ABSTRACT EQUILIBRATION IN ORBITING HEAVY ION REACTIONS ... · Balasubramanian Shivakumar Yale University March 1986 On the basis of this work, it seems apt to conclude that available

ABSTRACT

EQUILIBRATION IN ORBITING HEAVY ION REACTIONS

Balasubramanian Shivakumar

Yale U n iv e r s i ty

March 1986

On the b a s is of t h i s work, i t seems apt to conclude that a v a i la b le

experimental data are co n s is te n t with the in te rp re ta t io n of the f o r

mation, in the e a r ly s tages of a heavy-ion in te r a c t io n , of a ro ta t in g

d in u c le a r m olecular complex (DMC). The observed y i e l d s of massive reac

t io n products can be id e n t i f ie d with those DMCs th a t fragment during the

course of their first revolution, and the process o f fus ion can be iden

t i f i e d with those DMCs that l i v e fo r a la r g e r number of re v o lu t io n s . The

y ie ld s of massive fragments from such o rb i t in g re a c t ion s are emitted

from a system that re ta in s a d inuc lear shape. W ith in the co n s tra in t s

imposed by such a shape, energy, angu lar momentum, charge, and mass are

e q u i l ib r a te d . Fusion r e su l t s when the shape degree o f freedom i s a lso

e q u i l ib r a te d .

The concepts of e q u i l ib r a t io n and o r b i t in g are d iscussed in terms

of experimental observab les in order to place the to p ic in perspective

w ith in the f i e l d of heavy-ion re a c t ion s. Some data measured for the 28Si

+ 12C in te ra c t io n are then presented to h ig h l i g h t the experimental, \

s ign a tu re s that suggest an o r b i t in g in te r p re ta t io n . These data are used

to e s t a b l i s h the need fo r a study of the 28Si + 14N in te ra c t io n .

Motivated by an observation of the e q u i l ib r a t io n o f energy and angular

momentum in the 28Si + 12C measurement, and an in d ic a t io n of the obser

va t ion of the e q u i l ib r a t io n of mass in a p re lim in ary 28Si + ll+N o rb i t in g

ABSTRACT

measurement, a model i s developed to account fo r s im u ltaneous ly , in

q u a n t ita t iv e fa sh ion , the o r b i t in g and fus ion y ie ld s fo r the 28Si + 12C

f in teraction. Th is fu rther motivates the need fo r a d e ta i le d 28Si + 1*IN

measurement in order to e s t a b l i s h unambiguously whether o rb i t in g

in te ra c t io n s l a s t long enough to permit the occurrence of mass

e q u i l ib r a t ion.

The experiment invo lves the study o f forward ang le y ie ld s of

t a r g e t - l i k e reaction products in in te ra c t io n s between a 28Si beam and a

14N ta rg e t . The d e t a i l s o f the experimental procedure fo r the p e rfo r

mance of such a measurement are then presented, fo llowed by a d iscu ss ion

o f the data a n a ly s i s and reduction. From the measured r e la t iv e r a t io of

the product y i e ld s , i t i s contended that o r b i t in g react ion s l a s t long

Enough to permit the e q u i l ib r a t io n o f charge and mass. An improved ver

s ion of the model developed is found to be able to account for the

observed r e la t iv e y ie ld s o f the reaction products. P o s s ib le improvements

to the model form ualtion are then presented, and su gg e s t ion s are made

fo r future avenues of experimental and th eo re t ica l in v e s t ig a t io n .

EQUILIBRATION IN ORBITING HEAVY ION REACTIONS

Presented

i

A D is se r ta t io n

to the Facu lty of the Graduate School

of

Yale U n ive rs ity

n Candidacy fo r the Degree of

Doctor of Philosophy

by

Balasubramanian Shivakumar

March 1986

DEDICATIONIi

To Family and Friends

"True fo r t i tu d e of understanding c o n s is t s in not l e t t i n g what

we know to be embarrassed by what we d on 't know"

— Ralph Waldo Emerson

The Skeptic

ACKNOWLEDGEMENTS III

I t g ive s me great p leasure to acknowledge the support of the

numerous people who have contributed s i g n i f i c a n t l y to t h i s research

endeavour. Th is work could not have been done without th e ir help.

I t was A l la n Bromley who convinced me that I should pursue a career

in nuc lear phy s ic s . I have benefited immensely from h is guidance and

from h is continued personal in te re s t , both in me and in my work. I have

been in sp ire d by the breadth o f h is knowledge o f p h y s ic s , and by the

c l a r i t y with which he presents h is ideas. I thank him fo r the central

ro le he has played in shaping me as a p h y s ic i s t and fo r the generous

f in a n c ia l support he has provided over the years.

I owe the success of t h i s e f f o r t , in a la rge p a r t , to the inva

lu a b le help of Dan Shap ira . He has been a good fr ien d and has in sp ired

me by h is pass ion fo r conducting research. He has shown a round-the-

c lock in te re s t in my work, and has kept my mind a c t iv e v ia numerous s t i

m u lating d i s c u s s io n s . He has been a pat ien t sounding board fo r my often

sp e c u la t iv e ideas. I am indebted to Dan fo r being instrumental in my

p ro fe ss io n a l growth.

I thank Fred Bertrand for h is continued ad m in is t ra t iv e and f in a n

c ia l support at Oak Ridge and fo r p rov id in g me with a s t im u la t in g

research environment. ^

I thank Alan Harmon, Paul S te lson , Ken Teh, and Marty Beckerman for

he lp ing me with the p lann ing and performance of several experiments. I

have b e n e f i te d *g re a t ly from th e ir wisdom and continued support. I thank

S a k i r Ayik fo r the numerous th e o re t ica l d is c u s s io n s that have enhanced

ACKNOWLEDGEMENTS ! IV

the value of my experimental endeavours. I thank the computer and other

research support s t a f f fo r p rov id ing a research environment-that i s

amongst the very best.

My formative years as a p h y s ic i s t have been in f luenced by the dyna

mism of Moshe G a i . I thank Karl Erb, Curt Bemis and Jim Ford for pro

v id in g me with the in te l le c tu a l cha llenge that i n i t i a l l y lured me to Oak

R idge, and fo r g iv in g me the opportun ity to work there . I am a lso g ra te

fu l fo r the occas ions I have had to in te rac t with members o f the

research s t a f f at both Yale and Oak Ridge.

I thank, and commend the e f f o r t s o f , the acc e le ra to r operators, the

machine shop, the instrument shop, the c r a f t s , the g raph ic a r t s depart

ment, and other support s t a f f at Oak Ridge. They have impressed me by

th e i r g e n ia l i t y and the q u a l i t y of th e i r work. I have benefited, in par

t i c u l a r , through my interactions with Tom H igg in s , Ray Ward, Jim

Johnson, and Nathan Jones.

I thank C h r is t in e Wallace, Althea Tate, Mary Ann Schulz, and R ita

Bonito fo r p rov id ing me with v i t a l ad m in is tra t ive and se c re ta r ia l sup

port. They have been very generous with th e i r time. I thank Sara Batter

and V i r g in ia H i l l fo r being the wonderful people th a t they are.

I consider i t a p r iv i le g e to have been assoc ia ted with my fe l low

graduate students. Their f r ie n d sh ip has been in va lu ab le .

Last but not the le a s t , my fam ily has been very supportive over the

years. Numerous fr ien d s a l l over the world have a ls o given me a f fe c t io n

and encouragement. I t i s to a l l o f them that I ded icate t h i s th e s is .

TABLE OF CONTENTS V

1. ACKNOWLEDGEMENTS I I I

2. TABLE OF CONTENTS V

3. L IST OF FIGURE CAPTIONS V I I

4. L IST OF TABLE CAPTIONS X I I I

5. L IST OF ABBREVIATIONS XIV

6. PREAMBLE

To those who are not s c i e n t i s t s 1

7. INTRODUCTION

3

R e su lt s 17

O rgan izat ion 18

8. MOTIVATION

9. THEORY

30

52

10. EXPERIMENTAL PROCEDURE

Apparatus ^ 72

Proce ss in g 91

Optim ization 94

TABLE OF CONTENTS

11. RESULTS AND INTERPRETATION

R esu lts

In te rp re ta t io n

Est im at ion of experimental e rrors

12. FROM FACT TO FICTION

13. SYNOPSIS

14. APPENDIX 1

Bass model parameters

15. APPENDIX 2

Experimental parameters used in the 28Si + 11+N measurement

16. BIBLIOGRAPHY

LIST OF FIGURE CAPTIONS

1. C l a s s i f i c a t io n scheme of c o l l i s i o n s between heavy ions

based on a c l a s s i c a l impact parameter model.

2. A schematic d iv i s io n of the to ta l cross sect ion into

reg ions a ssoc ia ted with d i f fe re n t angular momenta.

3. A q u a l i t a t i v e a s so c ia t io n of t im esca les with d i f fe re n t

react ion mechanisms.

4. A schematic representation of the in te rac t io n between

two heavy ions in terms o f the observables energy and

ang le.

5. The mass d i s t r ib u t io n of reaction y ie ld s a ssoc ia ted

with d i f fe re n t reaction mechanisms.

6. The 28Si + 12C nucleus-nucleus p o te n t ia l .

7. Energy spectra for carbon isotopes measured in a 28Si

+ 12C reaction at forward ang les.

8. Mean combined e x c ita t io n of carbon and s i l i c o n nuclei

p lo tted as functions of labora to ry angle.

9. Center of mass (cm) angu lar d i s t r ib u t io n s fo r the to ta l

reaction y ie ld s at backward ang les.

10. The f in a l k in e t ic energy of carbon nuclei from the

28Si + 12C in te ra c t io n p lotted as functions of

center of mass energy.

1 1 .

1 2 .

13.

14.

15.

16.

17.

18.

19.

20.

LIST

The angle in tegrated cross sec t io n s fo r the 28S i +

12C o r b i t in g y ie ld . - 36

The angu lar momenta fo r the graz ing t ra je c to ry as

obtained from an o p t ica l model c a lc u la t io n . 39

A schematic p lo t o f the fu s ion cro ss sect ion as a

function of the inverse of the cm energy. 42

A p lo t o f the adjusted Q- value of d inuc lear

channels open to 28S i + 12C. 46

A p lo t of the adjusted Q- value of d inuc lear

channels open to 28Si + 1**N. 48

A schematic representation of the processes of

o r b i t in g and fu s io n . 53

A schematic diagram of the 28Si + 12C entrance

channel d inuc lear potentia l and the ad iab a t ic

mononuclear p o te n t ia l . ' 56

The f in a l k in e t ic energies of o r b i t in g products

from the 28Si + 12C reaction . 63

The o rb i t in g cross sec t ion s fo r the C, N, and

0 channels in the 28Si + 12C reaction . 66

The known energy le v e ls of a few d inuc lear

channels open to the 28Si + 12C reaction . 68

OF FIGURE CAPTIONS VIII

21. The fu s ion cross se c t ion s fo r the 28Si + 12C

system.

22. The experimental arrangement used fo r the 28Si

+ 1I+N measurement.

23. A schematic top view of the superson ic gas je t

ta r g e t .

24. A schematic s ide view of the superson ic gas je t

ta rg e t .

25. A schematic s ide view of the Hybrid Ion iz a t ion

; Chamber (H IC ) .

26. A schematic diagram of the NIM e le c tro n ic s used

in the data p rocess ing .I

27. A p lo t showing the e f fe c t s , of adding an AluminumI

s t r ip p e r f o i l , on the charge d i s t r ib u t io n s of the

react ion products.

28. E f f ic ie n c y of the HIC as a function o f p o s it io n

a long the fron t wire.

29. Detected energy of monoenergetic ions p lotted as

a function of th e ir p o s i t io n on wire W1 in the HIC.

30. Spectrum o f e l a s t i c a l l y scattered 28S i nuclei from

a 28Si + ^ N in te ra c t io n .



31. Spectra o f o r b i t in g y ie ld s detected on the front

and rear p o s i t io n sensing wires on the HIC.

32. Spectra of o r b i t in g y ie ld s from the 28Si + llfN

in te ra c t io n p lo tted as functions of energy and

energy lo s s as detected in the HIC.

33. The Z- gated energy vs p o s it io n spectrum of o rb i t in g

products fo r the n itrogen channel in the 28S i + lltN

react ion .

34. Spectrum o f oxygen y ie ld s from the 28Si + ^ N in t e r

ac t io n p lo tted as funct ion s of energy and wire

p o s i t io n .

35. P ro ject ion along the energy and p o s it io n axes o f the

14N y ie ld w ith in the gate.

36. 14N y ie ld s p lo tted as functions of wire p o s i t io n ,

opening ang le , and focal plane p o s it io n .

37. Y ie ld s of l ltN nuclei from the 28Si + ltfN in te ra c t io n

p lo tted as funct ion s of e x c ita t io n energy.

38. The y ie ld of 12C nuclei p lotted as functions of

the p o s i t io n along the front wire in the HIC.

39. The o rb i t in g cross sec t ion s of 12C nuclei from the

28S I + 14N in te rac t io n p lo tted as functions of

40. The y ie ld o f l ltN nuclei p lo tted as funct ion s of

the p o s i t io n along the front wire in the HIC.

i

41. The o r b i t in g cro ss sec t io n s o f 14N nuclei from the

28S I + 14tN in te ra c t io n p lo tted as functions of

Q- value.

42. The y ie ld o f U C nucle i p lo t ted as functions o f

the p o s i t io n along the fron t wire in the HIC.

43. The o r b i t in g cro ss sec t io n s o f U C nucle i from the

28S I + 14N in te ra c t io n p lo tted as functions of

Q- value.

44. The angle in tegra ted abso lute o r b i t in g cross se c t io n s

fo r the 28S i + ll4N in te ra c t io n p lo tted as1

fu n c t ion s o f cm energy.

45. The f in a l k in e t ic energies of o r b i t in g products from

1 the 28S i + l l fN in te ra c t io n p lo tted as functions

o f center of mass energ ies.!

46. A schematic p lo t o f the leve l d e n s ity in a nucleus

as predicted by the Fermi leve l de n s ity express ion .

47. O rb it in g cross se c t io n s fo r the C, N, and 0 channels

in the 28Si + 12C in te ra c t io n p lo tted as fun ct ion s

o f cm energ ies.



48. O rb it in g cross sec t ion s fo r the C, N, and 0 channels

in the 28S i + ll|N in te rac t io n p lotted as functions

o f cm energ ies.

49. Optimal vo ltage se t t in g s fo r wires 1 and 2 p lo tted as

a function of the pressure in the HIC.

50. Optimal vo ltage s e t t in g s fo r the cathode and the

anode as a function of the pressure in the HIC.

LIST OF TABLE CAPTIONS XIII

1. A com pila t ion of references pe rta in in g to the f u l l energy

damped component of d i s s ip a t iv e c o l l i s i o n s . 21

2. A l i s t of experimental parameters used in the 28Si + 14N

measurement fo r the detection of carbon and oxygen

iso to p e s . 166

1. cm center of mass

2. DMC D inuc lear Molecular Con figu ra t ion

3. HIC Hybrid Io n iz a t io n Chamber

4. PES Po tentia l Energy Surface

LIST OF ABBREVIATIONS

PREAMBLE: TO THOSE WHO ARE NOT SCIENTISTS

Let us t a lk about b i l l i a r d s . A cue i s used to propel a smooth

spher ica l ba l l towards another in an attempt to drop the second ba ll

in to one of s ix pockets located along the perimeter o f a fe lt - topped

t a b le . Such a game i s easy to p lay and can be learned in a matter of

hours. I t provides examples o f what are referred to in phys ics t e r

m inology as " e l a s t i c c o l l i s i o n s " . A part or a l l o f the energy of motion

o f the f i r s t ba l l i s t ran s fe rre d to the second in an attempt to d ire c t

i t in to a pocket.

Let us now make the game a l i t t l e more d i f f i c u l t by rep lac in g the

b i l l i a r d b a l l s with ones made of rubber as are used in racket b a l l . The

b a l l s now bounce o f f one another in a s l i g h t l y d i f f e r e n t way, but the

game i s s t i l l manageable. Anyone who has played racket b a l l or squash

can a t te s t to the fac t that the b a l l s become warm to the touch as the

game progresses. Th is w i l l happen in our game o f b i l l i a r d s too and i s a

r e s u lt of the compression of the b a l l s on impact. T h is i s an example of

what are referred to as " d i s s ip a t i v e c o l l i s i o n s " . There i s one more

th in g we w i l l begin to no tice in our game. The b a l l s are sp inn ing ! This

happens because the su rface of the b a l l s are no longer smooth and f r i c

t io n i s causing some of the re la t iv e motion to transform in to the

sp in n in g motion. Now the game i s beginning to become more complex an^,.

in stead o f a matter o f hours, i t w i l l take a few days to master.

So f a r , we have been us ing b a l l s which can o n ly bounce o f f one

1

PREAMBLE 2

another. The forces between the b a l l s are sa id to be re p u ls ive . What

would happen to our game i f the b a l l s could a t t r a c t one another too? Let

TMus cons ider t h i s . We cover the surfaces o f the b a l l s with Velcro . The

b a l l s can now not only bounce o f f one another but s t i c k to one another,

too! The game i s beginning to become more in te r e s t in g . I t i s a lso much

more d i f f i c u l t to p lay and probably requ ires a few months to master.

What next? I sh a l l now t e l l you about the somewhat equiva lent game

I have been p lay in g at a much more m icroscopic le v e l . I t i s a game where

TMthe b a l l s are l i k e Velcro covered pomegranates. An added com plication

i s that the b a l l s can exchange seeds between themselves while they are

stuck together! Consequently, the ba l l that I am t r y in g to send in to a

pocket can change in s iz e and mass as the re su lt o f a c o l l i s i o n . This

game i s now beginning to become exceedingly complex and i s represen

t a t i v e o f the k inds of games we p lay in nuclear p hys ic s today. In the

nuclear physics b i l l i a r d ba ll game the cue i s an a c c e le ra to r , the b a l l s

are n u c le i , and the ta b le with i t s pockets are a s c a t te r in g chamber and

d e tecto rs .

This d i s s e r t a t io n descr ibes an attempt to understand in m icroscopic

d e ta i l how such a game i s played in nuclear p hys ic s .

INTRODUCTION 3

Most phenomena in physics can be studied in terms of observables

such as d is tan ce , time, energy, angle, angular momentum and mass. These

q u a n t i t ie s are often ne ither d i r e c t ly nor p re c ise ly measurable but yet

can be used to d i s t in g u i s h between processes a t t r ib u ta b le to d i f fe re n t

mechanisms. The to p ic of t h i s d i s s e r t a t io n i s EQUILIBRATION IN ORBITING

HEAVY ION REACTIONS. I s h a l l , in t h i s chapter, d is c u s s t h i s to p ic in the

context o f the observab les mentioned above in order to place i t in

perspect ive w ith in the general f i e ld of heavy-ion re a c t ion s .

