

000000

000000000,00,00,00,0,

0.0.0.0.0,0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.

. 1010

.00 99

.0789

.0550

.2041

.0036

.0275

.3949

.0966

.0509

.0175

.0851

.0325

.0059

.2172

.1526

.0509

.2279

.0049

.3464

.0067

.0012

.3456

.2576

.0555,9103.0036,0418,00086639,000002001568006800 7600120019

0886021746660071139505171704128902590320

33666 3364533652 33646

21 4F6 4F

6//.3/2 3/2

J1

44444

44444444444444

5555555555555

555555555555

55

LEVEL 1

1853818538185381853818538

2585925859258592585925859258592585925859256592585925859258592585925859

11146111461114611146111461114611146111461114611146111461114611146

154571545715457154571545715457154571545715457154571545715457

2398823988

J2

788910

4555566677889

10

555566677889

10

55566677889

10

55

PAGE 5APPENDIX XI

TABLEU(K) *2

LEVEL 2

260599

212682889634072

25859111461545723988276538579

22180276795065

260599

212682889634072

111461545723988276538579

22180276795065

260599

212682889634072

1545723988276538579

22180276795065

260599

212682889634072

2398827653

2FOR HO+3

(U2)*2

00000

0000000000.0,0,0,0,

0.0,0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.1.0.0.0.0.0,0.0,

0.0.

.0

.0

.0

.0

.0

.0098

.2254

.0345

.0128

.0415

.6896

.0036

.0030

.0

.0

.0

.0

.0

.0

.1023

.0071

.0031

.0040

.0435

.0171,0004.0028.0072.0,0,0,0

072934250907011313051113019400150000

07060263

(04)*2

00000

00000000,0,00.0,0,0,

0,0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.0.

0.0.

.0156

.2385

.0085

.0

.0

.0138

.2700

.0138

. 1484

. 1417

.0226

.2047

.0067

.2857

.0152

.0351

.0919

.0

.0

.0364

.0281

.0642

.0487

.1703,0312,0011,0226,00420102000402530

181503531752124236160000330901124201025806080

04730132

(U6) *2

00000

00000000000.00,0

0,0,0,0,0,0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.0.

0.0.

.0091

.7090

.0007

.0093

.0417

. 1812

.0329

.2147

.02 68

.0182

.0003

.2909

.00 93

.06 42

.0044

.0332

.0013

.0492

.2687

.0176

. 1630

.0568

.0418

.5720,0124.0153, 88 96.03120930,004102420368

005011450483497203210002429801425701019007411693

01392050

J1

555555555

55555c.5555

666666666

66666666

6666666

77

LEVEL 1

239882398823988239882398823988239882398823988

27653276532765327653276532765327653276532765327653

857985798579857985798579857985798579

2218022180221802218022180221802218022180

27679276792767927679276792767927679

50655065

J2

66677889

10

566677889

10

6' 6677889

10

667788910

677889

10

77

PAGE 6APPENDIX XI

TABLEU(K) *2

LEVEI 2

857922180276795065

260599

212682889634072

276538579

22180276795065

260599

212682889634072

857922180276795065

260599

212682889634072

22180276795065

260599

212682889634072

276795065

260599

212682889634072

506526059

2FOB HO+3

(U2)*2

000000000

00

.1286

.0565

.1987

.5696

.0164

.0

.0

.0

.0

.0360

.09490.00050000000,

0,0,0,0,0.0.0.0.0.

0.0.0.0.1.0.0.0.

0.0.0.0.0.0.0.

0.0.

.1501

.7003

.0036

.0

.0

.0

.0

.1273

.0091

.0001

.0314

.0011,0087,0059,0.0

,0025,0509,148400004830,0000,0,0

14990314004G2540107700

15020055

(U4)*2

000000000

00000,0,0,0,0.0,

0.0,0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.

0.0.

.1695

.2568

.0657

.0240

.0059

.5239

.0083

.3321

.0

.0058

.2452

.0711

.5825

.1913

.0104

.0938

.0051

.1803

.0

.0681

.0819

.0051

.1324,0057.0389,0041,0071,0177

,3968,2992428400038201004804020455

1032058605021399110911813381

11930059

(U6) *2

000000000

0.00,00,0,0.0,0.0.

