LA-6257

c?●CIC-74 REPORT COLLECTION

I?EPROI)UCTIONCOPY

UC-34C

Reporting Date: February 1976Issued: August 1976

Double-Differential Beryllium Neutron Cross Sections

at II cident Neutron Energies of 5.9, 10.1, and 14.2 MeV

by

Darrell M. Drake

George F. Auchampaugh

Edward D. ArthurCharles E. Ragan

Phillip G. Young

scientific laboratory1 of the University of California

LOS ALAMOS, NEW MEXICO 87545

4 /\An Affirmative Action/Equal Opportunity Employer

UNITED STATESENERGY RESEARCH AND DEVELOPMENT ADMINISTRATION

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DOUBLE-DIFFERENTIAL BERYLLIUM NEUTRON CROSS SECTIONS

AT INCIDENT NEUTRON ENERGIES OF 6.9, 10.1, AND 14.2MeV

Darrell M.

by

Drake, George F. Auchampaugh, Edward D. Arthur,Charles E. Ragan, and Pbillip G. Young

ABSTRACI’

We measured beryllium neutron-production cross sections using the time-of-flight technique at incident neutron energies of 5.9, 10.1, and 14.2MeV,—--—

>~, /-’_ and at laboratory angles of 25°, 27.5°, 30°, 35°, 45°,60°, 80”, 100°, 110°, 125°,

and 146°. The differential elastic and Inelastic cross sections are presented.‘= ~o-