The name " o r b i t in g heavy-ion react ion s" a p p l ie s to nuclear

in te r a c t io n s wherein the two nuclei invo lved s t i c k to one another, under

the in f luence of an a t t r a c t iv e force, to form a nuc lear molecule. This

assumed r i g i d d in u c le a r molecular complex (DMC) l i v e s long enough to

execute a re v o lu t io n , perhaps se ve ra l, before i t breaks up in to two (or

l e s s frequently , more) fragments. The s ign a tu re s fo r the observation of

such a process are numerous and can be id e n t i f ie d through measurement

o f the observab les mentioned above.

The nature of the in te ra c t io n between two heavy ions i s dependent

on t h e i r d is tan ce o f c lo s e s t approach. This i s shown in f i g . 1 which

l i s t s var ious reaction mechanisms that have been invoked to describe the

phenomena observed in heavy-ion in te ra c t io n s . A crude separat ion has

been made based on the r e la t iv e magnitudes o f the d is tan ce o f c lo se s t

approach and an in te ra c t io n rad ius R-jnt* F°r r a d i i r < R i nt» there

i s u s u a l ly a d r a s t i c r e d is t r ib u t io n of energy, angu lar momentum and mass

between the in te r a c t in g n u c le i. These k inds of re a c t ion s can be broadly

categor ized as d i s s ip a t i v e c o l l i s i o n s and w i l l be d iscu ssed in t h i s

work.

INTRODUCTION 4

Figure 2 l i s t s the reaction mechanisms in terms of the angular

momenta invo lved. D i s s ip a t iv e c o l l i s i o n s occur fo r a l l o rb i ta l angular

momenta le s s than Further, the energy o f r e la t iv e motion in a c o l l i

s ion between two nucle i can be damped by f r i c t io n to an extent that

a llow s fo r the formation of a d inuc lear molecular complex. This happens

fo r a l l angu lar momenta below a c r i t i c a l value £ . Th is d i s s e r ta t io n iscr

r e s t r ic te d in angu lar momentum space to a d isc u s s io n o f angu lar momenta

below £ cp .

In terms of time, the fa s te s t nuclear react ion s occur on a

t im esca le o f 10“22 secs, which i s the c o l l i s i o n time fo r a typ ica l

e l a s t i c in te ra c t io n at energies o f ~ MeV per nucleon. F igure 3 l i s t s the

var iou s reaction mechanisms and a s so c ia te s a range of t im esca les with

each of them. The react ion s we are concerned with in t h i s d i s se r ta t io n

occur on t im esca le s longer than 10-21 se c s . .

F igure 4a i s a schematic diagram of a reaction between two heavy

io n s . T ra je c to r ie s with sm alle r angu lar momenta are a ssoc ia ted with

la r g e r d e f le c t io n angles and greater energy d i s s ip a t io n . F igure 4b shows

three such t r a je c to r ie s la b e l le d 1,2 and 3 a ssoc ia ted with de f le c t io n

angles o f increasing magnitude. The corresponding double d i f fe r e n t ia l

cro ss sect ion da/dEd0 i s shown in f i g . 4c. The t r a je c to ry 3 i s a sso

c ia te d with processes having emission spectra and em ission p r o b a b i l i t ie s

independent of angle. These are the kinds o f t r a je c to r ie s t h i s work w i l l

address.

With in c re a s in g d e f le c t io n angle and energy d i s s ip a t io n in the

c o l l i s i o n between two heavy ion s , there i s an increase in the number of

INTRODUCTION 5

F igure 1

C l a s s i f i c a t i o n scheme of c o l l i s i o n s between heavy ions based on a

c l a s s i c a l impact parameter model. The quan tity r denotes the

d is tan ce of c lo s e s t approach a ssoc ia ted with a given impact para

meter. The c h a r a c t e r i s t i c s of an in te rac t io n are determined by the

r e la t iv e magnitudes of r and an in te ra c t io n rad ius R-jpt* The model

shapes apply to the d is tan ce of c lo se s t approach (adapted from

( Sch84) ) . O rb it in g react ion s occur fo r r < R-jnt when an a t t r a c t iv e

force keeps the nuclei together fo r a time long compared to a

t y p ic a l c o l l i s i o n time of ~ 10-22 seconds.

FIGURE 1

1

Zo

<UJGCz’o*-<<rm, D O

0.2<0

su51h-<<rH-UJsa

T

REACTION FLOWREACTION CHARACTERISTICS

D ISTANT

C O LLIS IO NS

f >RInt

MODELSHAPES

_ c /

X )

PER IPHERAL

C O LL IS IO N S

r « Rl„t

----SOLID-CONTACT

CO LL IS IO N S

r<R Int

D EEPLYPENETRAT ING

CO LL IS IO N Sf « R lnt

ELAST IC SCATTERING AND COULOMB EXCITATION

INELASTIC SCATTERING AND ONSET OF NUCLEON EXCHANGE AND WEAK K INET IC -ENERGY DAMPING

ORBITING REACTIONSDAMPED OR DEEP-INELASTIC REACTIONSCHARACTERIZED BY:SUBSTANTIAL K INET IC -ENERGY DAMPING AND M ASS EXCHANGE. WHILE RETAINING PARTIAL MEMORY OF ENTRANCE-CHANNEL M ASSES AND CHARGES

FUSION-FISSION-LIKE REACTIONS CHARACTERIZED BY:LOSS OF PROJECTILE AND TARGET IDENTIT IES AND CO M PLETE DAMPING OF KINETIC ENERGY COMPOUND-NUCLEUS REACTIONS LEADINGTO EVAPORATION RESIDUES AND FISSION

TOTA

L RE

ACT

ION

CR

OSS

SE

CT

ION

INTRODUCTION 7

Figure 2

A schematic d i v i s io n o f the to ta l c ro ss sect ion in to reg ions a s so

c ia te d with d i f fe re n t o r b i t a l angu lar momenta. Acp i s the c r i t i c a l

angu lar momentum and i s the upper bound in A-space fo r the f o r

mation of a d inuc lear molecular complex. Ap 1S the angu lar momen

tum below which d i s s ip a t iv e phenomena are observed. Amax i s the

angu lar momentum below which nuc lear react ion s are observed. There

are t r a n s i t io n reg ions (curved l i n e s ) at each o f these charac

t e r i s t i c o rb i t a l angu lar momenta to in d ica te that the d iv i s io n of

the cro ss sect ion in to reg ions a ssoc ia ted with d i f fe r e n t reaction

mechanisms i s fuzzy.

FIGURE 2

O RN L-D W G 85-18586

ELASTIC COULOMB EXCITATION

QUASI ELASTIC TRANSFER

DEEP INELAST IC

do

d 7FUSIONFUSION-FISSION FUSION-EVAPORATION FAST FISSION QUASI FISSION O RBIT ING

max

INTRODUCTION 9

nucleons exchanged. This i s shown in f i g . 5 which presents the d i s t r i b u

t io n of the nuclear product y ie ld s from an in te rac t io n between a Krypton

beam and an Aluminum ta rge t . The element y ie ld s a t t r ib u te d to d i f fe r e n t

processes have a ls o been ind ica ted . The y ie ld s are d i s t r ib u te d in mass

from those beyond those of the ta rge t and p r o je c t i le through the reg ions

in between. The y ie ld s fo r o r b i t in g react ion s are, on the average, cen

tered around the p r o je c t i le and ta rge t masses whereas the y ie ld s from

f u s i o n - l i k e processes are centered around the sum and the average o f the

p r o je c t i l e and ta rge t masses. The magnitudes of the c ro ss sec t ion s under

study are o f the order o f a few hundred m i l l ib a r n s fo r o r b i t in g reac

t io n s and about one barn fo r fu s ion ( 1 barn = 10“2lf cm2 ).

Having described what i s meant by o rb i t in g heavy-ion react ion s i t

i s necessary to de fine the term e q u i l ib r a t io n . F igure 3 a s so c ia te s with

each o f the reaction mechanisms the e q u i l ib r a t io n o f the observables

energy, angu lar momentum, charge, mass, and shape.

When a l l the r e la t iv e rad ia l motion in the in te ra c t io n between two

nucle i i s transformed in to th e ir in te rna l e x c i ta t io n , energy i s sa id to

be e q u i l ib ra te d . In the same s p i r i t , the e q u i l ib r a t io n of angu lar momen

tum im p lie s the complete transform ation of the r e la t iv e motion of the

two in te r a c t in g nuclear surfaces in to i n t r i n s i c nuc lear e x c i ta t io n . The

experimental s ign a tu re fo r such processes i s the observation of angu lar

d i s t r i b u t i o n s independent of the sp in s and e x c ita t io n energies o f the

react ion products. The e q u i l ib r a t io n of energy and angu lar momentum,

w ith in the c o n s t ra in t s of a nuclear volume that re ta in s a d inuc lear

shape, re s u l t s in the formation of a DMC in the s t i c k in g l im i t . There is

then no r e la t iv e motion between the two nuclei forming the DMC and the

INTRODUCTION 10

Figure 3

A q u a l i t a t i v e a s so c ia t io n of time s c a le s with d i f fe re n t reaction

mechanisms. E : Energy, i : Angular momentum, M : Mass, Z :

Charge. As a reference, l i g h t t r a v e ls a ty p ica l nuc lear dimension

o f 10 fm. in 3.3 x 10-23 se c s . . As nuclear react ion s l a s t fo r

longer tim es, an in c re a s in g number o f degrees of freedom

eq u i1ib ra te .

FIGURE 3 11

TIME

O R N L-D W G 8518585

COMPOUND NUCLEUS FORMATION FUSION-E VAPOR ATION FUSION-FISSION EQUILIBRATION OF

E. C, M, Z AND SHAPE

DEEP INELASTICMULTI NUCLEON TRANSFEREQUILIBRATION OF E AND C

10-1 8

10-19

10-20

10-21

10-22

10- 2 3

QUASI FISSION FAST FISSION ORBITING EQUILIBRATION OF

E, C, Z. AND M

: : *

DIRECTELASTIC, INELASTIC FEW NUCLEON TRANSFER NO EQUILIBRATION

SECONDS

INTRODUCTION 12

F igure 4

a.

A schematic representation of the c o l l i s i o n between two heavy

io n s . Sm a lle r impact parameters are a ssoc ia ted with sm a lle r angu

l a r momenta, la r g e r d e f le c t io n ang les and increased energy d i s s i

pa t ion .

b.

A schematic drawing of three p o s s ib le t r a je c to r ie s . 1. A d ire c t

s c a t te r in g p rocess. 2 and 3. T ra je c to r ie s in v o lv in g a s c a t te r in g

to negative an g le s . T ra jectory 3 can a lso sc a t te r to backward

ang les and represents o r b i t in g re a c t ion s .

c .

A p lo t of the double d i f f e r e n t ia l c ro ss sect ion do/dE de vs.

energy and ang le . D i f fe re n t regions of the p lo t are a ssoc ia ted

with the three t r a je c t o r ie s of f i g . b..

(adapted from (Wi173) )

FIGURE 4 13

a)

c)

2.3 -

— 0 g r a z

4

c ro» * taction con tour*

♦egrax e

b)

INTRODUCTION

Figure 5

The Z -d i s t r ib u t io n of the angle in tegra ted cross se c t io n s (from

Heu85). The f u l l symbols and s o l id l in e ind ica te to ta l element

y i e l d s . The open symbols and open l in e s in d ica te p a r t ia l cross

se c t io n s . Open c i r c le s and dash-dotted l in e s in d ica te 1 /S in0 or

o r b i t in g components. Open squares and the dotted l in e in d ica te the

deep in e l a s t i c component (D IC ) . Open diamonds and the dashed l in e

in ic a te the quasi e l a s t i c (QE) component. The evaporation residue

(ER) y ie ld from the compound nucleus has a lso been in d ica te d .

NU

MB

ER

C R O S S S E C T I O N ( m b )

■ f

FIGU

RE 5

INTRODUCTION 16

molecule behaves l i k e a r i g id body.

The e q u i l ib r a t io n of mass and charge invo lves the exchange of

nucleons between the two nuclei forming the DMC. Through a measure of

the mass d i s t r ib u t io n of the reaction product y ie ld s one can learn about

the mass evo lu t ion of the DMC. I f the re su lt in g mass d i s t r ib u t io n s are

amenable to a s t a t i s t i c a l 'phase space' in te rp re ta t io n , the e q u i l ib r a

t io n o f charge and mass can be presumed to have occurred.

The equ il ib r ium shape of an ensemble of nucleons o f to ta l mass A i s

that in which they are confined to be in th e ir lowest potentia l energy

c o n f igu ra t io n . The shape atta ined by the ensemble o f nucleons can be

in fe rred through a measure of the mass d i s t r ib u t io n of the reaction pro

ducts. The s ignatu re of a fu l l e q u i l ib r a t io n in shape i s the preferen

t i a l emission of l i g h t reaction products (evaporation ) and/or products

having a mass ~A/2 ( f i s s i o n ) .

I t bears emphasis that the concepts o f e q u i l ib r a t io n of angular

momentum, energy, mass, and charge, as w i l l be d iscu ssed in t h i s work,

have been defined under the c o n s tra in t s imposed by a nuclear volume that

re ta in s a d inuc lear shape. The v a l i d i t y o f such an approach r e l ie s on

the observation that the shape degree of freedom takes much longer to

re lax than the other degrees ju s t d iscussed .

INTRODUCTION: RESULTS 17

I present herein evidence for an observation of the constra ined

e q u i l ib r a t io n of angu lar momentum, energy, mass, and charge*in o rb i t in g

heavy-ion re a c t ion s. I t i s my contention that the on ly degree of freedom

that i s not e q u i l ib ra te d in o rb i t in g reactions i s shape. A v a i la b le

experimental evidence suggests that o rb i t in g and fu s ion y ie ld s from the

in te ra c t io n between r e la t iv e ly l i g h t heavy ions can be understood quan

t i t a t i v e l y as the consequence of the evo lu t ion of a d in u c le a r molecular

complex formed in the e a r l ie s t phase o f the in te ra c t io n . Th is complex

l i v e s long enough ( fo r at le a s t one ro ta t io n ) before breaking up outward

to g ive the y ie ld o f r e la t i v e ly heavy o rb i t in g products and s i g n i f i

c a n t ly longer (severa l re vo lu t io n s ) before fu s in g in to a compound system

which subsequently decays with the em ission of l i g h t e r fu s ion products.

The evo lu t ion of the o rb i t in g system and i t s breakup have been success

f u l l y described through the so lu t io n o f two d i f fu s io n equations that

fo l lo w the e q u i l ib r a t io n of the system while trapped in a potentia l

pocket; the fu s ion y ie ld i s then described with equal success, but

without requ ir in g any d e ta i led d isc u s s io n of the actual fu s ion mecha

nism, by tak in g the fu s ion y ie ld as a l l that remaining a f te r the

o r b i t in g y ie ld i s accounted fo r . In p a r t ic u la r , the energy dependence of

the fus ion process emerges n a tu ra l ly from t h i s treatment.

Several improvements to our model immediately suggest themselves

and w i l l be in v e s t ig a te d . The work reported herein however represents a

s i g n i f i c a n t step toward q u an t ify in g the complex evo lu t ion of the

in te ra c t io n between two energetic heavy ions and at the same time ra ise s

a number of in te r e s t in g new to p ic s -both experimental and th e o re t ica l

- f o r in v e s t ig a t io n .

INTRODUCTION: ORGANIZATION 18

The concepts of o r b i t in g and e q u i l ib r a t io n have been brought to

center stage in th i s f i r s t chapter, with the general f i e ld o f heavy-ion

react ion s se rv in g as a backdrop. The var ious features o f these processes

have been sp o t l igh te d in terms of experimental v a r ia b le s . With the stage

se t , the show i s ready to begin.

Chapter 2, t i t l e d MOTIVATION, presents some data measured fo r the

28Si + 12C system and h ig h l i g h t s the experimental s ign a tu re s that

suggest an o rb i t in g in te rp re ta t io n . Some other measurements are

d iscu ssed that perta in d i r e c t ly to the top ic o f t h i s t h e s i s . These data

are used to e s t a b l i s h the need for a study of the 28Si + lifN system.

Chapter 3, e n t i t le d THEORY, descr ibes an attempt to describe the

28Si + 12C data in terms of the formation and evo lu t ion o f a DMC. Other

attempts to d iscu s s s im i l a r to p ic s are given cursory mention.

Chapter 4, e n t i t le d EXPERIMENTAL PROCEDURE d e t a i l s the way the

measurements were performed. An attempt has been made to provide enough

in form ation to f a c i l i t a t e future s im i l a r endeavours.

Chapter 5, e n t i t le d RESULTS AND INTERPRETATION d is c u s se s how the

data were analyzed and cross sec t ion s and other in form ation a rr ived at.

The re su lt s are then in terpreted as evidence fo r the observation of the

e q u i l ib r a t io n of charge and mass.

Chapter 6, e n t i t le d FROM FACT TO FICTION begins by re c o n c i l in g the

r e su lt s o f t h i s measurement with those of others. P o s s ib le experiments

and th e o re t ic a l s tu d ie s designed to answer outstand ing questions are

then suggested. The chapter concludes with unbrid led specu la t ion on

INTRODUCTION: ORGANIZATION 19

the connections between th i s work and other phenomena observed in heavy-

ion reactions and phys ics .

The chapter e n t it le d SYNOPSIS summarizes the accomplishments of

t h i s work.

The appendices tabu la te some of the inform ation not presented in

the main body of the th e s i s .

MOTIVATION

Measurements on a number of nuclear systems (see ta b le 1) have

shown the ex istence of la rge y ie ld s o f nuclear reaction products a t t r i

butab le to a d in u c le a r o rb i t in g process. In the case of the l i g h t e r

systems, the fo l lo w in g features are observed at backward ang le s.

( a ) . The mean k in e t ic energy of the emitted products i s indepen

dent of angle.

This i s su gg e s t iv e of the e q u i l ib r a t io n o f energy and angular

momentum as w i l l be explained in t h i s chapter.

(b ) . In the center of mass (cm) frame, the em ission p ro b a b i l i t y

da/d0 i s independent of angle and the d i f f e r e n t ia l c ro ss sect ion

da/dn then v a r ie s as 1/s ine (e i s the angle in the cm frame).

Th is in d ica te s that the ro ta t in g d inuc leus, presumed to be formed

in such c o l l i s i o n s , l i v e s fo r at le a s t a s i g n i f i c a n t portion of a

re v o lu t io n . A lso , t h i s observation im p lie s th a t the mass d i s t r i b u

t io n of o r b i t in g y ie ld s i s independent o f ang le . This i s a

necessary but not s u f f i c ie n t cond it ion fo r the e q u i l ib r a t io n of '

charge and mass.

( c ) . The mean of the k in e t ic energy d i s t r ib u t io n v a r ie s l i n e a r l y

with bombarding energy and occurs at an energy equal to that

(nuc lear + Coulomb + c e n t r i fu g a l ) stored in a ro ta t in g d inuc lear

m olecu lar complex.

(d ) . Large y ie ld s are observed, at backward a n g le s , with masses

near those of the p r o je c t i le and the ta rge t . The to ta l cro ss sec

t io n s fo r these processes i s several hundred m i l l ib a r n s .