0.0,0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.

0.0.0.0.1.0.0.

0.0.

.0789

.24 56

.0168

.1171

.2487

.00 00

.0007

. 1702

.3522

.0012

.0460

. 1580

.00 00

.0584

. 4bO6

. 1596

.0214

. 1726

.2616

.0402

.1094

.0024

.9295,07 22,69200142,0357,0211

120900692633123914 00307628101696

0418008768540013598582 882755

02970047

39152 39169 -16 UP 3/2 3/239176 39192 -15 4P 3/2 1/2

PAGE 7APPENDIX XI

TABLE 2U(K)*2 FOR HO+3

J1 LEVEL 1 J2 LEVEL 2 (02) *2 (U4) *2 (06) *2

7777

77777

00 00 C

O 00

00 0

0 00

99

10

5065506 550655065

2605926059260592605926059

9999

212682126821268

2889628896

34072

88910

788910

88910

8910

910

10

9212682889634072

260599

212682889634072

9212682889634072

212682889634072

2889634072

34072

0.02490.00180.00090.0

0.00160.00560.08650.07880.0

0.19510.02050.01790.0003

0.02600.31630.0134

0.68580.7340

3.3219

0.13440.00440.00410.0003

0.02230.00440.00020.19630.3112

0.31170.03170.00510.0681

0.04650.05681.0322

1.35471.4855

0.0011

1.52310.04020.01030.0059

0.01750.03350.12230.13910.3289

1.54600.15350.14990.0789

0.20192.04950.8500

0.02910.5524

1.4872

APPENDIX XII

3/2 27543 15/2 175 0.0 0.0 0.05083/2 27543 15/2 22222 0.0 0.0 0.0051

I

)BSEBVI

051

121200219314400443

6604663066706700672367546823

103011031110330103441035810395

1241912518126151270112730

1539115432154431547415527

1855718588

192661930719314193591935919418

20656207032073420786

PAGE 1

APPENDIX XII

!D CALC

-950121188198310397442

6607663966776696673067656835

102991030910336103481035910408

1240112535126051270512725

1539 31543915447154761552 9

1855 918588

192711929619318193441935019403

20655206982073620788

TABU! 1ER+3:LAF3

O-C

10101222431

-2-8-64-6

-10-11

22-5-30

-12

18-1610-35

-1-6-3-1-1

-10

-411-315915

15

-1-1

STATE J

4141414141414141

41414141414141

414141414141

4141414141

4F4F4F4F4F

4S4S

2H22H22H22H22H22H2

4F4F4F4F

15/215/215/215/215/215/215/215/2

13/213/213/213/213/213/213/2

11/211/211/211/211/211/2

9/29/29/29/29/2

9/29/29/29/29/2

3/23/2

11/211/211/211/211/211/2

7/27/27/27/2

HJ

13/2-11/2

3/25/21/2

-9/2-7/215/2

-11/2-9/2-7/21/23/25/213/2

-9/2-7/21/23/25/2

-11/2

7/21/23/25/2

-9/2

5/23/2

-7/23/21/2

3/21/2

1/2-9/2-11/2-7/23/25/2

-7/21/25/23/2

7/27/2

9223 9/29223 9/2

7806 0.3035 0.1534 0.01329166 0.0039 0.1255 0.4498

)BSEEVI

223702237422407

22684227 51

2460224680247E42484024862

265302655826583266472664726709

276C627620276312764627671

278 1327820278302790427935• • •• • «

28127

• • •282432825728265

3168831746

• • •3310633119331673320133201• * •

PAGE 2

APPENDIX XII

SD CALC

223642236922399

2268922741

24580247102474824«4024858

265362656726587266502665026713

2761027617276242763927665

2781627823278512789127939279592798828135

28221282402824928252

3171131765

3309433105331423315333203332063331733405

TABLE 1£R+3:LAF3

o-c

659

-410

22-29604

-8-3-2-2-3

-33776

-2-2

-2013-3

• • •• • •

-7

• • •3813

-22-18

• # •3

-2214-1-4* • •• • •

STATE J

4F4F4F

4F4F

4F4F4F4F4F

4G4G4G4G4G4G

4G4G4G4GHG

2K2K2K2K2K2K2K2K

4G4G4G4G

2P2P

2K2K2K2K2K2K2P2K

5/25/25/2

3/23/2

9/29/29/29/29/2

11/211/211/211/211/211/2

9/29/29/29/29/2

15/215/215/215/215/215/215/215/2

7/27/27/27/2

3/23/2

13/213/213/213/213/213/2,1/213/2

MJ

5/21/23/2

3/21/2

-7/21/23/25/23/2

1/2-11/2

3/25/2

-9/2-7/2

-9/2

V23/25/2

-7/2

-9/2-7/2-11/2

5/23/213/21/215/2

5/2-7/23/21/2

3/21/2

-9/2-7/2

-11/25/21/23/21/2

13/2 ol

!••*?. ' "

9/29/2

78067806

15/217/2

2222225890

00

.0

.0

.0

000

. U Ibb

.0077

.0202

u.0.0.