:= ~Inelastic is defined here as those reactions that proceed through the states at

~~~ ‘“ 1.69-, 2.43-, 2.8-, and 3.06-MeV excitation energy in ‘Be. Comparison of ourz!~ emission energy spectra with calculations using the ENDF/B-IV beryllium$E$je= op— cross sections shows that the ENDF/B cross sections strongly-- —1z-

s= g ov6reniphasize the low-lying states in ‘Be.

~eg—,~m.=

.—— ——_— ___ .— ____ ____-—

L INTRODUCTION

Beryllium has been proposed as a major con-stituent of controlled fusion reactors because of itaunique characteristic of emitting two neutrons foreach inelastic neutron interaction. These neutronscan be used to produce tritium, one of the major fuelcomponents of the reactor, Calculating the tritiumbreeding rate in proposed reactor vessel walls re-quires detailed knowledge of the energies andangular distributions of the neutrons emitted fromberyllium under bombardment by energeticneutrons. Almost no such information is availablefor beryllium, especially for the (n,2n) reaction.Therefore, we measured the energies and angulardistributions of the neutron emission spectra fromberyllium at incident neutron energies of 5.9, 10,1,and 14.2 MeV.

II. EXPERIMENTAL DETAILS

A. Neutron Sources, General

To measure differential continuum cross sections,such as that for the beryllium (n,2n) reaction, withmonoenergetic neutrons, it is desirable to choose aneutron source with a high yield of monoenergeticneutrons compared with background neutrons andwith a background spectrum that can be measured.For gas targets the neutron background is producedprimarily by charged particle reactions in theentrance foil and beam stop materials, and to a les-ser extent by three-body breakup reactions in thegas. The background associated with the entrancefoil and the beam stop materials can in principle bemeasured by removing the gas from the target celland by measuring the resultant neutron flux.

J

However, neutrons produced in three-body breakupand subsequently scattered from the sample cannotbe distinguished from those that are emitted by thescattering sample in reactions with the primaryneutron beam. Therefore, source reactions that donot produce breakup neutrons in the incidentneutron energy region of interest, are strongly prefer-red.

Several charged particle reactions are commonlyused at the Los Alamos Scientific Laboratory(LASL) Van de Graaff accelerators to produce near-ly monoenergetic neutron beams in the energy rangestudied. These are 2H(d,n)3He, 3H(p,n)3He,1H(t,n)3 He, 2H(t,n)4He, and 3H(d,n)4He. The

2H(d,n)3He and 3H(p,n)3He,first two reactions,have three-body breakup thresholds at 4.45- and8.34-MeV incident particle energy, which corres-pond to primary neutron energies of 7.70 and 7.57MeV, respectively. In addition, the breakupbackground from the 2H(d,n)3He reaction is muchgreaterthan that from the 3H(p,n)3He reaction. The1H(t,n)3He reaction, because of the large center-of-mass energy, produces no breakup neutrons in theenergy range of concern in this report, Furthermore,the primary neutron yield at O“ can be as much as 40

3H(p,n)3He reaction fortimes that of thecomparable resolution and incident beam current.Thus, in this experiment, being able to acceleratetritons and protons is a significant advantage. (Formore details about monoenergetic neutron sourcereactions, associated backgrounds, and the influenceof entmnce foil and beam stop materials, see Ref. 1.)We also took data Usingthe 3H(p,n)3He reaction toconfirm our 1H(t,n) 3He reaction data. The choice ofwhether to use the 3H(d,n)4He or the inversereaction to produce 14-MeV neutrons was based onexperimental considerations and will be discussed inmore detail in Sec. ILC.

B. 6- and 10-MeV Neutron Sources

The tandem Van de Graaff was used to produce5.9- and 10.1-MeV neutrons with the 1H(t,n)3Heand 3H(p,n)3He reactions, The charged particlebeam was bunched to a 1,5-ns pulse width by aklystron bunching system with a 1.25-MHz fre-quency.

The entrance foils to the target cell were either 5-or 10- mg/cm2 molybdenum. The cell was filled toapproximately 2.72 atm (40 psia) with either

2

hydrogen or tritium gas. For both source reactions agold beam stop was used. The calculated neutronenergy spread from straggling of the tritons in thegas and from kinematic broadening was + 120 keVfor 6-MeV neutrons and + 90 keV for 10-MeVneutrons. The energy spread for protons was sub-stantially less.

The scattering samples were placed about 164mmin front of the target cell at 0° to the charged particlebeam direction. The distance from the neutrondetector to the center of the sample was 2.70 m. Thescattering angle was changed by rotating theneutron detector about the center of the sample.