MOTIVATION

TABLE 1

A com pila tion of references p e r ta in in g to the f u l l energy damped

component of d i s s ip a t iv e c o l l i s i o n s . These measurements can be

in terpre ted in terms of the formation and evo lut ion o f an o r b i t in g

d in u c le ar molecular complex. The reactions are l i s t e d in the order

' p r o j e c t i l e + t a r g e t * . The energies refer to the p r o je c t i l e

labora to ry energy.

ro 00 U> CO to to tou> -f ro to 00 00 's i00 7 CO CO CO CO >Cl ”5

+ + + + + + + + + + + + +00 <n U1 «F -r ■F IO *— ro on cn H-' H-•VO •F 00 00 cn 00 's i OV CO VO .F ro-< z TJ -H CO O > O > O O z o O_i. o o* C O

►—* 1—» 1—» t—» VO 1—»r>o VO o VO o00 o O O o 1 cncn « "* 1 »—» w«* 1—* H-1 r—* VO I—*I—* cn cn 'sj o -p.-p* 4» -P* o cnro •* '*00 Mcn cn

00 00

ZJZ 00 *—♦ »—• cn co co co COo ro o o OD IT □* T 3 * O’TV- c o n H-I -*• 01 0* 0) ft*00 00 00 00 O 00 00 00 00 00cn cn cn co O) 4* co ro o

o’ ft* ft*

f -

to ro ro ro to ro to H-* »—» j—• h-* >—•to o o o o o © Vft ON cn cn -Tz z z z z Z Z ~n o o o Z COfD CD fD CD fD CD fD -<

CO+ t + + + + + + + + + + -HmVO VO 4T to to H-« 00 -F ■r -F ro z■r 'si O 'si o ON ro vO 00 -f OM :> r> > z o o -< -H O O >"3 C ft* — *fD ft* ft* — 1

•'sj*—» *—« i—‘ 00 00 cn 1—» cn 1—»n y i f s j O O 4 * •pt o VO oo *— 1 O 1 I i o o » o m

I— * ‘ 00 CO z<n cn I— * 1 mo o 00 zo

's j o• - <CO

3 n* z m co co co co CO oo CO 00 m“3 VO VO IT 3" =r 2T o —>. ft* -n

7T ft C 0 ft* ft* ft* ft* c rf 3 m'sj ^ CO 00 00 00 'sj 00 00 00 00 70'sj oo o cn co co ro vo cn cn cn o m

cr cr ct zom

roPO

TABLE

MOTIVATION 23

The observations (c) and (d) have encouraged Shapira et a l .

(Sha84b) to in te rp re t the data as evidence fo r the formation o f an

o r b i t in g d inuc lear molecular complex (DMC). The cross sec t ion s of

the reaction products are too la rge to be accounted fo r by com

pound nucleus evaporation and/or f i s s io n .

These observations can be in terpreted in terms of the formation

and subsequent decay of a DMC. The to ta l energy stored in the re la t iv e

d in u c le a r motion of a DMC can be in fe rred by measuring the energy

spectra of o rb i t in g products. F igure 6 i s a p lo t of t h i s energy as a

funct ion o f the f in a l o rb ita l angu lar momentum if and an in te r -n u c le a r

separat ion d. The f in a l k in e t ic energy E ^ n of a reaction product i s

given by an expression of the form

eL = v d > + v d> + 1,2 (1>

where Vn and Vq are the nuclear and Coulomb energies re sp e c t iv e ly , and y

i s the reduced mass of the system. The f in a l k in e t ic energy at each i?

corresponds to the he ights of the outer maxima of the a ssoc ia ted

nucleus-nucleus p o te n t ia l . The only quan tity in t h i s expression that

depends on the bombarding energy i s the term in v o lv in g the angular

momentum. Since ro ta t io n a l energy sca le s as the square of the angular

momentum, in terms of the cm energy t h i s expression can be recast as

E.f . = an + a, E *(2 )k in 0 1 cm

We there fore expect a l in e a r increase of the f in a l product k in e t ic

energy with in c re a s in g cm energy.

I sh a l l begin with a presentation o f the a v a i la b le 28Si + 12C

MOTIVATION 24

FIGURE 6

The 28Si + 12C nuc leus-nucleus p o te n t ia l . The po te n t ia l parameters

are l i s t e d in (Sha84b). The curves have been drawn fo r d i f fe re n t

values o f the r e la t iv e o rb ita l angu lar momentum sf = L.

TOT

FIGURE 6 25

ORNL-DWG 84-12626

4 6 8 10 12d (fm)

MOTIVATION 26

data. This i s the system that has been studied most ex te ns ive ly

(Sha84b) and serves as a good b a s is fo r a d iscu ss io n o f the observable

s ign a tu re s fo r the o r b i t in g process. 28Si beams of energies between 99

and 190 MeV from the BNL Tandem acce le ra to r f a c i l i t y were used to bom

bard natural 12C ta r g e t s . T a r g e t - l ik e reaction products were detected at

lab o ra to ry ang les between 2 and 24 degrees, and t h e i r f u l l energy

spectra were obtained. This corresponds to cm energ ies in the range 30

to 55 MeV and cm an g le s , in a k in e m a t ica l ly reversed reaction ( 12C beam

on a 28Si t a r g e t ) , in the range 115 to 175 degrees.

F igure 7 shows ty p ic a l carbon spectra measured at two energies for

the 28Si + 12C in te ra c t io n . The spectrum at 125 MeV shows several

d is c re te l in e s at low e x c ita t io n energ ies. These can be id e n t i f ie d with

the e x c ita t io n of energy le v e ls in 12C and 28S i . At h igher e x c ita t io n

energies there i s a smooth maximum corresponding to the overlap of many

such le v e ls in the combined e x c ita t io n o f 28Si and 12C. The 180 MeV

spectrum shows that the y ie ld i s centered at a h igher average e x c i t a

t io n energy, and the low ly in g s ta te s are no longer excited with high

p r o b a b i l i t y . Both spectra have about the same width in energy. From a

study o f the moments o f such spectra , namely the area and the mean, as a

fun ct ion o f angle and energy fo r d i f fe re n t reaction products, we can

id e n t i f y and c l a s s i f y the propert ie s o f o rb i t in g heavy ion r e a c t io n s^

The mean e x c ita t io n energy values from spectra s im i l a r to those of

f i g . 7 can be re la ted to the k in e t ic energies of the reaction products

o f o r b i t in g . F igure 8 shows the mean e x c ita t io n energ ies Ee x c , at three

lab o ra to ry energ ie s, fo r the 12C e x it channel, p lo t ted as function s of

lab o ra to ry angle. From eq. 1 we know that the f in a l k in e t ic energy i s a

MOTIVATION 27

<

FIGURE 7

Energy spectra fo r carbon iso topes measured in a 28Si + 12C reac

t io n at forward an g le s .

CRO

SS

SEC

TIO

N

FIGURE 7

ORNL-OWG 82-19208

12C (28Si, 12C )28Si

EXCITATION ENERGY (MeV)

MOTIVATION

FIGURE 8

Mean combined e x c ita t io n energy Eexc o f carbon and s i l i c o n nuc le i,

as measured through the energy spectra o f emitted carbon nuclei

( f i g . 6 ), p lo tted as a function of labora to ry angle. At a l l

energies p lo t te d , the mean i s independent o f angle.

^exc = E<:m “ ^ i n

E ]ab i s the labora to ry bombarding energy of the inc iden t 28Si

beam.

exc

FIGURE 8

ORNL-DWG 82C—18090

,2C ( 28S i ,12C ')28 S i '

36

30

i * s24 E1AQ =170 MeVLAB

>©

Ld

18{ { M l H { H

1

i i i * } i i } }

145 MeV

12 H i

125 MeV

6 12 18 24

LAB ANGLE (deg)

30

MOTIVATION 31

FIGURE 9

Center o f mass angu lar d i s t r ib u t io n s fo r the to ta l react ion y ie ld

at backward an g le s . Data are shown fo r three ex it channe ls. The

s o l i d l in e s correspond to a 1/s ine d i s t r ib u t io n .

dct

/6£1

(m

b /

sr)

FIGURE 9 32

MOTIVATION 33

FIGURE 10

The f in a l k in e t ic energy (FKE) of carbon nuclei p lo t te d as a func

t io n o f center o f mass energy.

FKE = Ecm - Eexc -Qo

where Qg i s the ground s ta te Q-value of the e x it channel. The

s o l i d l in e has been drawn to guide the eye.

The open and c losed data points were measured in d i f fe r e n t

experiments.

FINAL KINETIC ENERGY (MeV)

MOTIVATION 35

sum of nuc lear, Coulomb and c e n tr i fu g a l co n tr ib u t io n s . Since we are

d e a l in g here with f u l l y damped energy spectra , and the f in a l k in e t ic \

energ ies are measured to be independent of angle, t h i s s i g n i f i e s the

e q u i l ib r a t io n o f energy and angu lar momentum. I f e i th e r energy or angu

l a r momentum had not e q u i l ib ra te d , t h i s would have been evident in f i g .

8 as decreasing Eexc with in c re a s in g ang le .

F igure 9 shows the d i f f e r e n t ia l cross se c t io n s , obtained from the

same study, p lo t ted as a function of cm ang le . I t i s c le a r that the data

can be in te rpre ted as having I / s i n e d i s t r ib u t io n s , in d ic a t in g that

o r b i t in g molecular complexes l i v e fo r at le a s t a s i g n i f i c a n t port ion of

a re v o lu t io n .

F igure 10 shows the f in a l k in e t ic energy of the 12C nuclei p lotted

as a function of cm energy. The k in e t ic energy increase s l i n e a r l y with

Ecm as expected from eq. 2 to a value of ~23 MeV at a cm energy of ~42

MeV. A s im i l a r behavior i s observed fo r other react ion products. At

energ ies above 42 MeV the k in e t ic energy does not increa se fu r th e r. A

s im ple in te rp re ta t io n of th i s behavior i s in terms of the van ish in g of a

minimum in the entrance channel nucleus-nucleus p o te n t ia l shown in f i g .

6 (Sha84b). The parameters of the poten t ia l have been adjusted to

account fo r the data in f i g . 10. There i s a pocket in t h i s po tentia l for• * ?

a l l r e la t i v e angu lar momenta < 19R. Where there i s no pocket, thdf&"

i s no a t t r a c t iv e fo rce . In such an in te rp re ta t io n , a DMC can be formed

in the the entrance channel fo r only those p a r t ia l waves £1n <

where the entrance channel angu lar momentum Ain can be reduced by f r i c

t io n to values of the r e la t iv e angu lar momenta sf below 19>t. In the

MOTIVATION

FIGURE 11

The angle in tegrated cross sect ion fo r the o rb i t in g y i e ld . The

1/sine angu lar d i s t r ib u t io n observed at backward ang les i s assumed

to p e r s i s t in the forward hemisphere in ob ta in ing the data po in ts .

To the extent that i t does not, such an observation would re f le c t

d ire c t amplitudes which are not re levant to our d i s c u s s io n s .

(mb)

FIGURE 11 37

Ec.m.(MeV)

s t i c k in g l im i t , J^p-jj. “ 23fi. The f in a l k in e t ic energies o f expression 2

are determined approximately by the he ights of the b a r r ie r s

corresponding to the h ighest angular momentum popu la t in g "the DMC at

any energy E ™ . As shown in f i g . 6, t h i s energy o f ~ 26 MeV is not

very fa r from the 24 MeV where the k in e t ic energy i s shown to saturate

in f i g . 10.

F igure 11 shows the abso lute o rb i t in g cross sect ion for the ca r

bon, oxygen and n itrogen channels p lotted as a function o f cm energy.

I t should be noted that the cross sect ions are p lotted on a logar ithm ic

sca le . The n itrogen y ie ld i s about two orders o f magnitude below the

carbon at low energies and about one order o f magnitude below at the

higher energ ies. The sum over a l l channels of the o r b i t in g cross sec

t io n va r ie s from about 20 to 200 m i l l ib a r n s over the measured range of

energ ie s. The magnitudes of these cross sect ions exceed those expected

from compound nucleus evaporation c a lc u la t io n s (Sha84b) by a fac to r of

ten. A r igo rous in te rp re ta t io n of these data w i l l be g iven in the next

chapter.

The van ish in g o f the entrance channel potentia l pocket has other

consequences, some of which we sh a l l now d isc u s s . The concept of

o r b i t in g was asoc ia ted in e a r ly s tud ie s (Bra77) with the observation of

enhanced cross sec t ion s and resonance -like behavior at la rge angles in

the e l a s t i c s c a t te r in g o f some ions. These, in our in te rp re ta t io n , form

a subset of the to ta l o rb i t in g process which in v o lv e s , in add it ion to the

ground s ta te , a l l excited and t r a n s fe r s ta te s e n e rg e t ic a l ly acce ss ib le

to the o r b i t in g in te ra c t io n . The o rb i t in g y ie ld comes from a narrow band

of p a r t ia l waves c lo se to the graz ing p a r t ia l wave fo r a l l £i n < •

MOTIVATION ! 38}

MOTIVATION

FIGURE 12

The upper panel shows the angu lar momenta fo r the g raz in g t r a je c

to ry as obtained from an op t ica l model c a lc u la t io n u s in g potentia l

parameters from (Sa t8 0 ). A f r a c t io n of t h i s angular momentum, as

determined by the s t i c k in g l im i t , goes in to the o r b i t in g complex.

The o r b i t in g angu lar momentum sa tu ra te s fo r the 28Si + 12C system

at 19h.

The lower panel shows the cross sec t ion s measured at 180 degrees

fo r the ground and f i r s t 2+ excited s ta te in the 12C + 28Si reac

t i o n . The data are from (Bar85).

dtr/

dfi

(mb/

sr)

d<r/

dcr

FIGURE 12

ORNL-DWG 8 5 -7 2 2 9

T "1 " "

---- ,2C ♦ 28 SiA L GRAZING ----- -----□ L OR 3ITING

<

A *A

* *A

,

a

A

AA

nO

D

□ □ 13 □ □ □ □ p o o □ □ c

Or °

1 1 1

__ 28S i ( 12C.12C )28Si —

— * • • «

* . * L' ^«a •

0 C.rr,= <8°°I :

H " * " A • • * J•••

' . • J • I

•

* •

•*

• « • / * 1•

•#•• ••«• •••i ^^ --------

2

X/

---------

•

r ^ v :

_ i ' « / *

V V j

•»••

/*•

* A • •

* <y <• A :

i• > % *• #•

m i

•

•%•

>

•»\

20 30 4 0 50 60

Ec.m.<MeV>

MOTIVATION 41

A f ra c t io n of the incoming angu lar momentum i s transformed into the

i n t r i n s i c sp in e x c ita t io n of the DMC. Hence, with in c re a s in g bombarding

energy, i t i s the s ta te s of h igher sp in and e x c ita t io n energy rather

than the low ly in g s ta te s that are most favored to be populated. This i s

the behavior seen in f i g . 7. Figure 12 shows the cro ss sec t io n s measured

at 180 degrees fo r the ground s ta te and f i r s t excited s ta te in carbon

(Bar85) in a 28S i + 12C in te ra c t io n . A lso shown are the graz ing angular

momentum and o r b i t in g angu lar momentum p lo tted as a function of

energy. These have been obtained from an op t ica l model c a lc u la t io n . I t

i s c le a r that fo r sj > 19, the o r b i t in g t r a je c to ry , in £-space, s t a r t s

moving away from the g raz ing t r a je c to ry . This i s re f le c te d as an abrupt

downturn in the back angle y ie ld s as shown in f i g . 12. In terms of the

pote n t ia l p ic tu re of f i g . 11, t h i s im p lie s that with in crea s in g energy,

the in te r a c t in g nucleons cannot be trapped in to a d in u c le ar con-

f i g u a t io n , with the two nuclei in th e i r ground s ta te s . The nuclei need

to be excited both in sp in and energy fo r such trapp in g to occur.

In the a n a ly s i s of fu s ion data fo r l i g h t systems, i t has long been

suggested that the cross se c t io n s at h igher energ ies can be l im ited by

the entrance channel nucleus-nucleus po tentia l (Mos85). I t i s only those

p a r t ia l waves that can become trapped, that can con tr ibu te to the fus ion

y ie ld . F igure 13 i s a schematic p lo t of the fu s ion cro ss sect ion as a.

fun ct ion o f the inverse o f the cm energy. Three reg ions are ind icated

where the cro ss sec t ion f i r s t increases with energy ( I ) , le v e ls o f f

( I I ) , and decreases ( I I I ) . The r ise in region I r e f le c t s the increase

with energy of the number of p a r t ia l waves c o n tr ib u t in g to the fus ion

process. The f la t t e n in g o f f in region I I r e f le c t s increased competition

MOTIVATION 42

FIGURE 13

A schematic p lo t o f the fus ion cro ss sect ion as a fun ct ion of the

in ve rse o f the cm energy.

CRO

SS

SECT

ION

(c

r)

FIGURE 13 43

ORNL-DWG 82-20725

.•fK-• r

MOTIVATION 44

front o rb i t in g processes. This i s a lso the region where the ro le of f r i c

t io n becomes important, fo r the h ighest p a r t ia l waves, in trapp ing the

in te r a c t in g nuclei in to a d inuc lear co n f ig u ra t io n . Region I I I has been

a t t r ib u te d to both entrance channel and compound nuc lear l im i ta t io n s to

fu s io n (d iscussed in fo l lo w in g chap ter). In the entrance channel

in te rp re ta t io n , t h i s drop in cross sect ion i s re la ted to the van ish ing

o f a pocket in the entrance channel nucleus-nucleus p o te n t ia l . In terms

o f angu lar momenta, fo r the 28Si + 12C in te ra c t io n , reg ions I , I I , and

I I I correspond to A in < 19, ^9 < A1n < 23, and Ain > 23 re sp e c t iv e ly .

Recent fus ion data o f Harmon et al_. (Har86), fo r the 28Si + 12C

show p re c ise ly the behavior ind icated in f i g 13 and have been

in te rpre ted as evidence fo r entrance channel l im i t a t io n s . They

found the c r i t i c a l angu lar momentum fo r fusion to be entrance c

dependent.

system,

have

hannel

So fa r , from stu d ie s of reaction products at backward ang les in

28Si + 12C, in form ation on the nuc leus-nucleus p o ten t ia l has been

extracted and used to exp la in a va r ie ty of phenomena observed in

o r b i t in g heavy ion re a c t ion s. We have a lso learned, through a study of

the moments of the energy spectra ( f i g s . 7-11) that such reactions l a s t

long enough to permit the e q u i l ib r a t io n of energy and angu lar momentum.