00000000

PAGE 3

APPENDIX XII

TABLE 1EB+3:LAF3

OBSERVED CALC O-C STATE J MJ

261.Ol

ft • ft

• • •

• • •

34157341963422134260

350263505235085

3652236555366243672136805

388043884138834

394 54395393960639634

412384129741315

a • «

4138241497

• • •• • •• • •• • •• • •• • •• • •• m •

• • •

4249542526

4308843126

334823349433613

34167341973422834284

3504 23505335092

3652936537366363672136792

387943884 338844

39487395283960639638

412354130241330 ••413*714139141492

41809418334187441875419004192641980 .42071 .42087

4247142500

4309643121

• • •• • •• • •

-90-6-3

-150

-6

-618

-11013

10-1-9

-32110

-3

3-4-14• • •-95

> • •• • •» • •• •

» • •• •• •• •a •

2426

-75

4G464G

4G4G4G4G

2D12D12D1

2H22H22H22H22H2

4D4D4D

4D4D4D4D

212121212121

2L21212L2L2L2L2L2L

4D4D

4D4D

5/25/25/2

7/27/27/27/2

5/25/25/2

9/29/29/29/29/2

5/25/25/2

7/27/27/27/2

11/211/211/211/211/211/2

17/217/217/217/217/217/217/217/217/2

3/23/2

3/23/2

1/25/23/2

-7/23/2

V25/2

3/25/21/2

-9/25/23/21/2

-7/2

3/25/21/2

1/23/2

-7/25/2

5/23/2

-11/2-7/21/2

-9/2

-7/2-9/21/25/23/2

-11/213/217/215/2

3/21/2

1/23/2

" • > - . • • " ,

11/2 23563 11/2 2356311/2 23563 13/2 3626

0.3577 0.0555 0.01270.0012 0.0299 0.0065

PAGE 4

APPENDIX XII

TABLE 1EH+3:LAF3

OBSERVED CALC O-C STATE J MJ

436874374643746437604383443915

• • •

• • •

• • •

• • •

• • •

• • •

• a •

• • •

• • •

• • •

a • •

• • «

• • •

• a •

492234927249357

• • •• • •

* • «

• • •

* • a

• • •

43709437224372843749438214390943968

47313

4794147989479994801548035480974819348194

4837148374484274848348513

492104928749349

512955135551370514415151051512

-21241811136

• • •

• * •

# • •• • •• • •

• • •

• • •

• • •

• • •

• • •

• * a

* • •

* • •

• • •

• • •

13-14

8

• • •• • •• • a

a • •

• a •

• a a

21212121212121

4D

212L2L2L2L2L2L21

2H12H12H12H12H1

2D22D22D2

2H12H12H12H12H12m

13/213/213/213/213/213/213/2

1/2

15/215/215/215/215/215/215/215/2

9/29/29/29/29/2

5/25/25/2

11/211/211/211/211/211/2

5/21/23/213/2-7/2-9/2-11/2

1/2

-9/2-7/23/21/25/2

-11/215/213/2

5/23/21/2

-9/2-7/2

3/21/25/2

1/23/2

-11/25/2

-9/2-7/2

PAGE 5

APPENDIX XII

TABLE 1AER+3:LAF3 CENTERS OF GRAVITY

CALC CENTER

217671285831034612597

154551933720 715223762271224756

2663127637279222822433319

STATE

4115/24113/24S 3/24111/241 9/2

4F 9/22H11/24F 7/24F 5/24F 3/24F 9/2

4G11/24G 9/22K15/24G 7/22P 1/2

,5 , • 'J' " > -

J1

1/21/2V21/21/21/21/21/21/21/21/2

3/23/23/23/23/23/23/23/23/23/23/23/23/23/23/2

3/23/23/23/23/23/23/23/23/23/23/23/23/2

5/25/25/25/25/25/25/25/2

LEVEL

3331933319333193331933319333193331933319333193331933319