C. 14.2-MeV Neutron Source

Monoenergetic 14-MeV neutrons can be producedby the 2H(t,n)4He or the inverse, 3H(d,n)4He,reaction. We chose the 2H(t,n)4He reaction becausethere is somewhat less energy spread in the 80°neutron flux and because a cell filled with deuteriumis less hazardous than one filled with tntium. Thetriton beam was chopped in the terminal of the ver-tical Van de Graaff accelerator to a pulse width of 10ns at a frequency of 2 MHz and, after being ac-celerated to 2.5 MeV, was compressed to a pulsewidth of 1 ns by a Mobley buncher.2 The beampassed through a 10-mg/cm2 molybdenum foil andwas stopped by the deuterium gas in the target cell,

The samples were placed in the plane perpen-dicular to the beam, where the average neutronenergy was 14.2 MeV and the average kinematicenergy spread was about A 300 keV. The samplesand detector were located about 150 mm above thehorizontal beam plane. (See Fig. 1, Ref. 3.) The scat-tering angle was changed by rotating the sampleabout the beam axis. The detector was movedforward or backward as the angles were changed tokeep the flight path constant at 2.77 m,

D. Samples

The beryllium, carbon, and polyethylene scatter-ing samples were machined into right circularcylinders, 32-mm long by 32-mm o.d., with insidediameters of 0.5, 19.3, and 28.8 mm. The cylindricalaxis was oriented perpendicular to the charged perti-cle beam for the 5.9- and 10.1-MeV measurements

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and parallel to the beam for the 14,2-MeV measure-ments.

E. Neutron Detector

The neutron detector consisted of a 100-mm-diamby approximately 76-mm-thick Ne-213 liquid scin-tillator directly coupled to an RCA-8864phot.amultiplier.4 We noticed an improvement inthe discrimination against gamma rays byeliminating the usual W-Lucite coupling plate andplacing the NE-213 scintillator in direct contactwith the photomultiplier tube. The detector wasplaced in a large container made of copper,polyethylene, berated polyethylene, and lead andwas shielded horn the direct neutron source by abrass or tungsten shadow bar.

We set the detector bias near the pulse-heightminimum between the 26- and 59-keV 241Amgamma rays, which corresponds to a neutron energyof about 300 keV. The 241Amsource was mounted ina lead container near the side of the detector andcould be remotely positioned, thereby allowing us tocheck the bias periodically.

A standard pulse-shape discrimination (PSD) cir-cuit based upon the zero-crossover technique ofAlexander end Goulding6 was used to distinguishbetween neutron and gamma-ray pulses. This circuithad a pulse-height dynamic range of about 250:1,which permitted the entire secondary neutronenergy range from 0.3 MeV to 16.7 MeV to becovered with one bias setting,

A plutonium-beryllium neutron source wasperiodically placed at a standard position near theneutron detector to check the stability of the PSDcircuit. The drift in the PSD bias was negligible.

F. Electronics

The time-of-flight information was digitized intol/8-ns time channels by an EG&G No. TDC-1OOtime digitizer. The digitizer was started by a pulsefrom a constant fraction discriminator that was fedby the anode pulse from the photomultiplier. Thestop pulse originated from a beam sensor near thetarget. The data were stored in an XDS-930 com-puter in l/2-ns time bins and transferredto magnetictape for analysis on a CDC-7600 computer.

III. DATA REDUCTION

A. General

The number of neutrons detected with an ef-ficiency c(E’) per MeV that are scattxmedfrom asample of beryllium into a solid angle !2 is given by

A(E’)=C(E’)-B(E’)= $(E) M~(E; E’ ,Q)nfk(E’) *,

(1)

where @(E) is the number of neutrons of energy E in-cident on the sample, n is the areal atom density ofthe sample, M, is the correction for multiplescattering of neutrons of energy E into neutrons ofenergy E“’ and solid angle Q, B(E’) is the neutronbackground detected at the time corresponding to aneutron of energy E’, and C(E’) is the total numberof neutrons detected. A similar expression can bewritten for a hydrogen sample with the same dimen-sions

(kJv(E)IAH(E) . t)(E) tf~(Ii; E, Sl)n% ~ E(E) , (2)

where the sum extends over all channels that definethe area of the hydrogen elastic peak. Solving foro(E) in Eq. (2) and substituting it into Eq.(1)results in the following expression for the double-differential cross section

*= ~(~) J~@’) - ~@’)LErel(E’)~~(E;~’,O)

The differential cross section is

(3)