However, a l l the observations mentioned above are a l s o amenable to

in te rp re ta t io n as a r i s in g from the decay of a compound nucleus. Based on

the magnitudes of the observed back-angle y ie ld s fo r the 28Si + 12C

system, Shapira et_ al_. (Sha84b) had concluded that the y ie ld s were too

la rg e to be accounted fo r by compound nucleus evaporation and were

MOTIVATION 45

there fore a consequence of o r b i t in g . Ray jet a K (Ray85) have addressed

the same question through a study of the 28Si + 12C and 21+Mg + 160

systems, in an attempt to populate the same 'compound n u c le u s ', ^ C a , at

a f ixed e x c ita t io n energy and angu lar momentum through two d i f fe re n t

entrance channels. By f in d in g the r a t io of the 12C to 160 y ie ld s to be

d i f fe r e n t in the two re a c t ion s, they have concluded that these y ie ld s

come not from compound nucleus evaporation but from the decay o f a DMC.

Another way to d i s t in g u i s h betwen DMC and compound nucleus decay i s

through the measurement o f l i f e t im e s . A measurement o f the duration o f#

o r b i t in g in the 2*Wg + 12C case (Dun85, G la86), using a f lu c tu a t io n ana

l y s i s , y ie ld s times o f the order of 2 * 1 0 -21 secs. These are to be com

pared with c o l l i s i o n times of 1 0 " 22 secs, and compound nuclear

l i f e t im e s , ca lc u la te d from an expression in (Boh69)3 of 1 0 " 19 secs (see

f i g . 3 ).

The formation o f a compound nucleus i s by d e f in i t io n the re su lt of

the complete e q u i l ib r a t io n of the energy o f r e la t iv e motion, angu lar

momentum, and the shape degrees of freedom in the c o l l i s i o n between

ta rg e t and p r o je c t i l e n u c le i. The e q u i l ib r iu m shape of a compound

nucleus i s that o f a system o f nucleons in th e i r lowest po ten tia l energy

c o n f ig u r a t io n . DMC formation d i f f e r s in that the shape degree of freedom

i s not e q u i l ib ra te d . A l l o f the reaction dynamics o f d i s s ip a t io n occurs

in a system which m ainta ins a d in u c le ar shape. Within the cons

such a shape, energy and angu lar momentum are e q u i l ib ra te d . I t

expected that while evaporation from the compound nucleus resu

p re fe re n t ia l em ission of l i g h t p a r t i c le s , DMC breakup r e su lt s

em ission of more massive n u c le i. The mass d i s t r ib u t io n of prod

r a in t s o f

i s

t s in the

in the

jets

MOTIVATION

FIGURE 14

9

A p lo t of the adjusted Q-value of d inuc lear channels open to 28Si

+ 12C. The mass d if fe ren ce between the entrance channel 28S i + 12C

and each of the other channels have been adjusted by the

appropria te d if fe re n ce s in the Coulomb, nuclear and ce n tr i fu g a l

energ ies. A value £=23 has been chosen fo r t h i s p lo t because i t i s

the region in £ -space from which a preponderance of the o r b i t in g

y ie ld o r ig in a te s .

MeV

ORNL-DWG 85-18131

ADJUSTED Q VALUE OF DI NUCLEAR CHANNELS OPEN TO 28Si + 12C

50

45

40

35

30

25

T — 6 I I 1 1 =f=~17121 1 -1 6 I

---- 6 ^ = 2 3 _

---- 5---- 8

---- 10---- 10

---- 10 -----14---- 9---- 11 ----- 11 14

— 10 l9 — 3

__544 8 ----- 17 ----- 17

— ---- 13 ---- 1513

---- 15

---- 4---- 8 ---- 20 _

. -----12 ---- 16

THE NUMBERS BY THE LINES

I I 1

INDICATE

1 1

MASS NUMBER A 1

-J__ I I I2 3 4 5 6 7 8 9 10

CHARGE NUMBER Z

MOTIVATION

FIGURE 15

9A p lo t o f the adjusted Q-value of d in u c le ar channels open to 28Si

+ 11+N. The mass d if fe re n ce between the entrance channel 28Si + 14N

and each of the other channels have been adjusted by the

appropria te d if fe re n ce s in the Coulomb, nuclear and ce n tr i fu g a l

energ ie s. A value £=23 has been chosen fo r t h i s p lo t because i t i s

the region in .£ -sp ace from which a preponderance of the o r b i t in g

y ie ld o r ig in a te s .

50

45

40

® 35

30

25

ORNL-DWG 85-18130

ADJUSTED Q VALUE OF DINUCLEAR CHANNELS OPEN TO 28Si + ,4N

2 3 4 5 6 7 8 9 10CHARGE NUMBER Z

^ = 2 3 6 8

THE NUMBERS BY THE LINES INDICATE MASS NUMBER A,

emitted from compound nucleus decay shows no memory o f the entrance

channel, beyond the conservation of energy and angu lar momentum, and is

determined by phase space co n s id e ra t io n s. Equ ivalent in form ation on the

breakup o f a DMC is fragmentary as ye t , but i s e s se n t ia l to an

understanding o f the o rb i t in g process and of i t s connections with deep-

i n e l a s t i c s c a t te r in g and fu s io n . I f the e x it channel o r b i t in g y ie ld s can

be determined by phase space c o n s id e ra t io n s , t h i s would imply that such

react ion s l a s t long enough to a llow fo r the e q u i l ib r a t io n of mass and

charge flow.

De ta i led o r b i t in g data pe rta in in g to the y ie ld s and k in e t ic

energies of fragments in several e x it channels, measured over a wide

range of bombarding energies are cu rre n t ly a v a i la b le on ly fo r the 28S i +

12C system. These data, however do not provide com pelling evidence fo r a

phase space determination of the e x it channel y i e ld s . To obta in more

d e f in i t i v e data requires the formation of a DMC v ia an entrance channel

that i s not that most favored fo r breakup on energe t ic grounds. I t i s

fo r t h i s reason that we have se lected the 28Si + llfN system fo r study;

i t and the 28S i + 12C system are s im i l a r in to ta l mass but very d i f

ferent in terms of the number of e x it channels e n e r g e t ic a l ly a cc e s s ib le

at r e la t i v e ly low energ ies. Figure 14 shows the va lues of the potentia l

energy in several d inuc lear channels open to the 28S i + 12C to decay

in to . In order to obta in th i s p lo t , the ground s ta te mass d iffe renced

(Q -va lues) of each channel have been adjusted by the d if fe re n ce in

nuc lear, Coulomb and ce n tr i fu ga l energ ies between th a t channel and the

entrance 28Si + 12C channel. Figure 15 i s a s im i la r p lo t fo r the 28Si +

1**N system. The phase space a cc e ss ib le at each energy Ecm and angular

MOTIVATION | 50i

MOTIVATION 51

momentum £ to each of these channels fo r decay i s d i r e c t l y proportiona l

to the d if fe re n ce between Ecm and the potentia l energy. Therefore, based

on energy and phase space cons id e rat ion s the 12C e x it channel i s the

most favored fo r emission fo r both systems. I f the duration for o rb i t in g

i s sho rte r than the time required for mass e q u i l ib r a t io n , however, 12C

would be expected to be the most common product nucleus in the 28S i +

12C in te ra c t io n and l l fN in the 28S i + 14*N one. I f , however, the duration

of o r b i t in g exceeds the time required fo r mass e q u i l ib r a t io n , 12C would

be the most common produpt nucleus in both in te ra c t io n s .

In add it ion to important in form ation on the e q u i l ib r a t io n of mass,

a study of the 28Si + ll*N system should be useful in e lu c id a t in g the

ro le that the m icroscopic s tru cture of the c o l l i d in g nuclei may have on

the outcome of a c o l l i s i o n . Such information can be gleaned from the

d if fe re n ce s in the k in e t ic energies of the reaction products emitted

from t h i s system and the 28Si + 12C.

Having e s ta b lishe d WHY we need to study o r b i t in g phenomena in 28Si

+ 1I+N, we have to address HOW such a study should be done. I sh a l l p o s t

pone such a d isc u s s io n to the chapter e n t it le d EXPERIMENTAL PROCEDURE.

The fo l lo w in g chapter provides a r igo rous th e o re t ica l de sc r ip t io n of the

o r b i t in g process and e s ta b l i sh e s a connection between o rb i t in g and

THEORY

i

Th is sect ion w i l l be devoted p r im a r i ly to a d is c u s s io n of models

that assume, e ith e r e x p l i c i t l y or im p l i c i t l y , the formation" of a

d in u c le ar molecular complex (DMC) in the c o l l i s i o n between two heavy

ion s. Such theor ie s have been used in the past in attempts to understand

phenomena observed in molecular resonances (Erb85), deep in e la s t i c s c a t

te r in g (Vol76, Mat79, Nor74, Ayi76) and fus ion (Mos85, B ir79 , B ir81,

Van80, Bas73, Bas77, Bas74, Bas79, Hus85). In heavy nuc lear systems,

o r b i t in g phenomena have been studied under the rub r ic of f a s t - f i s s i o n

(Ng583) and q u a s i - f i s s i o n (Swi32). A d iscu s s io n of the connections bet

ween o r b i t in g , as d iscu ssed here, and these other p rocesses, w i l l be

presented in a la t e r chapter e n t it le d FROM FACT TO FICTION. A new model

i s presented, herein, ( S h i86a) that de sc r ibe s, s im u ltaneous ly , the pro

cesses of fus ion and o r b i t in g in terms of the formation and the evolu

t io n of a lo n g - l iv e d DMC. This model i s app lied to descr ibe extant data

fo r the 28Si + 12C system. This w i l l i l l u s t r a t e that the a v a i la b le data

can be in terpreted c o n s is te n t ly with an assumption of constra ined mass

and charge e q u i l ib r a t io n in o rb i t in g react ion s. The 28S i + 14N data

d iscu ssed la t e r in t h i s d i s s e r t a t io n w i l l provide unambiguous experimen

ta l evidence fo r such e q u i l ib r a t io n , and fu r th e r, a t e s t to t h i s theory.

A DMC formed in the in te rac t io n between two heavy ions often acts

as a doorway s ta te in the formation of a completely e q u i l ib ra te d com

pound nucleus. I t evo lves, during the e a r ly stages o f an in te ra c t io n ,

through the exchange of nucleons to d i f fe re n t c o n f ig u r a t io n s , always

assumed to be d inuc lear (see f i g . 16). In th i s model, each DMC has a

52

THEORY

FIGURE 16

A schematic representation of the processes o f o r b i t in g and

fu s io n . The o r b i t in g y ie ld s are emitted during the e a r ly stages of

an in te ra c t io n a f te r the e q u i l ib r a t io n o f energy, angu lar momen

tum, and mass. The shape degree of freedom i s s t i l l ' f r o z e n ' . The

process of fu s io n , as ind ica ted by dashed l i n e s , takes place on a

r e la t i v e ly longer t im esca le . The compound nucleus can be accessed

by a change of shape d i r e c t ly from d in u c le ar c o n f ig u ra t io n s and

a ls o through p a r t i c le exchange (not shown). The l a t t e r mode i s ,

in our op in ion , r e la t i v e ly improbable.

EVAPORATION RESIDUES

THEORY i 55

p r o b a b i l i t y to fragment d i r e c t ly in to the e x it channel having a c lo se ly

re la ted mass and charge r a t io , re su lt in g in the o r b i t in g y ie ld . The

doorway s ta te s that do not so fragment are then assumed to re lax , in the

l a t t e r stages o f an in te ra c t io n , in to a compound nuclear con f igu ra t ion

and are id e n t i f ie d as responsib le for the so -c a l le d fu s ion y ie ld . A

c a lc u la t io n of the d e ta i le d evo lution of the d inuc lear shape into that

of a compound nucleus i s a complex problem and i s circumvented in our

model, as w i l l be d iscussed .

There has been some specu lat ion concerning the c a lc u la t io n of

fu s ion cross se c t io n s through intermediate doorway s ta te s ( Van84,

Vol85) and one e f f o r t in th i s s p i r i t (Hus85). The problem encountered in

doing such c a lc u la t io n s i s i l l u s t r a t e d in f i g . 17. The cond it ion s fo r

formation of a DMC are determined in the e ar ly stages of a c o l l i s i o n by

the entrance channel 'sudden' nucleus-nucleus po tentia l shown schemati

c a l l y at the top o f the f igu re (a lso see f i g . 6). This potentia l

corresponds to a d in u c le ar shape. Fusion re su lt s from the change of such

a d inuc lear shape to a mononuclear shape. As the shape evo lves, so does

the e f fe c t iv e nuclear p o te n t ia l . The lower part of f i g . 17 i s a schema

t i c representation of such an 'a d ia b a t ic ' mononuclear p o te n t ia l ; whether

or not a system remains fused i s determined by th i s p o te n t ia l . A ca lcu

la t io n of the evo lu t io n , with time, of the 'sudden' po tentia l to the

' a d i a b a t i c ' one i s a n o n - t r iv ia l exerc ise . In the formalism presented

here, t h i s i s p re c ise ly the problem I circumvent. I assume that such an

evo lu t ion of the DMC does indeed occur, and that any system that remains

trapped in a d inuc lea r con f igu ra t ion fo r a s u f f i c i e n t l y long time, even

t u a l l y fuses. Fusion, in t h i s in te rp re ta t io n , i s there fore the long

l i fe t im e component of the trapped DMC.

I

THEORY 56

FIGURE 17

A schematic diagram of the 28Si + 12C entrance channel d inuc lear

'sudden' po ten t ia l (top in se t ) and the lt0Ca 'a d ia b a t ic ' mono

nuc lear p o ten t ia l (bottom in se t ) p lo tted as a funct ion of

d is ta n ce . The eq u i l ib r iu m c o n f ig u ra t io n ' l i v e s ' at the minimum of

such p o te n t ia ls (R=R^). The s c i s s io n point corresponds to the top

o f the p o ten t ia l b a r r ie r (R=Rg).

FIGURE 17

O R N L - D W G 86 - 8134

57

THEORY 58

Only recently have experimental fus ion (Har86) and o rb it in g

(Sha84b) data become a v a i la b le over a wide range of e x c ita t io n energies

fo r the 28Si + 12C system. The y ie ld s from both these processes are

found to be l im ite d at the same to ta l angu lar momentum. This observation

has been re la ted , in the previous chapter, to the van ish in g of a local

minimum in the entrance channel nucleus-nucleus p o te n t ia l . By being able

to account fo r both the fus ion and o r b i t in g data t h i s model e s ta b l ish e s

a connection between these two processes. Th is, we be lie ve , i s the f i r s t

time an attempt i s being made to c a lc u la te s im u ltaneously both the

fu s ion and o rb i t in g cro ss sec t ion s.

A f u l l d e sc r ip t io n of the c o l l i s i o n between two n u c le i , of course,

in vo lve s the dynamical and s t a t i s t i c a l aspects of the process. I

r e s t r i c t myself now to a d isc u s s io n of the s t a t i s t i c a l aspects alone and

desc r ibe the evo lut ion of a DMC w ith in the framework of an extended d i f

fu s ion model. Some dynamical aspects w i l l be d iscussed la t e r in t h i s

chapter. A set of coupled d i f fu s io n equations, one d e sc r ib in g the

coup lin g between d in u c le ar s ta te s ( v e r t ic a l arrows in f i g . 16), and the

other d e sc r ib in g the coup ling between d inuc lear s ta te s and fragmentation

channels (ho r izonta l arrows in same f i g . ) are so lved in order to explain

the measured fus ion and o rb i t in g y ie ld s in the 28Si + 12C in te rac t io n .

m

As shown in f i g . 16, a DMC couples to both d ire c t ex it channels and

to compound nuclear channels. The compound nucleus can a lso couple to

the e x it channels by evaporation and f i s s i o n but t h i s i s not considered

in t h i s form ulation because such y ie ld s are expected to be small com

pared to o r b i t in g y ie ld s . A s t a t i s t i c a l treatment fo r the coupling

THEORY 59

between the d in u c le ar s ta te s and the d ire c t e x it channels y ie ld s a

t ra n sp o rt equation fo r the fragmentation p ro b a b i l i t y . The p ro b a b i l i t y

P £ (N ,Z ,t ) of f in d in g a b inary e x it channel with a given o rb ita l angular

momentum % and fragmentation product (N,Z) at time t i s determined by

dt V N , Z , t ) = ^ V D , t ) V ( N , Z ) ' FV N’Z , t ) I r (N,Z) +0

where ^ i s the width for going from a DMC to the e x it channel

in c lu d in g the fragmentation product (N,Z) and fo r t ie

inverse process. The macroscopic v a r ia b le s d e f in in g the d inuc lear s t a

te s are D = (N ,Z ,E ,K ) where N and Z descr ibe the charge and mass of the

e x it channel in c lu d in g the fragmentation product (N ,Z ) , E the e x c ita t io n

energy and K the p ro ject ion of the i n t r i n s i c angu lar momentum along an

a x is perpend icu lar to the reaction p lane. n^(D,t) i s the occupation

p r o b a b i l i t y of a co n f igu ra t io n in the DMC as a function of time and is

desc r ibed , in the weak coup ling l im i t , by a second tran spo rt equation.

n * (D , t ) = ^ WDD' {d D n4( D ' , t ) - dD* n*(D , t ) } (4)

where dp i s the leve l density of the DMC in the d inuc lear con f igu ra t ion

D and Wqq1 i s the t r a n s i t io n p ro b a b i l i t y between d inuc lear con

f i g u r a t io n s . A s o lu t io n to equations 3 and 4 as a function of time then

prov ides a general d e sc r ip t io n of a l l heavy ion react ion s proceeding

through the formation of a DMC. '

Our s tu d ie s of o rb i t in g in the 28Si + 12C (Sha84b ), and pre lim inary

s tu d ie s in the 28S i + 14N (Sh i84) in te ra c t io n s show that the f in a l k ine

t i c energies o f the fragments are independent of the center of mass

an g le , that a l l the fragments have the same i s o t r o p ic angular

THEORY 60

d i s t r i b u t i o n s , and that the d i s t r ib u t io n of y ie ld s i s governed by

a v a i la b le phase space (Sha84a). These observations suggest "that the

observed fragments are emitted from an eq u i l ib ra te d DMC. We there fore

incorporate t h i s information in to the framework o f our formalism and

work in the equ il ib r ium l im i t of the tran spo rt equations 3 and 4. Hence,

P£ (N,Z) = I nAq (D) r (N jZ) +D (5)

where n®q(D) i s the equ il ib r ium occupation p r o b a b i l i t y o f the d inuc lear

s ta te s and can be w ritten as

n eq(D) =

1 I d i (N , , Z , ;R)N 1Z 1

(6)

R = Rm (N ,Z ,£ )

The widths in eq. 5 can be expressed as products o f a t r a n s i t io n

m atrix and a phase space fa c to r , using the Fermi golden ru le as

r D+(N,Z) = l<D|N,Z>|2 dt (N ,Z;RB ) (7)

and

r (N,Z)+D ° l<N»Z|D>l2 dA(N,Z;RM) (8)

With the added assumption of coupling on ly between d in u c le a r s ta te s and

e x it channels having the same charge and mass asymmetry, the ra t io of

the decay width and the inverse width in eq. 5 reduces to

(9)d . (N ,Z ; Rr )

P* (N’ Z) = y d (N 1 , Z ' ;R T

N 'Z ' 1 M

(Z ,Z ' > 2)

where d£ (N,Z;Re) and d^ (N ' , Z ' ;Rm) are the level d e n s i t ie s of the DMC at

e x c ita t io n energies evaluated at the top of the p o ten t ia l b a rr ie r R=Rg

and the potentia l minimum R=R(v|, re sp e c t iv e ly (see f i g s . 6 and 17). The

d e n s ity of s ta te s i s ca lcu la ted at each energy E, u s ing the Fermi level

d e n s ity expression as (Boh69)

THEORY 61

d j ( N , Z ; R ) = C j

exp[2{a(E - U j (N ,Z ;R ) }1/2](10)

{E - Uj (N ,Z ;R )}2

where, a i s the usual leve l density parameter taken here as 1/8 times

the mass number o f the DMC and Cj i s a constant. Equation 10 i s an

approximate expression fo r the leve l density o f the two fragments.