185831858318583185831858318583185831858318583185831858318583185831858318583

22712227122271222712227122271222712227122271222712227122271222712

2237622376223762237622376223762237622376

1 J2

3/23/25/27/27/29/29/29/2

11/211/211/2

3/23/25/27/27/29/29/29/29/211/211/211/213/215/215/2

3/25/27/27/29/29/29/29/2

11/211/211/213/215/2

5/27/27/29/29/29/29/211/2

PAGEAPPENDIX

TABLI! 2U(K)*2 FOB

LEVEL 2

1858322712223762071528224125971545527637103461933726631

1858322712223762071528224125971545524756276371034619337266316712217

27922

22712223762071528224125971545524756276 371034619337266316712217

2237620715282241259715455247562763710346

7XII

ER+3

(U2)*2

00000000000

00000.0,00,0,0,0,0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.

.0057

.0353

.0073

.0

.0

.0

.0

.0

.C

.0

.0

.0371

.0266

.0077

.0000

.0475

.0

.0

.0

.0

.0

.0

.0

.0,0.0

,0709,0b05.0027,0961,0,0,0000000

01520765 '383101010005009216500

(04)*2

00000000000.

000,0.0,0.0,0.0,0,0.0.0,0.0.

0.0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.

.0

.0

.0

.0204

.0263

.0272

.0460

.0083

.0

.0

.0

.0

.0

.0036

.0055

.1631

.0765

.0001

.0036

.1659

.0046

.2002, 1282.0,0.0

,0,0351,0577034223380022,0188171109130004023200

00500498001706292345021908460984

(U6)*2

00000000000

0000.00,0,0.00,0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.

.0

.0

.0

.0

.0

.0

.0

.0

.0316

. 1686

.0264

.0

.0

.0

.0

.0

.2569

.0228

.0014

.0103

.0773

.0097

.0040

.3419,2225,0035

,0,0,00054506160057112448310025090703471255

00998038011293491005600240028

22

2104021040

5 276536 8579

0.00.0

0.12330.1365

0.00120. 1604

i .•Kγmm

J1

5/25/25/25/25/2

7/27/27/27/27/27/27/27/27/27/27/2

7/27/27/27/27/27/27/27/27/27/27/2

9/29/29/29/29/29/29/29/29/29/2

9/29/29/29/29/29/29/29/29/2

LEVEL

2237622376223762237622376

2071520715207152071520715207152071520715207152071520715

2822428224282242822428224282242822428224282242822428224

12597125971259712597125971259712597125971259712597

154551545515455154551545515455154551545515455

0

1 J2

11/211/213/215/215/2

7/27/29/29/29/29/2

11/211/211/213/215/2

7/29/29/29/29/2

11/211/211/213/215/215/2

9/29/29/29/211/211/211/213/215/215/2

9/29/29/211/211/211/213/215/215/2

PAGEAPPENDIX

TABLEi 2(K) *2 FOR

LEVEL 2

19337266316712217

27922

20715282241259715455247562763710346

19337266316712217

28224125971545524756276371034619337266316712217

27922

125971545524756276371034619337266316712217

27922

1545524756276371034619337266316712217

27922

8XII

ER + 3

(02)*2

00000

00000000000

000,0,0,0,0,0,0.0.0.

0.0.0.0.

c.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.