obtained by in-tegrating Eq. (3) over the emission neutron energyE’. Because we are taking a ratio of two measure-ments, both using the same detector, only therelative efficiency of the detector is required fordetermining the cross section.

Polyethylene samples were used to obtain thehydrogen data. At small angles and high incidentneutron energies the hydrogen elastic peak was notcompletely resolved from the carbon elastic and in-elastic peaks. Therefore, data were taken with acarbon sample and used to correct the area of thehydrogen elastic peak. Many sets of polyethylene-carbon data were taken at each incident energy andfor various angles to determine the constant K(E).

3

B. Relative Neutron Efficiency

The relative neutron efficiency of our detector wasmeasured from 0.3 to 20 MeV using neutrons fromthe reactions 2H(d,n)3He, 3H(p,n)3He, 3H(d,n)4He,and by elastically scattering neutrons fromhydrogen. An efficiency plot is shown in Fig. 1. Thevarious reactions used in each energy range are alsoindicated. The evaluations of Liskien and Paulsen6were used for the charged particle cross sections, andthe hydrogen differential cross section’ was takenfrom the ENDF/B-IV cross-section library. The peakat approximately 15 MeV in the efficiency curve iscaused by the 12C(n,n’3a) reaction in the carbon ofthe scintillatnr and is visible only as a consequenceof the low bias on our detector,

C. Multiple Scattering Correction

Multiple scattering corrections were calculatedwith the LASL Monte Carlo code MCN.6 Thegeometry used in the calculations was an unshieldeddetector without a shadow bar and an isotropicmono energetic neutron source. The scatteredneutrons were tallied by energy and angle accordingto the type of reaction that created them: elastic, in-elastic, elastic-elastic, elastic-inelastic, inelastic-inelastic, and the sum of all five processes. Thecalculations using MCN with various fictitious sam-

iO.I-IL 1 , 1 , 1 , , , , ,

10 0.0NEUTRONENERGY(MoV)

Fig. 1.ReZutive efficiency of the neutron detector vsenergy. Reactions used to obtain this curvewere 3H(p,n)3He (V), lH(n,n)lH (8 ),3H(d, n)4He (e), and 2H(d, n)3He (A). The

l!?increase in e “ciency at approximately 16 MeVis from the C(n, n’,3a) reaction in the carbonof the liquid scintillator.

ple densitie8 showed that spectra computed with asample of 0.01 or less of normal density were notmeasurably distorted by the multiple neutron scat-tering processes. Therefore, to get M, we ran MCNwith a normal density sample and then repeated thecalculation with a sample of one-hundredth normaldensity. The multiple scattering correction was ob-tained by taking a ratio of these two Bpectrafor eachangle multiplied by the atom density ratio for thetwo samples, Tables of M, were generated forincident neutrons of energies5.9, 10.1, and 14.2MeVand for up to 20 values of emergent neutron energies.These tables were linearly interpolated to obtain thevalues of Maused in computing the cross sections.

D. Background Sources

For the 5.9- and 10.1-MeV measurements the foursources of neutron background that need to be con-sidered, particularly in the continuum region, are (1)breakup neutrons in the gas, which can be ignoredfor the lH(t,n)3He reaction, (2) neutrons from thecharged particle reactions in the foil and beam stop,(3) neutrons that scatter off the shadow bar into thesample and then rescatter into the detector, and (4)neutrons that scatter from the shield surroundingthe detector. By taking the following four spectra ateach incident energy and angle, most of the sourcesof background can be removed from the data. Theseare spectra with either hydrogen or tritium in thecell and the sample (a) in and (b) out, and spectrawith either the hydrogen gas removed or the tritiumgas replaced with helium gas and the sample (c) inor (d) out. Atypical set of these four spectra for 10.1-MeV incident neutrons from the 1H(t,n)3Hereaction at a 60° laboratory scattering angle is shownin Fig. 2. The spectra are combined by subtracting(b) from (a) and (d) from (c), and then subtractingthe resulting two spectra, The final spectrum,however, still contains a background from neutronsthat scatter off the shadow bar into the sample andthen rescatter into the detector. Monte Carlocalculations show that the effect of the shadow baron the spectrum is negligible.

For the 3H(p,n)3He reaction, the spectrum has anadditional background from the tritium breakupprocess, which is present only in the continuumregion, The yield from the 3H(p,n)3He reaction isalso lower, giving poorer statistic on this data.

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4

I 1 Ir En=lO.lMU 8L=60”! r I

Fig. 2.