U j(N ,Z , ;R ) denotes the poten tia l energy surface (PES) o f the DMC ca lc u

la ted in the s t i c k in g l im i t as

I t 0 (N ,Z ;R ) i s the to ta l moment of in e r t ia o f the DMC. Q(N,Z) i s the

ground s ta te Q-value of the entrance channel with respect to the

fragmentation (N ,Z ). Vn (N ,Z , ;R ) and Vc(N,Z;R) are the nuclear and

Coulomb p o te n t ia ls . Equations 10 and 11 imply an alignment o f the

o r b i t in g n u c le i , as has been observed recently (Dun85, Gla84, Ray86).

The observable q u a n t it ie s can now be ca lcu la ted u s ing eq. 9. The

to ta l fragmentation p ro b a b i l i t y in to an e x it channel with a product

(N,Z) ( o r b i t in g cro ss sec t ion ) i s ca lcu la ted by summing over a l l p a r t ia l

waves up to an £max (defined in eq. 16) as

Uj(N,Z;R) = Vn(N,Z;R) + VC(N,Z;R) +-

*maxP(N.Z) = £2- I (24+1) Pt (N,Z)

£=0(12)

The average k in e t ic energy in the e x it channel i s a f r a c t io n of the

to ta l ro ta t io n a l energy in the DMC and i s ca lcu la ted as

where f = I r e l (N ,Z ;R b ) / I t o t (N ,Z ;R B ) •

THEORY 62

The fus ion p r o b a b i l i t y i s obtained for each p a r t ia l wave by su b trac t in g

from un ity the p ro b a b i l i t y for d ire c t fragmentation. The fa s ion c ro s s

sect ion i s given as

•*maxa I ( 2 * 1 ) [1 - P ] (14)T k 2 A=0 *

where the to ta l fragmentation p r o b a b i l i t y fo r each p a r t ia l wave i s

obtained by summing over a l l p o s s ib le fragm entations as

P , = I P »(N»Z) (15)N,Z

I t i s important to note th a t eq. 14 i s d i f fe r e n t from the usual

u n i t a r i t y cond it ion in that the sum over p a r t ia l waves i s re s t r ic te d to

•*max* Th is upper bound on the A summation i s a v i t a l in gred ien t in t h i s

model and im p lie s that i f the system cannot become trapped in a

d in u c le a r c o n f igu ra t io n , there w i l l be ne ither o r b i t in g nor fusion

y ie ld .

Some of the dynamics o f the in te ra c t io n can now be d iscussed in

terms of the co n d it ion s required fo r the formation o f a DMC. A DMC i s

formed fo r a l l p a r t ia l waves A up to a c r i t i c a l a n g u la r momentum Ac r fo r

which the PES of equation 11 has a pocket. P a r t ia l waves greater than

Acp cannot be trapped and lead to e l a s t i c , q u a s i - e l a s t i c , and deep in e

l a s t i c p rocesses.

At low energies t h i s cond it ion i s rea lized when the incoming ions

have enough energy to surmount the entrance channel po te n t ia l b a r r ie r

V ji(N ,Z ;R ). Th is po tentia l i s s im i l a r to the PES g iven by eq. 11 but

conta in s only the o rb ita l angu lar momentum and the r e la t iv e moment o f

i n e r t ia of the DMC. The two con d it ion s can be formulated in terms o f a

THEORY 63

FIGURE 18

The f in a l k in e t ic energ ies of o r b i t in g products from the 28Si +

12C re a c t ion . The data are from (Sha84b).

FIGURE 18 64

ORNC-O W G 8 3 - ( T J T 2

28S i + ,2C ORBITING

C E N T E R OF MAS S E N E R G Y (MeV)

THEORY 65

c r i t i c a l rad ius fo r trapp ing R .. Trapping occurs at an energy E fo r a l l

£ up to an £ when r max

E > V (Rt ) and £ < £ (16)£max max cr

The trapp ing rad ius i s defined in analogy to (Bas74) as the p o s it io n of

the entrance channel b a r r ie r Rg for a l l V£(N,Z;R) e x h ib i t in g a pocket,

and i s smoothly in te rpo la ted to the value R = Rj + R2 fo r a l l VA(N ,Z ;R )

without a pocket.

We now apply t h i s model to a d e sc r ip t io n o f the fu s ion (Har86,

Hug81, Les82, Gar82) and o r b i t in g (Sha84b) data measured fo r the 28Si +

12C system. In t h i s c a lc u la t io n we choose fo r the nuc lear potentia l the

em pirica l prox im ity po ten tia l of Bass (Sha84b, Bas74). The Q-values are

obtained from mass ta b le s and the moments of in e r t ia are approximated by

t h e i r r i g i d body va lues. The only ad ju stab le parameters in t h i s c a lc u

la t io n are, there fore , those that determine the nuc lear potentia l and

the leve l de ns ity . The poten tia l parameters can be f ixed by using

e ith e r the fu s ion or the o r b i t in g data. The l a t t e r are chosen here.

The f in a l k in e t ic energies of the o rb i t in g fragments e s s e n t ia l l y

g ive us the he igh ts of the potentia l b a r r ie r s fo r each of these channels

as a function of energy. These data, as p lotted in f i g . 18,can there

fore be used to f i x the potentia l parameters used in t h i s c a lc u la t io n .

The parameters are adjusted as in (Sha84b) to de sc r ib e the features seen

in the data. The jogs in the c a lc u la t io n simply r e f le c t the i n i t i a t i o n

o f new h igher p a r t ia l waves in the c a lc u la t io n .

F igure 19 compares the p red ic t ion s fo r the ab so lu te cross sect ions

THEORY 66

FIGURE 19

The o r b i t in g c ro s s - s e c t io n s fo r the C, N and 0 channels in the

28Si + 12C re a c t ion . The data are from (Sha84b)

Ii

MIL

LIB

AR

NS

( 0 0 .0

(0.0

(.0

0.(

0.0 (

ORNL — DWG 85 — 17367

2 8 S i + < 2 C O R B I T I N G C R O S S S E C T I O N

25 30 35 4 0 4 5 50 55 60

C E N T E R OF M A S S EN ERG Y (MeV)

o>

FIGURE 19

THEORY

FIGURE 20

The known energy le v e ls o f a few d in u c le ar channels open to

28Si + 12C react ion . The leve l spectra have been taken from

(Led67). •

FIGURE 20 69

THEORY 70

The fus ion cro ss sec t ion s

from (Har86, Hug81, Les82

FIGURE 21

for the 28Si + 12C system. The data are

, and Gar82).

ORNL — DWG 85 — 17368

2 8 Si + 1 2 C F U S I O N C R O S S S E C T I O N

1400

1200

1000

8 0 0

60 0

4 0 0

200

0

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

(CENTER OF MASS ENERGY )”” 1 (MeV) - 1

1.....

LESKCGARYHUGIHARM(

r

▲B

) ' ' '

A☆ DN

z " 1----- ^

/

r A<m 82

V

1 1 - i — r f I ■ I I I I I I — T---r— 1— I- 1 I T' 'I I I I I T i l l T T M I I

THEORY 72

fo r o r b i t in g with the data. In p r in c ip le , an adjustment o f leve l den

s i t i e s for each channel can be used to modify the pred icted re la t iv e as

well as the ab so lu te o r b i t in g y ie ld s . The standard Fermi gas expression

with g loba l parameters as expressed in eq. 10 i s chosen here. With th i s

param etr iza tion I account c o r re c t ly for the c ro ss se c t io n s o f the two

s t ro n ge st channels 0 + Mg and C + S i . The pred icted N + A1 y ie ld i s low,

but an examination of the actual leve l scheme of the odd-odd nucleus

26A1 shows that such a g loba l leve l d e n s ity pa ram etr iza t ion , i f correct

fo r say the C + Si channe l, w i l l underpredict the leve l density fo r the

N + A1 at a l l energ ie s. The known energy le v e ls in the case of a few

nucle i are shown in f i g . 20 to i l l u s t r a t e t h i s p o in t . S ince the N + A1

channel i s weak, any improved param eterization o f i t s leve l density w i l l

have a n e g l i g ib le e f fe c t on the model p re d ic t io n s fo r the other chan

n e ls and in t h i s f i r s t version of the model we have not undertaken the

very su b s ta n t ia l e f f o r t that would be required fo r such a param etriza

t io n .

F igure 21 compares our equ iva len t p re d ic t ion fo r the fus ion cro ss

se c t ion in 12C + 28Si with a v a i la b le data. The three reg ions o f the

fu s io n c ro ss se c t io n , the increase , s a tu ra t io n , and decrease as

demonstrated by the recently measured data (Har86) are reproduced in

q u a n t i t a t iv e fash ion (see f i g . 13).*

We now examine some of the d e t a i l s of our c a lc u la t io n . I have, as

mentioned p re v io u s ly , chosen to use the Bass p rox im ity po ten t ia l (Bas74)

and a f ixed leve l density parameter. Any param etr iza tion o f the poten

t i a l should be able to reproduce two q u a n t i t ie s ; namely the value o f the

THEORY 73

p oten t ia l at the minimum U(R = Rf/|) and at the outer maximum V(R = Rb ).

By p re d ic t in g c o r re c t ly the value of the poten tia l at t h i s maximum, the

model p re d ic t s the value of the experim entally measured k in e t ic energy.

The Bass p o te n t ia l , while adequate fo r the carbon, n itrogen and oxygen

channels leads to an overpred ict ion of the k in e t ic energy in the boron

channel (see f i g . 18). For more asymmetric channels, the d isc repanc ie s

are even g rea te r . The problems here have to do with the way that the

nuc lear ra d i i are parametrized in the Bass proxim ity p o te n t ia l .

The magnitude o f the o r b i t in g y ie ld s are determined by the value o f

the p o ten t ia l at i t s minimum (see f i g s . 14 and 15). Hence, once the

value of the po te n t ia l at the maximum has been f ix e d , we can, in p r in

c ip le , vary the value of the po ten t ia l at the minimum to f i t the

o r b i t in g c ro ss sect ion at a p a r t i c u la r energy. In t h i s manner we could

p o s s ib ly a r r iv e at a be tte r param etrization o f the p o te n t ia l . In the

Bass p o ten t ia l param etr iza t ion , when the k in e t ic energ ies are overpre

d ic ted as in the case of the asymmetric channels, the corresponding

o r b i t in g y ie ld s are a ls o overpredicted. However, s ince these channels

are weak, they do not s i g n i f i c a n t l y modify the con c lu s ion s we have drawn

so fa r from our c a lc u la t io n s and we have not considered i t worthwhile,

as y e t , to attempt a more complex param etr iza tion .

I t i s important to emphasize at t h i s juncture that ’the nucleus.**"-

nucleus p o ten t ia l we obtain by f i t t i n g the o r b i t in g and fus ion data i s

merely a param etriza t ion . There s t i l l remains a small ambiguity

regard ing the rad iu s at which the maxima and minima of the poten tia l

occur. Caution should there fore be exercized in u s ing such p o te n t ia ls in

THEORY 74

c a lc u la t io n s p e r ta in in g to the evo lu t ion of the d in u c le a r to a mono

nuc lear shape.

In ad d it ion to the fa c to r s ju s t d iscu ssed , we have the freedom

represented by a leve l density parameter. A leve l d e n s ity param etriza-

t io n u s ing a s in g le constant can e a s i l y be shown to f a i l to p red ic t the

o r b i t in g y ie ld s in channels in v o lv in g odd-odd nuc le i (see f i g . 19). A

part of the problem i s that we are d e a lin g here with low i n t r i n s i c e x c i

t a t io n in the DMC. An in c lu s io n of p a ir in g co rre c t ion s to the leve l den

s i t y param etriza tion w i l l there fore f a i l to r e c t i f y the problems in

p re d ic t in g the y ie ld s in the weakest e x it channels. I d e a l l y , the leve l

d e n s ity should be ca lc u la te d by performing a convo lu t ion in te g ra l over

the known energy le v e ls o f the two nucle i c o n s t i t u t in g the DMC. In the

form alism presented in t h i s chapter I have used an approximation to t h i s

i n t e g r a l .

We can now compare our model with some others that have been deve

loped to de scr ibe deep i n e l a s t i c processes. In a study o f many nucleon

t r a n s fe r re a c t ion s (Vol76, Mik77) i t had been concluded that the y ie ld s

in the e x it channels could be parametrized us ing an exponential depen

dence on the mass d if fe re n ce s between the entrance and the e x it chan

n e ls . An improved f i t to the data was obtained i f the d if fe ren ce s in the

Coulomb and the c e n tr i fu g a l fo rces were a ls o taken in to account. Th is

observat ion f in d s expression w ith in my model in equations 10 and 1 1 .

The charge d i s t r ib u t io n in the e x it channels has a lso been studied

(Mat79) in terms of the penetration through a b a r r ie r on a c l a s s i c a l l y

trapped t r a je c to ry . Express ions s im i l a r to equations 9, 10, and 11 were

THEORY 75

used in order to descr ibe the reaction product charge d i s t r ib u t io n from

the 170MeV 40Ar + 108Ag reaction . The evaporation residue cross sect ion

at t h i s energy was a ls o estimated. Coulomb, c e n t r i fu g a l and nuc lear fo r

ces were accounted fo r in ob ta in ing the nuc leus-nuc leus p o te n t ia l . An

important d if fe re n ce between the c a lc u la t io n I have presented and the

two ju s t d iscussed i s that while eq. 9 in vo lve s the leve l density at two

r a d i i R^ and Rg , (V o l76) and (Mat79) do th e i r c a lc u la t io n at Rg alone.

Th is d i s t in c t io n i s c ru c ia l in a study o f l i g h t nuc lear systems.

Total o r b i t in g c ro ss se c t ion s can a lso be ca lc u la te d u s ing t r a je c

to ry models (B ir79 , Van80) by summing the y ie ld s o f those p a r t ia l waves

that are trapped s u f f i c i e n t l y long to produce y ie ld at backward ang les

( Hui86) . In these models, the o rb i t in g y ie ld comes from a band o f par

t i a l waves ( M » 1 ) in between those co n tr ib u t in g to fu s ion and to deep

i n e l a s t i c s c a t te r in g . The models support no attempt to c a lc u la te the

y ie ld s in the d i f fe re n t e x it channels. In the model I have presented,

the o r b i t in g and the fus ion y ie ld come from the same band o f p a r t ia l

waves, with most o f the o r b i t in g y ie ld coming from the h ighest p a r t ia l

waves w ith in the band. Th is l a t t e r view i s supported by both the fus ion

(Har86) and o r b i t in g (Sha84b) data. Both processes are shown to be

l im ite d at the same angu lar momentum. A lso , the w idths o f the o r b i t in g

spectra (see f i g . 7) appear to correspond to M ~ 3h.m

Models that succeed in d e sc r ib in g the three reg ions o f the fus ion

cro ss sect ion shown in f i g . 13 are based p r im a r i ly e i th e r on po tentia l

pocket (Bas74, B ir79 , Van80) or c r i t i c a l d is tance (Gla74, Ga74, Bas74)

c r i t e r i a . In the t r a je c to ry models (B ir79 , Va80) t h i s d e sc r ip t io n i s

THEORY 76

incorporated by in te g ra t in g the c l a s s i c a l equations of motion inc lud in g

d i s s ip a t io n . Fusion occurs whenever the ions are trapped w ith in the

pocket o f a nuc leus-nuc leus p o te n t ia l . In the model I have presented, in

c o n tra s t , t rapp in g i s a necessary but not s u f f i c ie n t cond it ion for

fu s io n . The processes of o r b i t in g and fusion compete fo r the trapped

y ie ld . C r i t i c a l d is tan ce models vary mostly in the way the c r i t i c a l

rad iu s fo r fu s ion i s parametrized. I f the in te ra c t in g ions reach t h i s

rad iu s they are presumed to fuse. The ca lc u la te d energy dependence o f

the fus ion and o r b i t in g cro ss se c t io n s in the energy region I I o f f i g .

13 depends on the way the c r i t i c a l rad iu s i s defined. In the Bass model

(Bas74) t h i s rad iu s i s a lte red d isco n t in u o u s ly from the region of the

p ote n t ia l b a r r ie r to the sum o f the h a l f density rad ii o f the

i n te r a c t in g n u c le i . In the model for fus ion and o r b i t in g presented here,

a c r i t i c a l rad iu s fo r trapp ing Ry i s obtained by smooth in te rp o la t io nt

u s in g a constant rate o f change of the in te ra c t io n rad iu s with angular

momentum (dRy / dJ^p) w ith in the l im i t s used by the Bass model. In our

model as emphasised p re v io u s ly , trapp ing does not imply fu s ion . I t a lso

bears emphasis that in our model strong f r i c t i o n i s assumed to be pre

sent at a f ixed c r i t i c a l rad iu s as in the c r i t i c a l d is tan ce models.

T h is d i f f e r s from the t r a je c to ry c a lc u la t io n s where a sm a lle r f r i c t io n a l

fo rce i s presumed to act over a la r g e r rad ia l range.

4+'-Fusion c ro ss se c t io n s have a lso been predicted on the b a s is o f ’ a

co n s id e ra t io n of the evo lu t ion of a d in u c le ar system (Hus85, Mat79). In

the in te rp re ta t io n of (Mat79), the compound nucleus i s treated as ju s t

another fragm entation channel. In the model o f (Hus85), the fusion cro ss

se c t ion i s c a lc u la te d u s ing a two step compound model. D e t a i l s of these

THEORY 77

c a lc u la t io n s are s t i l l forthcoming.

In ad d it ion to the entrance channel models ju s t d iscu sse d , there

are those (Lee81, Van79, Van81) that are based on the assumption th a t i t

i s a compound nuclear l im i t a t io n rather than an entrance channel one

that determines the sa tu ra t io n of the fus ion cross se c t io n (reg ion I I

of f i g . 13). These models are based on the hypothesis that in l i g h t

systems, the compound nucleus i s unable to carry the the a v a i la b le angu

l a r momentum at a p a r t ic u la r e x c ita t io n energy because of a lack of

a v a i la b le high sp in le v e ls . In heavier systems t h i s l im i t a t io n i s

assumed to a r i se from the angular momentum ( c e n t r i f u g a l l y ) induced

f i s s i o n of the compound nucleus. A d isc u s s io n o f the m erits and demerits

o f the entrance channel and compound nuclear approaches as p e r ta in in g to

the 28Si + 12C system can be found in (Har86).