.0

.0

.0

.0

.0

.1542

.1221

.0155

.0119

.0894

.6234

.0032

.1258

.0867

.0

.0

.0033

.1649

.0000

.0152

.0034

.5073

.0006

.0140

.0

.0

.0

.0040

. 1220,0138.00410021.1953,0631,0003,00

136900752170071537904283010900

(04)*2

00000

00000,00,00,00,

0,00.0.0.0,0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.

.0581

.0373

.1794

.0

.0

.0103

.0409

.0935

.0372

.0483

.0067

.2653

.0164

. 1264

.3393

. 1465

.0048

.3703

.0123

.0052

. 1887

.2776

.0393

.0544

.0997

.0200, 1206

.0782

.00610066,00600690,06480122008715872101

075102613167010102360372153355i"'0867

(06) *2

00000

00000,0000,00

0,00.0.0.0,0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.

0.0.0.1.0.0.0.0.0.

. 1847

.0806

.3419

.2221

.0472

. 1001

.0070

.4337

.0109

.0273

. 1194

. 1545

.3984

.0168

.0001

.6272

.0005

.2168

.0163

.0244

.1494

.1616

.2710

.0177,0310

.1171,0048

,7932,0203,0032,0049152028370228710000720969

050704693650267100080112082846210142

I * ' " " .

PAGE '9APPENDIX XII

TABLE 20(K) *2 FOR ER + 3

J1 LEVEI 1 J2 LEVEL 2 (U2) *2 (U4) *2 (U6) *2

9/29/29/29/29/29/29/29/2

9/29/29/29/29/29/29/2

11/211/211/211/211/211/2

11/211/211/211/211/2

11/211/211/211/2

13/213/213/2

15/215/2

15/2

2475624756247562475624756247562475624756

27637276372763727637276372763727637

103461034610346103461034610346

1933719337193371933719337

26631266312663126631

671267126712

217217

279 22

9/29/211/211/211/213/215/215/2

9/211/211/211/213/215/215/2

11/211/211/213/215/215/2

11/211/213/215/215/2

11/213/215/215/2

13/215/215/2

15/215/2

15/2

24756276371034619337266316712217

27922

276371034619337266316712217

27922

1034619337266316712217

27922

19337266316712217

27922

266316712217

27922

6712217

27922

21727922

27922

0.0.0,0.0.0.0.0.

0.0.0.0.1.0.0.

0.0.0.0.0.0.

0.0.0.0.0.

0.0.0.0.

0.0.0.

0.0.

1.

.0165,0251.0381,0285,2951,0590,0,0

0018,0937023700001078,00

078403520002033202760463

00210004023571581010

0049100591560998

172301950001

24630213

8431

0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.

0.0.0.0.0.0.

0.0.0.0.0.

0.0.0.0.

0.0.0.

0.0.

1.

,05460004,07531635.1068,1059,02437139

0153,160134632117367223370056

036413850486170600020017

07261513062141380000

2513264852630579

173111720015

38030039

0174

0.53960.03280. 10470.06100.14140.35310.21470.0822

0.00780.01680. 15700.15160.01060. 13680.0558

0.02770.03720.01331.09150.39420.2426

0. 10680.04980.05020.09271.1445

0.06690.25700. 11670.6787

0.22981.43250.0257

1.86110.0735

0.0676

* . 'i

i - •••:-•<&'