Time-of-flight spectra for 10.l-MeV incidentneutrons on beqyllium for a laboratory scatter-ing angle of 60°. The source reaction islH(t n)3He and the four spectra are: samplein - ~as in (o), sample in - gas out (A), sampleout - gas in (4), and sample out - gas out (m ).

Therefore, only the elastic cross sections were deter-mined from the data obtained using the 3H(p,n)3 Hereaction. The values were in good agreement withthose obtained from the inverse reaction.

For the 14-MeV measurements, relatively fewneutrons were produced by the low-energy tritons inthe entrance foil, and the main source of neutronbackground was caused by less than ideal shieldingof the detector from the direct 14-MeV neutrons. Forthis reason, only sample-in and sample-out datawere taken at each angle for these measurements.

E. Data Code

A FORTRAN code was written to reduce the rawspectra to cross sections using Eq. (3). This code per-formed a channel by channel subtraction of the ap-propriate background spectra as outlined above,computed the relativistic energy and the relative ef-ficiency for each channel, corrected for multiplescattering, and tabulated the cross section withstatistical error (in mb/MeV. sr) in both thelaboratory and the center-of-mass systems.

IV. RESULTS

The double-differential cross sections for 5.9-,10.1-, and 14,2-MeV incident neutron energies areshown in Fig. 3. These cross sections are given in the

laboratory system. The errors represent thestatistical uncertainty of each data point. Theenergies of the low-lying levels in ‘Be are indicatedwith arrows, The fist maximum below the elasticpeak probably includes a contribution from the 1.68-MeV state in ‘Be. However, our energy resolution,except for the measurement at 5.9 MeV, is not suf-ficient to separate this contribution from that ofother states nearby. For 6.9-MeV neutrons we see nobranching to the 1.68-MeV state. The broadening atthe base of the elastic peak for 6.9-MeV neutrons atan angle of 126° is due to improper bunching of thecharged particle beam,

The differential elastic and inelastic cross sectionscorresponding to the 1.69-, 2.43-, 2,8-, and 3,06-MeVstates in ‘Be (hereafter referred to collectively as the“2.43-MeV” state) for 6.9-, 10,1-, and 14.2-MeV inci-dent neutrons are given in Table L These cross sec-tions were obtained by integrating the appropriatepeaks in the energy distribution curves in Fig. 3, Theerrors given in Table I on each cross section repre-sent a quadrature of the statistical and systematicerrors. The systematic errors used at the threeenergies for the elastic cross sections were 13T0,13T0,and llYo, respectively, These included uncertaintiesin the normalization constant (K), efficiency, multi-ple scattering, and, for the inelastic cross sections,an uncertainty in the definition of the peak area.

The cross sections for neutrona emitted to statesabove the “2.43-MeV” state, referred to as double-differential continuum cross sections, are given inTables II-IV. For these cross sections the systematicuncertainty varied with energy and angle butaveraged about 11?40.

The cross sections presented in Tables I-IV areneutron production cross sections and thereforeshould be divided by the number of neutrons emit-ted in the reaction. For the elastic reaction thisnumber is one, and for the inelastic reaction it isusually considered two because no gamma-ray emis-sion from the excited states in ‘Be has been observedeven at 14 MeV.9 Inelastic scattering leaves the ‘Benucleus in a state which preferentially decays byneutron emission.

The angle-integrated cross sections are given inTable V. These elastic and inelastic cross sectionswere obtained by using Wick’s1° inec@itY[ u(O”) > (kd4r)2, where k is the center-of-masswave number and c7Tis the total cross section ] toextrapolate the elastic distribution to 0° and by us-ing reasonable extrapolations to 0° and 180° for the

5

K?

, ,11, Illl,mOL960”

lo~

E,~5.9 MeV > c IOz

(a) 101 Lot t , 1.1 , ,f?,!ul L-u.lJ-

10.0 10. .NEUTRON ENERGY (MeV)

U.1m

Fig. 3.Double-differential cross sections for (a) 5,9-MeV, (b) 10. l-MeV, and (c) 14.2-MeV incidentneutrorw on beqyllium. The cross sectiorw aregiven in the laboratory eystem. The arrows in-dicate the positione of the low-lying states in‘Be which may contribute to the observedma;ima in the cross sections at the indicatedenergies. In Fig. 3(a) the low-energy shoulderon the elostic peak at e L = 125° h due to poorbunching of the churged particle beam.

10 no 1.0 10.0

NEUTRON ENERGY (MeV)

10 10.0

I

I

I

1

10 Iclo

.

.

NEUTRON ENERGY (MeV) “-”-

6

AEn(MeV)

0.4- 0.50.5 -0.60.6 -0.70.7 -0.80.8- 0.90.9- 1.01.0-1.25

1.25 -1.51.5-1.75

1.75 -2.0

(?L

25°27.5°

30°35°45”60°80°