In conc lu s ion , the model I have presented in t h i s chapter has been

very successfu l in accounting s im u ltaneously fo r the processes of

o r b i t in g and fu s ion . Th is model w i l l be app lied in the chapter e n t i t le d

RESULTS AND INTERPRETATION to describe my new data fo r the 28Si + ll*N

in te ra c t io n . P o s s ib le extensions of the model to account fo r phenomena

such as f a s t - f i s s i o n w i l l be presented in the f in a l chapter.

Appendix 1 l i s t s ad d it iona l information p e rta in in g to the c a lc u la -m

t io n s described in t h i s chapter.

Our e a r l ie r chapter e n t it le d MOTIVATION d iscussed WHY we need to

study o rb i t in g react ion s in the 28Si + system. Th is chapter

d isc u s se s HOW such a study was done. 28Si beams between 100 and 170 MeV,

provided by the ORNL HHIRF Tandem acce le ra tor f a c i l i t y were used to bom

bard a 14N superson ic gas je t ta rge t o f areal d e n s ity 10ug/cm2. Target

l i k e reaction products (3 < Z < 10) were detected at labora to ry angles

between 3 and 7 degrees corresponding to center o f mass angles between

165 and 175 degrees in the k in e m a t ica l ly reversed react ion ( 1*tN beam on

a 28Si t a r g e t ) . Complete energy spectra fo r the va r io u s reaction pro

ducts were measured us ing the experimental arrangement shown in f i g . 22.

Reaction products were detected at the focal plane o f an Enge s p l i t - p o le

spectrograph us ing a hybrid io n iz a t io n chamber (H IC) detector system. I

sh a l l now d is c u s s , in d e t a i l , some aspects o f the experiment, namely,

the beam tra n sp o rt , the superson ic g a s - je t ta rg e t , the detector system,

and the data a c q u is i t io n and processing systems.

A modified version of the Aarhus rad ia l e x trac t ion Penning source

( A l t 86) was used to provide negat ive ly charged 28S i beams fo r in je c t io n

in to the HHIRF Tandem acce le ra to r (Jon84). Typical currents provided by

the source during the course of the experiments were in the range of 800

to 1600 na. The acce le ra to r was operated at terminal p o te n t ia ls in the

range 14.3 to 17.8 MV, to provide 28Si beams at the ta rge t with in ten

s i t i e s in the range 20 to 80 pna, and charge s ta te s in the range 6+ to

9+. Since the experiment required high in te n s i ty beams o f low

divergence (phase space acceptance ~ 0.2 ir mm m sr ) , i t was found

EXPERIMENTAL PROCEDURE j

78

EXPERIMENTAL PROCEDURE: APPARATUS 79

FIGURE 22

The experimental arrangement used fo r the 28Si + ll*N experiment.

Q l , 2, 3,4 are quartz viewers. S j and S 2 are ro ta tab le c i r c u la r

s l i t s ad ju s tab le to 0.75, 1.75, 3,|and 25 mm diameters. 0 ^ 2 , 3 are

d i f f e r e n t ia l pumping s l i t s . SA and GA are s o l id and gas absorbers

re sp e c t iv e ly . Pj and P2 are p o s i t io n sens ing w ire s .

GENERAL LAYOUT FOR EXPERIMENTS WITH GAS JET TARGET

ORNL-DW G 83-19298R2


advantageous to run the acce le ra to r u s ing a gas s t r ip p e r in the terminal

rather than a f o i l s t r ip p e r .

The beam l in e between the bending magnet and the ta rge t s ta t io n i s

about 8m in length and has four pumping s ta t io n s ( three 8- in ch A ir

Products cryogenic pumps and one ion pump), a quadrupole magnet about 3m

from the ta rg e t , and a stee rer about 2m from the t a r g e t . A four-jaw

ad ju s tab le rec tangu lar s l i t system, set u su a l ly at 2mm x 4mm, i s used

to de fine the beam energy and to provide e le c t r i c a l feedback for acce

le r a to r s t a b i l i z a t i o n . F igure 22 shows two ad d it ion a l s l i t s S i and S£ of

c i r c u la r c ro ss sec t ion and diameter 0.75mm. These s l i t s ensure that the

acce lerated beam does not s t r ik e the d i f f e r e n t ia l pumping s l i t s 0^ 2 , 3*

Beam p r o f i l e d ia g n o s t ic s are provided by four quartz viewers ( Q i ,2 ,3 ,4)*

I t has been my experience that when the acce le ra to r beam i s focussed

onto Qi and Q4 and the "walk" removed, few a d d it io n a l adjustments are

required in order to send the beam, through the s l i t s S i and S2, to the

t a r g e t . The present ease in tun ing i s a re su lt o f an intense e f fo r t on

my part, with the help o f o thers, to a l i g n the centers of the s l i t s ,

fo c u s s in g and d ia g n o s t ic elements on the beamline to w ith in 200 pm o f a

f ixe d l in e of s i g h t . Add it iona l beam d ia g n o s t ic s are provided in the

ta rg e t region v ia beam current in te g ra t io n . In p ra c t ic e , the currents

in teg ra te d on the e l e c t r i c a l l y i s o la te d aperture Di are minimized to

about 3% of the current in tegrated on the body of the gas je t ta r g e t ,

which serves as the beam dump. This adjustment i s e s se n t ia l to a

measurement of abso lu te cross se c t io n s , and to measurements at very fo r

ward ang les.

EXPERIMENTAL PROCEDURE: APPARATUS

FIGURE 23

A schematic top view of the superson ic gas je t t a r g e t .

FIGURE 23

ORNl OWG 83 10644R

TANDEM BEAM LINE

HIGHQUALITYOPTICALWINDOW

OPTICALWINDOW

ENGE MAGNET ENTRANCE

SLIT

ORNL SUPERSONIC GAS JET TARGET SCHEMATIC TOP VIEW

EXPERIMENTAL PROCEDURE: APPARATUS

FIGURE 24

A schematic s ide view of the superson ic gas je t t a r g e t .

FIGURE 24

O RN L-D W G 83-19293R

C R Y O G E N IC PUMP

C R Y O G E N IC PUMP 1400 L/s

(STAGE 4)

The 1I+N ta rge t fo r the experiment was produced u s in g the HHIRF

superson ic gas je t ta rge t f a c i l i t y (Sha85a,b). Schematic top and s ide

views of the apparatus are shown in f i g s 23 and 24 re sp e c t iv e ly . There

are four d i f f e r e n t i a l l y pumped volumes shown as I , I I , I I I , and IV

pumped by two 2 -s tage Roots blowers and two cryopumps, re sp e c t iv e ly . The

ta rg e t i s a sheet o f gas that expands through a convergent-d ivergent

Laval nozzle in to region I . The dimensions o f the ta rg e t in the region

o f the in te ra c t io n are 3 x 3 x 1.5 iren. The areal d e n s ity o f the ta rge t

can be co n tro l le d by vary ing the gas pressure at the in le t to the

nozzle , and fo r n itro ge n , can be adjusted con tinuous ly in the reg ion 1

to 15 pg/cm2. The nozzle assembly can be t r a n s la te d and rotated to per

mit op t im izat ion o f the ta r g e t - io n beam in te ra c t io n . The ion beam enters

the region of the ta rge t through a s e r ie s of d i f f e r e n t ia l pumping s l i t s

and i s stopped on a tantalum d i s c w ith in volume I I . Reaction products

are detected through an e x it aperture assembly mounted on an inner

s l i d i n g seal that can be rotated in the angu lar range 0 to 60 degrees.

The body of the gas je t i s shown by the heavy l in e s in f i g . 24. The

sc a t te r in g chamber supports the outer s l i d i n g seal which i s connected

through e le c t r i c a l i s o l a t o r s to the Enge magnet entrance s l i t . The body

o f the gas je t i s i s o la te d e l e c t r i c a l l y from the four pumps. The en t ire

apparatus there fore serves as the Faraday cage fo r beam current in te g ra

t io n . A d d it ion a l norm aliza t ion inform ation i s provided from the output

o f a monitor detector located at 45 degrees to the beam d ire c t io n . The

flow of the ta rge t gas (a mixture of 99% N2 and 1% Xe) i s regulated by

an MKS 250A pressure c o n t r o l le r connected to a Baratron pressure t r a n s

ducer (Sha85a). The Xe in the ta rge t i s added to prov ide inform ation to


permit a norm alization of the product y ie ld s to the y ie ld s of e l a s t i

c a l l y scattered p a r t i c le s detected in the monitor de tector. When the gas

j e t i s in operation and the in le t pressure i s 600 t o r r , the pressures in

the four volumes are 1.38, 0.35, 3.9x10" **, and 3.4x10" 6 t o r r respec

t i v e l y , with the pressure in the beam l in e always below 3x10- 8 t o r r . The

p u r ity o f the ta rge t i s dependent on the p u r ity o f the in le t gas. Since

the ta rge t m ateria l i s being pumped away con t inuous ly , there i s no ca r

bon or other ta rge t bu ild -u p . Th is i s a ub iqu itous problem with s o l i d

t a r g e t s which a ls o impose l im i t s , because of charge bu ild -u p and thermal

damage, on the beam in te n s i t y that can be used. A la ck o f contaminants

in ta rge t s i s c ru c ia l to experiments such as those reported herein where

continuum spectra are being measured.

The reaction products are focussed by an Enge s p l i t pole

spectrograph (Spe67) in to a hybrid io n iz a t io n chamber (H IC) (Sha80b).

The spectrograph enhances detection e f f ic ie n c y by p ro v id in g both ver

t i c a l as well as horizonta l fo cu ss in g . The de tect ion s o l id angle i s

determined at the entrance to the spectrograph by a m u lt ip le s l i t

system. The maximum usable s o l id angle o f 2.4 msr i s l im ite d by the e x it

aperture of the g a s - je t assembly. The rad ius o f curvature o f the o rb i t

on which a p a r t i c u la r nuclear species o f a p a r t i c u la r energy, mass and

atomic charge i s bent i s uniquely determined by the c h a r a c t e r i s t i c s of

the spectrograph, in p a r t ic u la r the magnetic f i e l d . The f i e ld strength

i s measured by an NMR magnetometer (SENTEC type 1000) using two H2O pro

bes capable of measuring f i e ld s in the range 4-21 KG. With an

appropria te f i e ld s e t t in g , reaction products can be focussed in to the

HIC.

EXPERIMENTAL PROCEDURE: APPARATUS : 87\


FIGURE 25

Schematic s id e view of the hybrid io n iz a t io n chamber (H IC )

(Sha80b). A. P o s i t io n s e n s i t iv e p roportiona l counters.

B. Reject p roportiona l counter. C. a E e lec trode . D. Io n iz a t io n

chamber F r isch g r id . E. Grid c a p a c i t iv e ly coupled to the cathode

p ro v id in g the energy s i g n a l . F. Cathode s t r i p s . G. Cathode H.

Counter entrance window.

CDGX?

nocn

ORNL DWG 79-8259R

00CO

The atomic number of a detected ion i s determined by measuring the

to t a l energy deposited, and the rate at which energy i s deposited by

that ion in t r a v e r s in g a region conta in ing gas (w ith in the H IC). F igure

25 shows the HIC. The two p o s it io n s e n s i t iv e wires la b e l le d A provide

the inform ation needed to determine the rad ius of curvature of a par

t i c u l a r o r b i t . The to ta l energy s ign a l i s obtained from the cathode,

la b e l le d G, which forms part o f a Faraday cage, the M e t a l l i c s t r i p s ,

la b e l le d F, which help maintain a uniform f i e ld g rad ie n t, and an a lu -

minzed Mylar window, la b e l le d H, through which ions enter the detector.

The energy lo s s (AE) in form ation i s obtained from the segmented anode C.

B i s a veto wire de tect ing p a r t ic le s that are not stopped w ith in the

counter. With the E, AE, and p o s it io n information provided by the detec

t o r , p a r t ic le s can be uniquely id e n t i f ie d by energy E, atomic mass A,

and atomic number Z. Some operationa l parameters fo r the detector are

l i s t e d in appendix 2.

The s i g n a l s from the HIC are fed to p ream p lif ie rs before being sent

through a patch panel from the experimental to the counting room. F igure

26 i s a schematic diagram of the e le c tro n ic s used in the experiment* .

The wire s i g n a l s ( l e f t and r ig h t from wires 1 and 2) are fed in to t im ing

s in g le channel ana lyse rs (TSCA). P o s i t io n information i s obtained from

each wire from the time to amplitude converter (TAC) by measuring the• i i‘

.• in d if fe re n ce in r i s e times of the s i g n a l s coming from the two ends o f the

wire. The energy s i g n a l s are fed together with the outputs of the TACs,

to ana log to d i g i t a l converters (ADC) in a CAMAC crate. An "EVENT" i s

t r ig g e re d when there is e ith e r a s ign a l from the HIC cathode or the

monitor de tector. A fo u r - fo ld lo g ic un it i s used to generate strobes fo r

EXPERIMENTAL TECHNIQUE: APPARATUS 90

EXPERIMENTAL PROCEDURE: PROCESSING 91

FIGURE 26

A schematic diagram of the NIM e le c t ro n ic s used in the data

p rocess in g .

A - A m p li f ie r , PA - P ream p lif ie r , TSCA - t im ing s in g le channel

a m p l i f ie r , TFA - Timing f i l t e r a m p l i f ie r , TAC - Time to amplitude

converter, D isc - D isc r im in a to r , G&D GEN - Gate and de lay genera

to r , ADC - Analog to d i g i t a l converter, Cl - Current in te g ra to r ,

GL - Gated la tc h , ZC - Zero c ro s s in g .

The s i g n a l s are: Wires W1 and W2. L and R re fer to l e f t and r ig h t

re sp e c t iv e ly . Energy s i g n a ls a E I , a E2, and E. Monitor s ig n a l MON.

m . L . d ' i ' « ' V

W1L APA

^ A T S C A

l > H s 'T A C

■ v c >

zc

T S C A

1A O C P I

F R O M E V E N T

H A N D L E R

I S C A L E R

1S C A L E R V E T OT L E V E L A D A P T E R <0

ro

FIGURE 26

the TACs and a gated la tch which i s a b i t pattern record o f the detec

to r s that f i r e d . Strobes are a lso generated fo r the ADCs to do th e i r

convers ion. An 'event* s ign a l i n i t i a t e s an "event hand le r" in the CAMAC

cra te to prepare to process data. The "event hand ler" then reads

appropr ia te ADCs, s c a le r s , and la tche s and puts the va r iou s parameters

together in to a standard format. A f i r s t - i n , f i r s t - o u t (F IFO) r e g is t e r

i s subsequently f i l l e d with data fo r continual t r a n sm is s io n to the

Perkin Elmer 3230 host computer. When t h i s t ran sm iss ion i s tak in g p lace,

the "event handler" provides a 'bu sy ' s ign a l which i s used as a veto fo r

the fo u r - fo ld lo g ic un it and b locks the p roce ss ing o f data. Appropriate

de lays are provided in each o f the s ign a l l in e s to ensure that the

s i g n a l s a r r iv e at the CAMAC cra te w ith in a time window o f 2 psec. Each

o f the p o s i t io n and energy s i g n a l s are a ls o connected to s c a le r s as are

the outputs o f the beam current in te g ra to r . A d d it ion a l s c a le r s 'vetoed '

by the "event handler" 'bu sy ' are used to determine the "dead time" o f

the experiment.

W ithin the host computer, the data are processed by a u ser-w r it ten

a c q u is i t io n ta sk . A l l "events" are recorded d i r e c t l y onto magnetic tape.

They are a lso made a v a i la b le to a monitor ta sk re s iden t in the computer

core that produces h istograms on d is k . These h istogram s are then

a c c e s s ib le to a d isp la y task that can produce an ’on l i n e ' d i sp la y o f

any of the experimental parameters. A lso res ident in the computer are

several other se rv ice ta sk s (Mi 185) that help in the s t a r t i n g , s topp ing,

and m onitoring o f the data ta k in g p rocess. The magnetic tapes can sub

sequently be 'rep layed ' to enable the extract ion o f useful in form ation

from the raw experimental data.

EXPERIMENTAL PROCEDURE: PROCESSING i 93

EXPERIMENTAL PROCEDURE: OPTIMIZATION 94

Having d iscussed some of the experimental hardware and the data

a c q u is i t io n process, I sh a l l now focus on some of the optim ization and

preparat ion that has to be done to enhance the data tak in g c a p a b i l i t ie s

o f t h i s experimental arrangement. Count rates ach ievab le in the exper i

ment are l im ite d by the host computer at ~ 10,000 counts/sec . and by the

HIC at ~ 2,000 co u n ts/se c .. These rates are ro u t in e ly reached while

measuring e l a s t i c s c a t te r in g at forward an g le s . S ince the presently

reported measurement invo lves a study o f forward angle y ie ld s of t a r g e t

l i k e reaction products, processes which have cross se c t io n s about three

or four orders of magnitude below the e l a s t i c a l l y scattered events, i t

becomes d e s ira b le to prevent the e l a s t i c a l l y scattered 28Si nuclei from

ente r ing the de tector. This a llow s us to enhance the data tak in g rates

o f useful in form ation by a l low in g us to work with th ick e r ta rge ts and

h igher ion beam currents than would otherwise be p o s s ib le . The kinema

t i c s of react ion s u s ing p r o je c t i le s heavier than ta rg e t s forces the

react ion products in to the forward hemisphere. Their v e lo c i t ie s are com

parab le to those of the p r o je c t i l e . Since the ta rge t 14N, in t h i s

experiment, i s only h a l f as massive as the p ro je c t i le 28S i , one can take

advantage of th e i r d i f fe re n t energy lo s se s in pass ing through an

absorb ing medium to prevent the 28Si ions from s t r i k in g the HIC. This is

accomplished by p la c in g s o l id and gas absorbers in fron t of the detector

as shown in f i g . 22. While the 28Si ions are stopped in the ab so rber^ ,,

the l i g h t e r t a r g e t - l i k e reaction products go through to the HIC. The

e f fe c t iv e absorber th ickness can be varied by changing the pressure of

the gas in the gas absorber so as to bare ly stop the 28Si n u c le i. This

ensures detect ion of the l i g h t e r n u c le i , at high e f f ic ie n c y , over the

widest p o s s ib le dynamic range.


The HIC i s 30 crns deep and 40 cms wide. I t i s mounted at 45 degrees

to the spectrograph focal plane. In t h i s p o s i t io n , the t r a je c to r ie s of

the p a r t i c le s entering the detector are approximately normal to the

entrance window. With absorbers placed in front of the HIC, the energy

re so lu t io n of the detector i s reduced because t r a je c t o r ie s in the h o r i

zontal plane at s l i g h t l y d i f fe re n t inc ident angles have d i f fe re n t path

lengths through the absorber and hence su f fe r d i f fe re n t energy lo s se s .