A P P E N D I X X i l l

PAGE 1

APPENDIX XIII

TABLE 1TM+3:LAF3 CEHTERS OF GRAVITY

OBSERVED CALC O-C STATE

20058588336127111455915173

21352

28061

34886

356043655938344

• • •

17558188391

127211459715181

21314

28001

34975

355793661538268

75300

2540

-54-9

-37-7

38

60

-88

25-5576

• • •

3H63F43H53H43F33F2

164

1D2

116

3P03P13P2

1S0

PAGE 3APPENDIX XIII

TABLE 20(K) *2 FOR TM + 3

J1 LEVEL 1 J2 LEVEL 2 (U2) *2 (U4) *2 (06) *2

0000

11

2222222

222222

33333

4444

3562135621356213562135621

3660336603366033660336603

1 366033660336603

15180151801518015180151801518015180

280282802828028280282602828028

1459814598145981459814598

5828582858285828

4 127354 127354 12735

5 83965 8396

2244

12234456

2234456

234456

34456

1518028028582812735

366031518028028145985828127358396153

1518028028145985828127350396153

28028145985828127358396153

145985828127358396153

4 58284 127355 83966 153

4 127355 83966 153

0.36180.02970.00.0

153 0.0

56

8396153

0.16070.13740.45210.57140.00.00.00.0

0.14250.06420.00360.30260.29690.00.0

0.19310.16380.56890.12570.00.0

0.06250.00250.08170.62850.0

0.01040.12750.09090.5395

0.26720.0-.310.2357

0.91920.1074

0.00.00.27960.02350.0

0.00.00.00.19640.10990.40290.28570.0

0.04430.30730.07450.05620.17110.29070.0000

0.00510.06980.09610.01240.00120.3131

0.00300.00050.35220.34670.3164

0.40590. 13110.12990.7261

0.16500.47620.1081

0.36680.2314

0.00.00.00.00.0756

0.00.00.00.00.00.00.08920.1239

0.00.00.00.04400.07630.58440.2550

0.00.00.02150.23000.01820.0958

0.06250.16880.28440.00.8413

0.26510.21130.92640.24 21

0.57040.00950.5916

0. 12140.6385

153 153 1.2517 0.6916 0.7759

APPENDIX XIV

-1-

APPENDIX XIV - TABLE 1

Calculated Values of fix for Ln :LaF3

Pr3+

Nd

Pm

Sm

Eu

Gd

Tb

Dy

Ho

Er

Tm

JJ2xl0"20cm2

0.12

0.35

0.5

1.0

1.19

1.1

1.1

1.1

1.16

1.07

0.52

fl4xl0"20cm2

1.77

2.57

1.9

0.5

1.16

1.2

1.4

1.4

1.38

0.28

0.59

fi6xl0"20cm2

4.78

2.50

2.2

1.5

0.39

0.5

0.9

0.9

0.88

0.63

0.22

Reference

a

a

b

b

c

b

b

b,d

e

f

b.g.h

aKrupke (1966)

bApproximate values from present work

cWeber (1967a)

dKrupke (1974)

eWeber et al. (1972)

fWeber (1967b)

9Weber (1967c)

hPappalardo (1976)

-2-

APPEMDIX XIV - TABLE 23+Observed and calculated radiative life-times for Ln :LaF,

Pr

Nd

Pm

Sm

Eu

Tb

Dy

Ho

Er

Tm

ExcitedState

\

\

F3/25F14 rG5/2

\

\

\5°3\F9/2

%5FP3/2

4S*3/2

\

\

ysec

902

73

635

566

2160

9200

7700

6900

809

1450

896

826

779

430

1020

137

1560

TObserved(usec)

520

47

670

-

-

5400

4700

6700

-

-

-

-

290

1000

54

960

Reference

a

b

c

c

d

c

c

e

f

a,g

a,g

aWeber (1967c), (1968)bRiseberg and Weber (1976), Weber (1967c)

cPresent WorkdWeber (1967a), measured at 77CKeWeber et al. (1972)fWeber (1967b)

^Compare recent calculations by Pappalardo (1976)

-3-

A PENDIX XIV - TABLE 3

Partial lifetimes a Branching Ratios in the3+

Relaxation of Excited States in Tb :

Transition Partial Electric- Partial Magnetic- &RPi pole Lifetime (msec) Pi pole Lifetime (msec)

5D3-*-5D. 125.4 3.413 0.24

fn m 0

0.009

5.606 0.16

109.3 0.015

1.590 0.54

0.027

7F27F3

\

\

\

V'.7F,7F2

%

\

\

\

91.01

51.93

108.4

28.61

30.32

87.15

( DQ) TD - 0«809 msec.

425.6

275.9

466.4

208.3

144.1

27.52

114.0

(5D4) T R = 1.45 msec.

0.003

0.005

0.003

15.28 0.10

505.1 0.013

1.800 0.86

0.013

aThe intensity parameters used in the calculations are given in Appendix XIV -Table 1. The matrix elements of IT ' appear in Appendix IX.