100°110°125”145°

TABLE I

BERYLLIUM DIFFERENTIAL NEUTRON CROSS SECTIONS

5.9 MeVInelastic

(“2.43 -MeV”Elastic state)(mbfsr) (mblsr)

443 * 57 80+13

320*42 65*11

180 *23 57 * 1075 * 10 42i7

23 * 3.1 32*526 ~ 3.4 28 f 4.8

32 *4.o 30*50231 *4.O 28 ~ 4.7

10.1 MeVInelastic

(“2.43-MeV”Elastic state)(mblsr) (mb/sr)

480 *62 68* 14

285 * 37 49 * 10

151*2O 43*9

40*5 35*7

15 *2.O 26 + 5.2

24i 3.1 22 * 4.4

15 *2.O 26 * 5.2

14.2 MeVInelastic

(“2.43 -MeV”Elastic state)(mblsr) (mb/sr)

388 *43335 * 37234*26

119*1331.1 * 3.4 18.4 * 5.511.5 * 1.3 14.2 * 4.623.0 * 2.5 13.8 *4.1

9.5 * 1.1 9.9 * 3.0

TABLE 11

BERYLLIUM DOUBLE-DIFFERENTIAL CONTINUUM CROSS SE(XIONS FOR En = 5.9 McV(mb/sr/MeV)

e=

25°

108 * 1693 * 1483*12

69?9-53*7

43*5

39*536*432*4

29.5 * 3.5

35°

103 * 1588? 1372 * 1067*956*7

44?535*431*4272324* 2.9

45°

99* 15

82 k 1269 i 10fj4*8

50*740*533~4

25.6 * 3.123 * 2.722 i 2.6

60°

82+ 12

69* 1049*743*636*4

36*426* 3.1

21 *2.518*2.117*2.O

80°

70* 1153*833*4

30?427*327 * 3.2

18.7 * 2.215 ~ 1.815 + 1.8

100°

45*737*622 ~ 2.8

19.2 * 2.519.0 * 2.515.5 * 1.912.3 f 1.5

11 * 1.3

110°

42*638*619* 3.0

17* 2.216* 2.114 f 1.8

11 *1.412* 1.4

125°

34?529? 4.318* 2.317* 2.219* 2.5

14* 1.711 *1.310* 1.2

inelastic distributions. The n,2n cross sections are V. DISCUSSIONcomputed aesuming that all inelastic processes emittwo neutrons. The n,a and the n,t cross sectionOaretaken from the ENDF/B-IV beryllium cross-sectionlibrary.11

A. Self-Consistency Checks

The cross sections were checked for self-consistency in the following ways. The multiple scat-tering correction were checked by taking data with

7

TABLE 111

BERYLLIUM DOUBLE-DIFFERENTIAL CONTINUUM CROSS SECTIONS FOR Em= 10.1 McV..(mb/srfMeV)

AIZn(MeV)

0.4- 0.50.5 -0.60.6- 0.70.7- 0.80.8- 0.9

0.9- 1.01.0-1.25

1.25 -1.51.5-1.75

1.75 -2.02.0- 2.52.5 -3.0

3.0- 4.04.0- 5.0

5.0- 6.0

AEn(MeV)

0.4- 0.50.5-0.60.6- 0.70.7- 0.80.8- 0.90.9- 1.01.0-1.25

1.2s-1.501.50- 1.7s1.75-2.02.0- 2s2.5-3.03.0- 4.04.0- 5.05.0- 6.06.0- 7.07.0- 8.08.0- 9.0

t7L

25”

61* 1263 * 9.5

63 * 6.961* 7957* 6.8

51 * 6.142* 4.632* 3.526* 2.922* 2.422 * 2.425 * 2.720* 2.213* 1.4

11 * 1.2

35°

63 * 1268* 10&j* 8.6

61 * 7.951 *6.1

42* 5.033 * 3.6

27* 3.024 k 2.6

21*2.318 * 2.019*2.1

14.4 * 1.69.1 * 1.0

45° 60° J30° 100° 125°

55* 1058* 8.754* 7.050* 6.544* 5.337* 4.429* 3.2

25 * 2.722* 2.417* 1.915 * 1.7

11* 1.27.3 k 0.85.5 i 0.6

47*7.548* 7.248* 6.244& 5.7

39* 4.3

34* 3.7

27* 3.0

21 *2.318* 2.016*108

14* 1.512* 1.3

7.5 i 0.8

5.6 * 0.6

36* 5.834* 5.129* 4.6

26* 3.423 *2.8

21 * 2.318* 2.016* 1.814* 1.512* 1.3

9.5 * 1.06.8 * 0.74.5 * 0.5

24* 4.627* 5.7

28* 5.328* 3.625 * 3.2

20* 2.217* 2.413 *1.411 *1.2

8.9 * 1.0

6.2 * 0.74.4 * 0.53.3 * 0.4

TABLEIV

BERYLLIUM LX3UBLE-DIFFERENTIALCONTINUUMCROSSSECHONSFOR Em= 14.2MeV(ntb/sr/MeV)

23~&524& 5.023 k 3.7

22* 4.020*3.O19* 2.315 * 1.713* 1.410* 1.1

8.0 * 0.95.3 * 0.63.7 * 0.42.2 * 0.316*2

27.5°

35* 1059*958i851*644*542*537*430* 3.323* 2.520* 2.219* 1.318* 2.015* 1.7

11.3* 1.29.7 * 1.1

10.7* 1.210.7* 1.210.7* 1.2

35°

55*953*848*645*542*539*432*426* 2.920* 2.220* 2.2

18.5* 2.214.5* 1.711.0* 1.3

80*1.o8.1* 1.09.2* 1.19.oi 1.18.0i 1.0

45°

44*846*745*644*540*S36*429* 3.225* 2.820* 2.218* 2.0

16.5* 1.813.5* 1.510.2* 1.17.4k 0.87.8i 0.98.7* 0.68.0* 0.9

60°

44*746*639*537* 4.431* 3.730* 3.324* 2.621* 2.317* 1.914* 1.513* 1.4

10.5t .1.28.0* 0.95.6i 0.66.3 * 0.77.0i 0.85.2* 0.6

80°

29* 4.4

33 *4.3

32 t 4.529* 3.8

27* 3.5

24 t 2.6

18.5 * 1.915.5 * 1.613.0* 1.311.5 * 1.29.0t 1.07.0i 0.84.8* 0.54.6* 0.56.4* 0.76.4* 0.74.5* 0.5

100°

23 f 3.522* 3.121* 2.320* 2.420t 2.418i 2.0

14.5* 1.5)3.5 * 1.410.0* 1.18.3i 0.96.3k 0.75.0* 0.64.1* 0.44.6* 0.54.3 * 0.s4.2i 0.52.9+ 0.3

125°

17.5* 3.320.0* 3.219.5&2.716.5i 2.316.0* 2.115.5* 1.913.5* 1.512.0* 1.38.5* 0.96.4* 0.85,2f 0.64.2* 0.53.9* 0.43.7* 0.42.6 * 0.32.2* 0.3

145°

23 i 3.922* 3.719i2.818* 2.517* 2.216f 2.113* 1.411* 1.2

8.7* 1.07.5* 0.95.6* 0.64.0* 0.s4.4* 0.s4.1* 0.52.0 * 0.2

?

.

8

●

✎

Incident

NeutronEnergy

(MeV)

5.910.114.2

TABLE V

BERYLLIUM ANGLE-INTEGRATED NEUTRC)N CROSS SECTIONS

~lnel(n,n’)

Oel(n,n)(2.43-MeV @lnel(n,n’ )

state) (continuum) 0(n,2n) o(n,ct)a o(n,t) O(total)(rob) (rob) (rob) (rob) (rob) (rob) (rob)

1146 * 149 470 *80 654 *94 562 * 62 50 0 1758* 1611021 * 133 341 *68 764*115 552?67 20 0 1593 * 149

995 * 109 199 ? 64 967 * 145 583&80 10 18 1606 i_ 135

aENDF/B-IV. * 1