Th is problem would have been acute i f the detector were not operated in

the normal incidence con f igu ra t io n (there i s a cos© dependence on the

path length and the f ra c t io n a l v a r ia t io n o f cose i s h igher at 45 than at

0 degrees). I t was found d e s ira b le to operate with h igher gas pressures

in the io n iz a t io n chamber than in the absorber. Th is ensured that the

detector and the absorber windows were deflected in the same d ire c t io n

thereby m inim iz ing the d if fe rence s in path lengths o f t ra j 'e c to r ie s

f a l l i n g on d i f fe re n t v e r t ic a l p o s i t io n s on the de tector window.

The reaction products from the re su lt of an in te ra c t io n between a

p r o je c t i l e and ta rge t are emitted with a range o f atomic charge s ta te s

q. The actual charge sta te d i s t r ib u t io n i s determined by the ta rge t

th ickness and the energy o f the ion spec ies. On p a ss in g in to the Enge

spectrograph, depending on the atomic charge s ta te , an ion with a given

energy i s bent in to o rb i t s of d i f fe re n t r a d i i . S ince the HIC i s 40 cms

wide, on ly some o f these o rb i t s are detected. This creates a problem

with e f f ic ie n c y . F igure 27 is a p lo t of the energy versus the momentum

of Carbon, N itrogen, Oxygen , and F luorine nuclei detected in the HIC

fo r the 28Si + l l fN reaction . In a l l f ig u re s , the upper group of three

l in e s corresponds to the charge s ta te q = Z and the lower group to


FIGURE 27

A p lo t showing the e f fe c t s of adding an A1 s t r ip p e r f o i l at the

entrance to the spectrograph. The lower four f ig u re s were taken

without t h i s f o i l , and the upper four f ig u re s with the f o i l . In

each f i g u r e , the upper group of three l in e s corresponds to charge

s ta te q=Z, and the lower group to q = Z - l . Within each group, the

in d iv id u a l l in e s correspond to d i f fe re n t isotopes of the same

element. The ad d it ion of the f o i l moves the y ie ld from the lower

charge s ta te to the h igher.

FIGURE 27

O R N L-Owe 85-9756

140 MeV 28Si + ,4N 6 = 7°

CARBON NITROGEN "

OXYGEN FLUORINE

MOMENTUM MOMENTUM

CARBON NITROGEN

>oCEUizUJ

MOMENTUM MOMENTUM

OXYGEN FLUORINE

>*oCEUJzU J

MOMENTUM MOMENTUM


q = Z - 1. Within these groups, the in d iv id u a l l in e s correspond to the

d i f fe re n t isotopes of the same element. In the lower four f ig u re s , i t i s

c le a r that the y ie ld i s d is t r ib u te d over two charge s ta te s . A lso , by

lo ok ing at the energy axes of these p lo t s i t i s evident that the HIC i s

not wide enough to capture the whole dynamic range of both charge s t a

te s . Hence i t i s d e s ira b le to induce a l l reaction products with the same

Z to have the same charge s ta te . This can be accomplished with a ce r ta in

degree of success by p lac in g a s t r ip p e r f o i l at the entrance to the

spectrograph. The upper four p lo t s of f i g . 27 show the re su l t s of such a

m o d if ic a t io n to the experimental arrangement using a 100 yg/cm2 A1 f o i l .

I t i s evident that the bulk of the i s o to p ic y ie ld s are detected in th e ir

h ighest (q = Z) charge s ta te . Such a procedure i s needed only in

s i t u a t io n s where the ta rge t used i s not th ick enough to produce

eq u i l ib r iu m s t r ip p in g of the p r o je c t i le and reaction products.

When the ta rge t i s pos it ioned o p t im a l ly , the ion beam s t r ik e s i t at

the de n s ity knot c lo se s t to the e x it of the Laval nozzle (Sha85a). The

nozzle has to be pos it ioned at the beginning o f each experiment; in our

case, t h i s was done using the ion beam i t s e l f . The nozzle was f i r s t

lowered well below the p o s it io n of the beam and the gas je t was turned

on. The e l a s t i c a l l y scattered p a r t i c le s were detected in the HIC. The

nozzle was then ra ised g ra d u a l ly u n t i l we saw e l a s t i c s c a t te r in g from,

the nozzle m a te r ia l. The nozzle was then lowered by about h a l f a m i l l i

meter.

An adjustment has a lso to be made to determine the re la t iv e angle

readings of the gas je t apparatus e x it aperture and the Enge magnet


entrance aperture (see f i g . 23). The narrowest (0.11 deg.) magnet aper

ture was chosen for th i s measurement. Once aga in , e l a s t i c events were

detected in the HIC with the magnet angle set at 5 deg.. The gas je t

e x it aperture was then moved so as to maximize the rate at which reac

t io n products were detected in the HIC. The d if fe re n ce in the sca le

read ings corresponding to the p o s i t io n s o f the two apertures was noted,

and maintained in subsequent angu lar s e t t in g s .

I t was found during the course o f such adjustments that the e f f i

c iency of the HIC var ied with the p o s i t io n where the ion entered the

counter. Th is has been a t tr ib u te d to a sagg in g o f the detector mount.

The support was such that the center o f the le f t s id e o f the detector

(as seen by the ion s) was below the reaction plane. P a r t i c le s from an

alpha p a r t i c le source o f known in t e n s i t y , pos it ioned at the ta rge t lo ca

t io n were moved across the detector by vary ing the magnetic f i e ld . The

number of p a r t i c le s detected per second was then determined at several

f i e l d s e t t in g s . The measurements were repeated a f t e r mechanical jack

screws were used to leve l the de tector. I t i s c le a r from f i g . 28 that

t h i s procedure e lim inated the 20% change in de tector e f f ic ie n c y , with

p o s i t io n , along wire W1 (denoted PI in f i g . 22).

The spectrograph focusses ion t r a je c to r ie s such that they converge

onto a focal plane and d iverge beyond i t (see f i g . 22 ). In reg ions c lo se

to the edge of the detector, there are ion t r a je c t o r ie s that succeed in

pass in g the p o s it io n wires but subsequently h it the s ides o f the

counter. Such ions do not deposit th e i r whole energy in the HIC. Figure

29 p lo t s the energy of the ions detected as a fun ct ion of th e i r p o s i t io n


FIGURE 28

E f f ic ie n c y o f the HIC as a function of p o s i t io n a long the front

wire (W l). P lotted on the Y -ax is i s an alpha p a r t i c le detection

rate ( p a r t i c l e s / s e c . ) . The data show the e f fe c ts o f a sagg in g

detector mount.

RA

TE

FIGURE 28

O A N L-O W G 6S-I7813

500 1000 1500POSITION CHANNEL

EXPERIMENTAL PROCEDURE: OPTIMIZATION

FIGURE 29

Detected energy of monoenergetic ions p lo t ted as a fun ct ion of

th e i r p o s i t io n on wire W1 in the HIC. The data demonstrate edge

e f f e c t s .

ENER

GY

CH

AN

NEL

FIGURE 29

0 500 1000 1500 2000WIRE 1 CHANNEL


along wire Wl. I t i s c le a r that we are beginning to see edge e f fe c t s in

the E data below channel 450 and above channel 1450. Such e f fe c ts are

not found seen in the a E data because the corresponding e lectrodes are

in the front of the counter. By ga t in g with software on the f i r s t w ire,

we can d isca rd events where the inc ident ions h i t the s ide of the

counter. Data i l l u s t r a t i n g t h i s phenomenon w i l l be shown in the next

chapter.

Several other parameters were determined in order to maximize data

ta k in g e f f ic ie n c y ; I present some of t h i s in form ation in the form o f a

rec ip e . The computer codes used in these c a lc u la t io n s are described in

(Mi 185).

1. Decide on the reaction channels to be s tu d ie d .

2. Do a c a lc u la t io n of the reaction kinematics to determine the

energies o f the reaction products (over expected range of e x c i t a

t io n e n e rg ie s ) .

(code used: KINEQ)

3. Determine the th ickn ess o f the HIC entrance window and absorbers

(windows and pressure in the gas absorber) to stop the e l a s t i c a l l y

sca tte red ion s .

(codes used: ABSORB, STOPX) ^> *

4. Determine the gas pressures required in the HIC in order to stop

the reaction products.

(codes used: ABSORB, STOPX)


5. Choose magnetic f i e ld s to center the most probable Q-values of the

reaction products in the HIC (range of d istance RDIST along the

foca l plane ~13 to 60 cms).

(code used: FATRUMP)

6. Determine e lectrode vo ltages to be used in the HIC at each of the

pressure s e t t in g s (see appendix 2).

RESULTS AND INTERPRETATION

Th is sect ion w i l l be devoted to a d e sc r ip t io n of how we e x trac t,

from raw experimental data, useful information such as the cross se c

t io n s and k in e t ic energies of the reaction products of o rb i t in g . In the

process, sources of experimental d i f f i c u l t y and e rrors w i l l be pointed

out. We w i l l then in te rpre t the re su lt s as evidence fo r the observation

o f mass e q u i l ib r a t io n .

The f i r s t experimental measurement I sh a l l de sc r ibe invo lves a

determ ination of the th ickness of the 14N / Xe ta rg e t . This i s

accomplished by de tect ing e l a s t i c a l l y scattered p a r t i c le s emitted from

an in te ra c t io n between a 28S i ion beam and the ta r g e t . The sm a lle st

entrance aperture on the magnet was used fo r t h i s measurement. The

magnet and the detector were energized op t im a lly in order to detect the

e l a s t i c a l l y scattered p a r t i c le s . F igure 30 shows the y ie ld s o f such 28Si

ions p lo tted as a function of p o s it io n along the fron t wire in the HIC.

Four atomic charge s ta te s of 28S i , id e n t i f ie d to be q = 10+,11+,12+ and

13+, are shown. The two peaks fo r each o f the charge s ta te s correspond

to s c a t te r in g from the N? and the Xe c o n s t i tu t in g the t a rg e t . The lack

in re so lu t io n o f the 10+ y ie ld i s a consequence o f edge e f fe c t s . Such

spectra were measured at 130, 140 and 160 MeV 28S i lab o ra to ry bombarding

energ ie s. By summing over the charge s ta te y ie ld s in the peaks

corresponding to the two ta rge t components, under the assumption of■T"

Rutherford s c a t te r in g , the ta rge t th ickness was determined to be 2.81 x

1017 atoms/cm2 fo r N2 and 1.38 x 1015 atoms/cm2 f o r Xe. The measured

r e la t iv e abundance of n itrogen to xenon atoms was 204:1; very c lo se to

106

RESULTS 107

FIGURE 30

Spectrum o f e l a s t i c a l l y scattered 28Si nuclei from a 28S i + li+N

in te ra c t io n . The channel numbers o f the maxima are used in con

junct ion with in form ation on the Enge magnet o p t ic s in order to

obta in a c a l ib r a t io n , in mm, of the p o s i t io n sensing w ires.

CO

UN

TS

FIGURE 30 108

5600

4200

2800

1400

0

ORNL-DWG 85-17147

130 M eV (28Si,2 8 Si) 0 L =5deg

10+

III

T ~

12' ID 1SUM = 119497

N-

13

0 300 600 900 1200 15(?0 1800POSITION (arbitrary units)

RESULTS 109

the expected r a t io of 200:1. The abso lu te e rror in these measurements

was le s s than 10% and includes con tr ib u t ion s from both the variance of

detector e f f ic ie n c y with p o s it io n along the front wire and any error

introduced by inexact beam current in te g ra t io n . The var iance of detector

e f f ic ie n c y we a t t r ib u te to an in s u f f i c ie n t width, in the v e r t ic a l d i re c

t io n , o f the HIC absorber window fo r t r a je c to r ie s with t h e i r focus fa r

removed from the lo ca t io n of the p o s it io n sensing wire. The ta rge t i s

free from contaminants and i t s th ickness i s known not to vary with time.

As mentioned in the previous chapter, we can e a s i l y sa tu rate the

data tak in g c a p a b i l i t ie s o f the HIC by a llow ing the e l a s t i c a l l y s c a t

tered 28S i to enter the detector. S ince the ta rge t th ickn ess i s known,

we no longer need to detect the e l a s t i c events in order to be able to

normalize the reaction cross sec t ion s to the e l a s t i c . We can therefore

introduce a su i t a b le combination of gas and s o l id absorbers in front of

the HIC to prevent the 28Si from entering the de tector. The HIC pressure

and the vo ltage s o f a l l the e lectrodes need then to be ra ised in order

to detect the products o f o rb i t in g in te ra c t io n s . F igure 31 shows spectra

o f o r b i t in g products detected on the fron t and rear p o s i t io n w ires. Not

a l l p a r t i c le s that succeed in pass ing the fron t wire manage l ikew ise

past the second. We should r e c a l l , at t h i s juncture, that the segmented

AE anode l i e s between the p o s it io n sensing wires (see f i g . 25). Hence,

not a l l p a r t ic le s that produce a AE s i g n a l , produce a W2 s i g n a l . This

w i l l be demonstrated la t e r in th i s chapter.

F igure 32 shows the y ie ld s of o rb i t in g products p lo tted as func

t io n s of th e ir energy and energy lo ss as detected in the HIC. A low

RESULTS

FIGURE 31

Spectra o f o r b i t in g y ie ld s detected on the front and rear p o s it ion

sens ing wires in the HIC. The sca le on the p o s i t io n ax is g ives an

unca lib rated channel number.

CO

UN

TS

ORNL-DWG 85-17152

10E3

1000

100

10

010E3

1000

100

10

0

100 MeV 28Si+14N 6 L =5deg

WIR E 2 SUM=4ID 2

10759

iiVP

\

. J l l\

__ l l . u l

Wl RE 1 SUM = 4ID 1

0758

jk

, . -Jill

11 1

« ki A

0 300 600 900 1200 1500 1800POSITION

RESULTS t

FIGURE 32

Spectra of o r b i t in g y ie ld s p lotted as functions o f energy and

energy lo s s as detected in the HIC.

ORNL-DWG 85-17149

100 MeV 28Si+14N 0L=5deg

180

120

l a )

low

AE,

PRESS

RAW

URE FOI_D OVER

1 2 0

60

O

AE,N

GATED

B -.0

.

xM. _ tPi \jc. tV*

J A )

a e 2 RAW

n 4

y f e ? . ■

0 -.41 ■ ..

(</)

CMUJ<

GATED

M I.

60 120 180 240 0 60 120 180ENERGY LOSS (arbitrary units)

pressure fo ld -ov e r i s ind icated fo r the raw aE I carbon y ie ld . This a r i

ses because the pressure of gas in the HIC i s not adequate to stop the

carbon ions with the h ighest energ ies, f u l l y w ith in the counter. Spectra

a and b have su b sta n t ia l background counts. These a r i s e because of a

decrease in the measured E s ign a l at the edges of the counter as

d iscu ssed in f i g . 29. By in troduc ing a software gate between wire chan

ne ls 450 and 1450, the spectra are improved s i g n i f i c a n t l y as shown in

panels c and d.

We can then draw gates in software to d i s t in g u is h between the

var iou s elements to obta in spectra such as those shown in f i g . 33. This

f i g u r e shows the nitrogen y ie ld p lo tted as functions o f energy, and

p o s i t io n along the front wire. There are two groups o f three l in e s

corresponding to the nitrogen being detected with the atomic charge s t a

te s 7+ and 6+. The y ie ld i s concentrated in the h igher charge s ta te , as

expected, because of the presence of a s t r ip p e r f o i l at the entrance to

the spectrograph. The dynamic range of p a r t ic le s detected in the HIC are

l im ite d by two fa c to r s ; namely the d ispe rs io n of the magnet and the

pressure in the HIC. The f i r s t fa c to r a r i s e s because of the f i n i t e width

o f the HIC. Below channel 90, and above channel 400 on the p o s it io n ax is

in the spectrum shown, there are no counts because these represent the

l im i t s of the software gate imposed to account fo r the edge e f fe c ts on

the E s i g n a l , as d iscussed in f i g . 29. For the n itrogen spectrum o f f i g .

33, t h i s m an ifests i t s e l f as a low energy c u to f f fo r the 7+ charge sta te

y ie ld . For the 6+ y ie ld , however, t h i s i s a high energy cu to f f . This i s

one reason why, at each energy, we have to c o l le c t data at d if fe re n t

magnetic f i e ld s e t t in g s in order to detect o p t im a lly , the d i f fe re n t e le

ments. Before I d iscu ss pressure c u to f f s , I should po int out that the

RESULTS ! 114

RESULTS

FIGURE 33

The Z-gated energy vs wire p o s it ion spectrum o f o r b i t in g products

fo r the n itrogen channel in the 28Si + 11+N reaction . The p os it ion

a x is in t h i s f ig u re p lo t s d is tan ce , in m i l l im e te rs , a long the

fron t w ire, from an unspecif ied o r ig in . The p o s it io n information

i s obtained from a c a l ib r a t io n using the p o s it io n channel in fo r

mation from f i g . 31.

O R N L - D W G 8 5 - 1 7 1 5 1

100MeV14N(28Si,14N) SL= 5 deg

CHARGE STATE 7 +

FIELD HIGH ENERGY CUT OFF

A

VCHARGE STATE

6 +

FIELD LOW ENERGY CUT OFF

FOCUSED

DEFOCUSED H,GH^ f£E£ ty RE1 1

CUT OFF

400 2 0 0 30 0 4 0 0

POSITION (arbitrary units)5 0 0

RESULTS 117

p o s i t io n spectra are defocussed at the high energy end of the 7+ y ie ld

and focussed at the low energy end. This has to do with the re la t iv e

p o s i t io n of the foca l plane of the spectrograph and the plane of the

p o s i t io n sensing wire. These two planes in te rse c t c lo se to channel 400,

and are at an angle of about 45 degrees to each other.

The reaction products go through several la y e rs of energy absorbing

m ateria l before entering the HIC. Some products, such as the e la s t i c

y ie ld , are stopped before they enter the HIC. Th is a lso happens to the

y ie ld s of some of the lower energy products of o r b i t in g react ion s. Even

i f these react ion products do manage to enter the counter, not a l l of

them depos it enough energy in the HIC to permit unambiguous iden

t i f i c a t i o n o f th e ir charge and mass. They are lo s t in the low energy

fo ld -o v e r of the E vs aE spectrum ( f i g . 32). I f , however, the pressure

of gas in the HIC i s not s u f f i c ie n t to stop the p a r t i c le s w ith in the

counter, we observe a high energy fo ld over as shown in f i g . 34. The

in d iv id u a l l in e s corresponding to the d i f fe re n t iso topes of the same

element overlap , making a separat ion of th e i r y ie ld s ambiguous. This

fo ld -o v e r a ls o a f fe c t s the energy s i g n a l , fo rc in g us to extract energy

in form ation from the p o s it io n s i g n a l . Th is can be accomplished using

magnet c a l ib r a t io n inform ation.