samples of different inner radii. The elastic and in-elastic cross sections obtained agreed to within 3%and the continuum cross sections to within 10%. Theelastic cross sections obtained with the lH(t,n)3Heand 3H(p,n)3He reactions at 5.9 and 10.1 MeVagreed to better than 4%. The statistics on the con-tinuum 3H(p,n)3He data were very poor, andtherefore no meaniful comparison could be madewith the 1H(t,n)3He data.

Instead of normalizing the elastic data to the n,pcross section using the neutrons scattered frompolyethylene, the detector was rotated to 0° tomeasure the relative neutron flux directly. This al-lowed the elastic cross section at forward angles to becalculated without relying on the scattering hornpolyethylene or on the relative efficiency shape.Comparison of the cross sections computed this waywith the cross sections computed by using the n,pcross section showed agreement to 3%.

B. Data Comparison

In Fig. 4 the present differential elastic cross sec-tions (circles) for 5.9-, 10.1-, and 14.2-MeV incidentneutron energies are compared with the ENDF/B-IVberyllium cross sections (triangles).11 They areplotted as a function of the cosine of the laboratoryscattering angle. The total errorsare plotted for eachdata point. The data agree with the evaluated crosssections within the experimental errors.

Our angle-integrated cross sections are comparedin Table VI with the ENDF/B-IV cross sections andwith a recent measurement of the n,2n cross sectionsby Veeser.12The agreement among the three sets of

n,2n cross sections is good considering that all n,2ncross sections were measured by the integral techni-que, which counts both neutrons in a large liquidscintillator tank, whereas we measured the energy-angular distributions separately and integratedthem to obtain our n,2n cross sections.

The paucity of neutron energy distribution dataon beryllium at the incident energiesand angles con-sidered in this report, except perhaps at approx-imately 14 MeV, makes it difficult to make extensivecomparisons. At 14 MeV there are two sete ofdata—that of Prud’homme et al.13 who measuredenergy-angular distributions for 14.7-MeV incidentneutrons from 0.5 to 7 MeV at scattering angles of45° and 90°, and that of Hermsdorf et al.14 whocovered the secondary neutron energy range from 2to 14MeV at angles of 52.9°, 77.7°,89.8°, and 131.1°for 14.6-MeV neutrons, If we ignore the slight dif-ferences in the incident neutron energies betweenour data and these two sets of data and linearly in-terpolate angle in our data tables, we can then makea comparison. This comparison is shown in Fig. 5 forPmd’homme’s 45° and 90° data (dashed line),Hermsdorf’s 89.8° and 131.1° data (dash-dot line),and our data (solid line). Our data are higher atforward angles and lower than Hermsdorf’s data atback angles, However, all three sets are in goodagreement at 90°,

For 5.9 and 10.1 MeV there are essentially no con-tinuum energy distribution data. Because most fu-sion reactor calculations use the ENDF/B-IV librarycross sections, we thought it instructive to generateenergy distributions from these files at 5.9, 10.1, and14.2 MeV. The ENDF/B-IV distributions arecalculated from models for the emission of the first

9

En=5.9 MoV

lo~ 1 I I 1 1 1 1 1 I

1.0 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6

(a) Cos(eL)

(b) Cos (q

I I I I I I I I IA 4

10E

#En● 14.2 MeV

.,~-0.6

F I i I 1 I I I 1 f-l

(c)I.O 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.6

202 q

Fig. 4.Comparison of the present differential ekstic cross section (.) and the ENDFIB IV differen-tial elastic cross section (A) for (a) 5.9-MeV, (b) 10. l-MeV, and (c) 14.2-MeV incidentneutrons on beryUium. The Zaborato~ cross sections are plotted as a function of the cosine ofthe laborato~ scattering angle, The total errors are platted, See text for more detaila on theerrors,

.

P

.

.

10

COMPARISON OF

TABLE VI

BERYLLIUM NEUTRON CROSS SECTIONS

Incident

Neutron

Energy

(MeV)

Oel(n,n) o(n,2n) O(total)

present ENDF/B-IVa present ENDF/B-IVa Veeserb present ENDF/B-IVa

(rob) (rob) - (rob)

1146 * 149 1180 562 ? 621021 * 133 1070 552?67

995 * 109 925 583?80

(rob) (rob) (rob) (rob)

560 576*41 1758 * 161 1817555 1593 * 161 1660

510 482 * 39 1606* 135 1478

5.910.114.2

(14.7 MeV)

‘Reference 11.preference 12.

L____________________ 4

OL=1319

-1 .- —.= ------ 1

lo~7

NEUTRON EN:RGV (M:V)

Fig. 5.Comparison of betyllium double-differentialcross sections for approximately 14-MeVneutrons at Zuboratory angles of 45°, 90°, and1310: our data (14,2 MeV) solid line,

13 (14.7 MeV) dashed line,Prud’homme et al.4 (14.6 MeV) dash-dotand Hermsdorf et al.

line.

and second neutrons, assuming that the inelasticreaction emits two neutrons. The energy resolutionof our experiment was folded into the8e spectra,Three spectra are compared with our data atlaboratory angles of 80° (5.9 MeV), 45” (10,1 MeV),and 125° (14.2 MeV) in Fig. 6. The ENDF/B-IV dataare represented by the short and long dash lines andour data by the solid lines. The calculations made atother angles show the same characteristic-that thelow-lying states in 9Be are overemphasized in theENDF/B-IV cross-section library.

At the other extreme is a purely statistical phasespace calculation that completely ignores the ex-cited states of a nucleus. Such a phase space calcula-tion is sometimes useful in predicting the energy dis-tribution of the particles from a three- or more-bodyfinal state configuration. We calculated the relativeneutron energy distribution for the three-body finalstate configuration consisting of two neutrons andthe 8Be nucleus for our incident neutron energiesand angles. Some of these results are plotted in Fig.6 (dashed lines). An arbitrary normalization factorhas been applied to these curves for ease of com-parison with our data. Clearly the phase spacecalculation oversimplifies the neutron productionmechanism in beryllium by failing to account for themaxima in the cross sections that correspond totransitions to states in ‘Be.

The ENDF/B-IV results and phase space calcula-tions show the difficulties inherent in calculatingemitted spectra from models and emphasize the

11

1!

(b)

t

t &=lO.l MeV 8L=45”

102

10

I

al 10 !0.0NEUTRON ENERGY (MoV)

lt?~ I 1 I I I 1 Ill I I I 1 1 1 111 JI

Fig. 6.Comparison of be@um double-differential crom sections for a lubomto~ angk of (a) 60°,(b) 45°, and (c) 125° and an incident neutron energy of (a) 6.9, (b)10.1, and (c) 14.2MeV. Ourdata are plotted as a solid line, the ENDFIB data aa a short and long dazh line, and the un-normalized four-body phase space calculation CMa dashed line.

*

.

12

strong need for supporting measurements that deter-

mine such spectra. This need is particularly impor-

tant when the material is a prime component in the

structure of any fusion reactor design.

VI. ACKNOWLEDGMENTS

We would like to thank David Turner of the LosAlamos Scientific Laboratory for his help andguidance in setting up the Monte Carlo calculations,

REFERENCES

1. M. Drosg, G. F. Auchasnpaugh, and F. Gurule,“Signal-to-Background Ratio for Neutron Produc-tion between 10 and 14 MeV by the Reactions3H(p,n)3He, lH(t,n)3He, and 2H(d,n)3He,” LosAlamos Scientific Laboratory report (to be issued).

2. L. Cranberg, R. A, Femald, F. S. Hahn, and E.F. Shrader, “Production of High-Intensity IonPulses of Nanosecond Duration,” Nucl. Instmm.Methods 12, 335 (1961).

3. D. M. Drake, E. D. Arthur, and M. G. Silbert,“Fourteen-MeV, Neutron-Induced Gamma-RayProduction Cross Sections,” Los Alamos ScientificLaboratory report LA-5662-MS (1974).

4, N. W. Hill, J. W. T. Dabbs, H. Weaver, “Op-timized Detection of FissionNeutrons with Large Li-quid Scintillators, ” Physics Division AnnualProgress Report, ORNL-4937 (1973).

5. T. K. Alexander and F. S. Goulding, “AnAmplitude-Insensitive System that DistinguishesPulses of Dependent Shapes,” Nucl. Instrum.Methods 13, 244 (1961).

6. H. Liskien and A. Paulsen, “Neutron Produc-tion Cross Sections and Energies for the Reactions

T(p,n)3He, D(d,n)3He, and T(d,n)4He,’’Nucl. DataTables 11, 569 (1973).

7. ENDF/B-IV, Hydrogen data file available ontape as MAT 1269, distributed by BrookhavenNational Laboratory (1974),

8. E, D. Caehwell, J. R, Neergaard, W, M. Taylor,and G. D. Turner, “MCN: A Neutron Monte CarloCode,’’ Los Alamos Scientific Laboratory report LA-4751 (1972),

9. J. Benveniste, A. C, Mitchell, C. D. Shrader,and J. H. Zenger, “Gamma Rays from the Interact-ion of 14-MeV Neutrons With Beryllium,” Nucl.Phys. 19, 52 (1960).

10. G. C. Wick, “A Theorem on Cross Sections,”Phys. WV. 75, 1459 (1949).

11. ENDF/B-IV, Beryllium data file available ontape as MAT 1289, distributed by BrookhavenNational Laboratory (1974).

12. L. Veeser, Los Alamos Scientific Laboratory,private communication (1976),

13. J. T. Prud’homme, I. L. Morgan, J, H. Mc-Crary, J. B. Ashe, and O. M. Hudson, Jr., “A Studyof Neutrons and Gamma Rays for Neutron-InducedReactions in Several Elements,” Air Force SpecialCenter report AFSWC-TR-60-30 (1960).

14. D. Hermsdorf, A. Meister, S. Sassenoff, D.Seelyer, K, Seidel, and F. Shakin, “DifferentielleNeutronenemissionsgverahnitte ati(Eo;E,D) bei14.6 MeV Einschus-energie t%rElemente Be, C, Na,Mg, Al, Si, P, S, Ca, Ti, V, Cr, Mn, Fe, Co, Ni, Cu,Zn, Ga, Se, Br, Zr, Nb, Cd, In, Sn, Sb, I, Ta, N, Au,Hg, Pb, und Bi,” Zentralinstitut fiir Kernforachungreport ZFK-277 (1974).

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