Shown in f i g . 35 are the p ro je c t io n s along the energy and posit^en

axes of the 7+ l l*N y ie ld of f i g . 33. D isc re te maxima are observed in the

energy spectrum that are washed out in the p o s it io n spectrum because of

the e f fe c t s of fo cu ss in g in the spectrograph. We can, in p r in c ip le , use

the p o s i t io n inform ation from wires W1 and W2 to c a lc u la te what the

RESULTS ! 118

FIGURE 34

Sectrum of Oxygen y ie ld s from a 28Si + 1I+N in te ra c t io n p lo tted as

fun ct ion s o f energy and wire p o s i t io n . The f igu re shows the

e f fe c t s o f a high energy fo ld -ov e r because the HIC does not have

enough gas pressure to stop the oxygen ions w ith in the detector.

240

160

80

0

0 100 200 300 400-P O S ITION (arbitrary units)--------------- '

t

ORNL-DWG 85-17146

140 MeV 4N (28Si,,60) eu = 5deg

LOW PRESSURIl FOLDOVE: r

t

L J

9

* - V .■I" _ * .

i

RESULTS 120

FIGURE 35

P ro je c t io n along the energy and p o s i t io n axes of the 1‘*N y ie ld

w ith in the gate.

ORNL-DW G 85-17148

100 MeV 14N (28Si,14N) eL = 5 deg

120

(/>

100 § 1003>»o

e soX )

o

50 5 cr in zUJ

60

40

V\

M

r

A N-*■ ? S L \ ^v p v

•

% /

100 200 3 0 0 400

POSITION (arbitrary units)

RESULTS 122

p o s i t io n spectrum should look l ik e on the focal p lane. F igure 36 shows

the p o s it io n spectra of the n itrogen y ie ld s of f i g . 34. A lso shown are

the ca lcu la te d angle and focal plane spectra o f the same y ie ld s . These

are obtained by 'ray t r a c in g ' . In th i s procedure, the p o s it io n in fo r

mation from the two w ires, fo r a p a r t ic u la r t r a je c to ry , are used to see

where such a t r a je c to ry in te r se c ts the focal plane. These points of

in te r se c t io n are then used in determining the corresponding focal plane

spectrum. I t i s c le a r that such a procedure produces p o s i t io n spectra

that show maxima ju s t l i k e the energy spectrum of f i g . 35. I t i s a lso

c le a r from f i g . 36 that i t i s fo r only those t r a je c to r ie s that have

both front and rear wire s i g n a l s that the 'ray t r a c in g ' procedure i s

a p p l ic a b le . I t i s fo r t h i s reason that we cannot use the focal plane

spectra to determine c ro ss sect ions and k in e t ic energ ies of reaction

products. We are forced, there fore , to use the inform ation provided by

the fron t wire fo r t h i s purpose.

F igure 37 shows the y ie ld of l l fN nucle i p lotted as functions of

e x c ita t io n energy. These spectra are very s im i la r to those obtained fo r

the 28Si + 12C measurement. The d isc re te maxima can be id e n t i f ie d with

the e x c ita t io n of energy le v e ls in 28Si and ^ N . I t i s from a study of

the moments of such spectra that we have e s ta b l ish e d the presence of

o r b i t in g processes in the 28Si + ll*N in te rac t io n (Sh i84, Sha85b). Thesem

spectra have been obtained from pro ject ion s onto the energy a x is , as was

done in f i g . 35.

Figure 38 shows p ro ject ion s onto the p o s it io n a x is from spectra

s im i l a r to f i g . 35, at several labora to ry bombarding energ ie s, for the

RESULTS

FIGURE 36

l l t N y ie ld s p lo tted as functions o f: ( ID42) Wire 1 p o s i t io n , (ID43)

Wire 2 p o s i t io n , ( ID44) opening angle subtended by ion t r a je c

t o r i e s , ( ID45) P o s i t io n on a focal p lane. The focal plane and

ang le spectra are ca lcu la ted by 'ray t r a c in g ' .

COUN

TS

O R N L -D W G 85 -1 7150

100

1

100

1100

50

100 MeV14N(28Si,14N) 6L=5deg1

FOCAL PL_ANE it SLID 45

JM = 1789

ANGLE

A SID 44

JM = 1789

WIRE 2 y\ SIID 43

JM= 2189

WIRE 1

if ^ni fID 42

LI M= 2189L0 100 200 300

POSITION (arbitrary units)400

f>0

FIGURE 36

RESULTS ; 125

FIGURE 37

Y ie ld s o f l l fN nucle i from the 28S i + 14N in te ra c t io n p lo tte d as

fu n ct ion s o f e x c ita t io n energy. The spectra are shown fo r labora

to ry bombarding energies between 100 and 130 MeV.

FIGURE 37

ORNL-DWG 85-18129

,4N (28Si, W N) 28Si 0 LA b = 5°

30 20 10 0

EXCITATION ENERGY (MeV)

12C channel. The to ta l counts in such spectra were then normalized by

the to ta l current in tegrated during the corresponding measurements, in

order to obta in d i f f e r e n t ia l c ross se c t io n s .

F igure 39 shows the an g le - in te g ra te d abso lute o r b i t in g cross sec

t io n s fo r 12C nuclei p lotted as functions of Q- value. These spectra

were obtained from spectra such as those o f f i g . 38, using a non - l ine ar

c a l ib ra te d reb inn ing procedure. The o s c i l l a t i o n s in the spectra are an

a r t i f a c t o f t h i s procedure. I t can be shown, through a study of the mean

values of such spectra , that we are observing the e f fe c t s o f angular

momentum l im i t a t io n on the formation of the 28Si + ll*N di nuclear mole

cule as had been observed in the 28Si + 12C case (see f i g . 10).

F igures 40-43 show spectra , equ iva lent to f i g s . 38 and 39, fo r the

14N and n C e x it channels. These channels have been chosen to h ig h l ig h t

the behavior o f o rb i t in g processes in the entrance channel and a non-

se lfcongugate channel. The lt+N e x c ita t io n i s lower than the 12C because

o f the p o s i t iv e Q- value of the l a t t e r channel. The X1C e x it channel has

a negative Q- value and the observed e x c ita t io n energ ies are there fore

lower than those of the 11+N.

The e x c ita t io n energy and an g le - in tegra ted abso lu te o rb i t in g cross

se c t io n s fo r the 12C, 14N and 160 ex it channels are shown in f i g . 44,

p lo tted as functions of center of mass bombarding energy. In o b ta in ing

these cross se c t io n s , the l / s in 0 behavior observed at backward angles

fo r the d i f f e r e n t ia l c ro ss sect ions were assumed to p e r s i s t in to the

forward ang le s, and acco rd in g ly accounted for.

RESULTS | 127

RESULTS ' 128

FIGURE 38

The y ie ld o f 12C nuclei from the 28Si + 14N in te ra c t io n p lo tted as

fu n ct ion s o f the p o s i t io n along the front wire in the HIC. The

data shown are fo r 28S i labora tory bombarding energ ies between 100

and 170 MeV.

CO

UN

TS

FIGURE 38 129

ORNL-DWG 85-17143

14N (28Si,12C) 0L = 5 deg8 0

4 0

0 7 0

3 5

0 1 7 0

8 5

O 1 6 0

8 0

0 1 5 0

7 5

0 1 4 0

7 0

0 1105 5

0 9 0

4 5

0

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 b 4 0 0 4 $ 0

W I R E C H A N N E L

■ L

1

I D 8o i i i j x oS U M - 5 9 4 6 —

r * * u £ 0 M e V

m j f a , I .I D 7

- S U M = 5 4 8 2 ~

1 6 0 M e Vi t * *

n r * ~

M 1 I V 4

" 1

I D 6

- S U M = 1 7 2 7 3 -

^ ^ 5 0 M e V

- I - * "

" V ,

*I D 5

- S U M = 1 2 8 3 3 -

M e V

i . j i

|

I D 4

— C I I U - 1 1 C 7 1 —

rV

O U M - I j g ( 1 —

■ ^ £ 0 M e V

H i i

|

I D 3

___ C l I M M O C Q Q ___O U M ^ f c i V y - ?

1 2 0 M e V

A U n ,

I

I D 2

— O f I M - Q C C R ____

/

o U M —‘ <7 u O O

1 1 0 M e V

j M

* L - ,I D 1

- S U M = 6 9 1 6 —

1 0 0 M e V

k f c « |__________________

/

X u

RESULTS 130

FIGURE 39

The o r b i t in g c ro ss se c t io n s of 12C nuc le i from the 28Si + 14N

in te ra c t io n p lo t te d as functions o f Q- value. The data shown are

fo r 28S i lab o ra to ry bombarding energ ies between 100 and 170 MeV.

U R E 3 9

300 p

150 -0

200100 -

0BOO100 -

019085 -

016080 -

0 _12060 -

0 _9045 —0 _

6030 -

0 -O

131

,4N (28Si,12C)

ORNL-DWG 85-17144

-5 -10 -15 -20 -25Q-VALUE MeV

-30 -35 -40 - 4 5

RESULTS

i132

FIGURE 40

The y ie ld o f 14N nuclei from the 28Si + 11+N in te ra c t io n p lo tted as

fu n ct ion s o f the p o s it io n along the fron t wire in the HIC. The

data shown are fo r 28S i labora to ry bombarding energ ies between 100

and 170 MeV.

CO

UN

TS

FIGURE 40 133

ORNL-DW G 85-17145

M N (28Si,M N) 8L = 5 deg30

150

50250

50

250

4020

0 4020

0 40200

4020

0 4020

00 50 100 150 200 250 300 350 400 .**450

WIRE CHANNEL

,j , ' JD8pnfs(l n , auw-unu

4 W ^ ,70MeV

1.......7

ID 7Cl IM-9QfY7oUm-coUf160 MeV

hHtoAJ

/ W kMjUjALi. ID 6ci iM-/irv7n.

_ a.A

n^nTj ■ OUm “U(UH^jj.150 MeV

m ^ L s* ID 5

SUM=2693U * i ^j^140M e\T

ID4SUM=3001

^ O M e V "m * ™

b1 ID 3

OUIVI JOvlO

U * - f MeV

JI*A.i.ijai . ID 2_ Cl 111-0^7-

T f p i f \ n^ oUM-cOUO( V ^ ,0MeV

A1

ID 1Cl IM -OlOQ-Wk\

V *

OUlVl " tLl w«7100 MeV 1

RESULTS

FIGURE 41

The o r b i t in g c ro ss se c t io n s of 14N nucle i from the 28S i + 14N

in te ra c t io n p lo tted as functions of Q- value. The data shown are

fo r 28Si labora to ry bombarding energies between 100 and 170 MeV.

dcr/

dE

mic

roba

rns/

MeV

FIGURE 41 135

ORNL - DWG 85-17142

,4N (28Si,14N)

-5 -10 -15 -20 -25 -30

Q-VALUE MeV

RESULTS 136

FIGURE 42

The y ie ld o f U C nuclei from the 28S i + 14N in te ra c t io n p lotted as

fun ct ion s o f the p o s it io n along the fron t wire in the HIC. The

data shown are fo r 28Si labora tory bombarding energies between 100

and 170 MeV.

COU

NTS

FIGURE 42 137

14N (28Si,11C)

ORNL-DWG 85-17140

20

10

020100

4020

030150

20

10

02010

020

10

010

5

0

111 - i t10 8SUM =1126

■l e i i E i s i a170 MeV

jinftfk. 1

i. -itID 7 ‘

_ SUM=968

.i-JLhit t W M 4 i160 MeV

k*_ I

. iID 6SUM=2455

*w w 150 MeV

I

. Jfi iSi j... 1ID 5SUM=1767

W St140 MeV

lL>ua_ A• In nMA Win .

ID 4SUM=1466

H S U E Sm m

H130 MeV

xJI. 1

■I J iID 3SUM=1257120 MeV

I1 1 1ID 2

_ SUM = 8 8 4 _J W IViil uni

110 MeV J. I

. i i .n . l .f

ID 1Cl Hi KOI

■ I K l l m K

1 m bUM * DUi 100 MeV

150 100 150 200 250 300

WIRE CHANNEL350' 400 45©

RESULTS

FIGURE 43

The o r b i t in g cro ss se c t io n s of n C nuclei from the 28Si + 11+N

in te ra c t io n p lo tted as functions o f Q- value. The data shown are

fo r 28S i labora to ry bombarding energies between 100 and 170 MeV.

dcr/

dE

mic

roba

rns/

MeV

FIGURE 43 139

ORNL-DWG 85-17141

14N (28Si,1fC)

Q-VALUE MeV

INTERPRETATION 140

From f i g . 44 i t i s obvious that at nearly a l l inc ident channel

energ ie s, the 12C and the 160 y ie ld s are la rg e r than those of llfN. As

d iscussed in the chapter e n t it le d MOTIVATION, we can there fore conclude

that the duration of o rb i t in g in the 28Si + ^ N in te ra c t io n is su f

f i c i e n t l y long to permit charge and mass e q u i l ib r a t io n . The ex it channel

with the lowest Q- value i s found to have the la r g e s t c ro ss section (see

f i g . 15). I f the Fermi level density expression (eq. 8) were adequate

fo r a d e sc r ip t io n of t h i s a v a i la b le phase space, the product y ie ld s

would be determined uniquely by th e ir respective Q- va lues. In par

t i c u l a r , fo r our measurement, the ordering o f y ie ld s , in decreasing

i n te n s i t y , would have been 12C, 14N and 160 re sp e c t iv e ly . The excess of

160 over 14N we be lieve has i t s o r ig in in d if fe rence s in the m icroscopic

s tru c tu re of the 28Si + 14N and 26A1 + 160 channels. There is substan

t i a l l y g reate r phase space a v a i la b le to the 26A1 + 160 channel than to

the 28Si + 11+N (see f i g . 20 fo r in form ation pe rta in in g to the energy

le v e ls in the nuclei under d is c u s s io n ) .

In summary, we have observed mass and charge e q u i l ib r a t io n in

o r b i t in g heavy-ion react ion s. While the e q u i l ib r a t io n of angular momen

tum, energy, charge, and mass occur in both o rb i t in g react ion s and com

pound nucleus form ation, the shape degree of freedom i s not e q u il ib ra ted

in o r b i t in g react ion s.m

Let us now compare the p red ic t ion s o f the model we have presented

in a previous chapter with data for the 28Si + llfN in te ra c t io n . Figure

45 p lo t s the f in a l k in e t ic energies of o rb i t in g products in th i s

in te r a c t io n , fo r the 12C, 11+N and 160 e x it channels, as functions of cm

energ ie s. The s o l id l in e s throgh the data points are the p red ic t ion s of

RESULTS AND INTERPRETATION 141

FIGURE 44

The a n g le - in te g ra te d abso lu te o r b i t in g c ro ss sec t ion s fo r the 28Si

+ 14N in te ra c t io n p lo tted as function s o f center of mass energy.

ORNL-DW G 85 — 17370

28Si + 14N ORBITING CROSS SECTION

A

4A

i A

A

a _ . .

A

n

iA

i

Q 1

k

9

* Bi

• ;f l

> &

i ■

£3

.... . ...

»— i i i ■ — i--- r i i 1

a CARB ■ NITRC • O X Y G

---1 i >---

ON) G E NEN

i i i i "

30 35 4 0 45 50 55

C E N T E R OF M A S S E N E R G Y (MeV)

60

INTERPRETATION 143

the model. The poten tia l parameters used are the same as those used to

descr ibe the 28Si + 12C in te ra c t io n (see chapter e n t i t le d THEORY). This

param etr iza tion i s shown in f i g . 45 to be adequate fo r a d e sc r ip t io n of

the k in e t ic energy data.

As mentioned p rev iou s ly , s ince the model under d isc u s s io n r e l ie s on

the Fermi leve l de n s ity expression fo r a p red ic t ion of the a v a i la b le

phase space, i t w i l l p red ict 1*I N y ie ld s la r g e r than the 160, in contra

d ic t io n to what i s measured experim entally . Hence, the model, in i t s

present form, i s inadequate fo r a d e sc r ip t io n of the lltN + 28Si data.

A simple m od if ica t ion to the leve l density c a lc u la t io n can be used

to remedy a part o f t h i s problem. F igure 46 i s a schematic p lo t o f the

leve l de ns ity in any nucleus, as predicted by the Fermi leve l density

express ion . The curve b g ive s the leve l density p as a function of

energy E. The curves a and c are d isp laced along the energy ax is from

curve b by energy amounts AE 'and a E re sp e c t iv e ly . They, in general,

represent h igher and lower leve l d e n s i t ie s re sp e c t iv e ly , than curve b.

We can there fore s im ulate some of the m icroscopic d if fe re n ce s between

the var ious e x it channels by in troduc in g 'p a i r in g c o r re c t io n s ' of magni

tudes a E ' fo r channels whose leve l d e n s i t ie s are being underpredicted.

F igure 47 shows the re su lt s of such a m od if ica t ion fo r the n itrogen

channel in the 28Si + 12C in te ra c t io n . The channel y ie ld ,w h ich was p^_-

v io u s ly underpredicted (see f i g . 19) i s now accounted fo r in quan

t i t a t i v e fa sh ion .

F igure 48 shows the re su lt s of a c a lc u la t io n , in c lu d in g p a ir in g

co r re c t io n s , fo r the 28S i + 11+N o r b i t in g y ie ld s . While the re la t iv e


FIGURE 45

The f in a l k in e t ic energies of o r b i t in g products fromtthe 28Si +

14N in te ra c t io n p lo tted as functions of center of mass energies.

The s o l id l in e s are p red ic t io n s of the model described in a pre

v ious chapter.

FINA

L K.

E.

(MeV

)

figure 45

E c.m. (MeV)


FIGURE 46

A schematic p lo t o f the leve l density in a nucleus as predicted by

the Fermi level density expression (curve b ) . The curves a and c

i l l u s t r a t e the e f fe c t s of 'p a i r in g c o r re c t io n s ' AE'and aE respec

t i v e l y , on the p re d ic t io n s for the leve l density .

FIGURE 46 147

O RN L-D W G 86-8133


FIGURE 47

O rb it in g cross sect ions fo r the C, N, and 0 channels in the 28Si +

12C in te ra c t io n p lotted as functions of center of mass energies.

The curves are the p re d ic t io n s , in c lu d in g 'p a i r in g c o r r e c t io n s ' ,

o f the model. The data are from (Sha84b).

MIL

LIB

AR

NS

100.0

10.0

1.0

0.1

0.01

2 5 . 0 3 0 . 0 3 5 . 0 4 0 . 0 4 5 . 0 5 0 . 0 5 5 . 0 6 0 . 0

CENTER OF MASS E N E R G Y (MeV)VO

2 8 S i + 1 2 C O R B I T I N G

OXYGEN

l i i i ------- 1— i i i------- 1— i— i— i— — i— i— i— i-------1— i— i— i— i i— i— i— — i— i— i— r

FIGURE 47

INTERPRETATION

o r b i t in g cross sect ions are accounted fo r , the abso lu te cross sect ions

are s y s te m a t ic a l ly overpredicted. A p o s s ib le explanation fo r th is

d iscrepancy may l i e in the non-zero entrance channel sp in of the 28Si +

14N system. The model, in i t s present form ulation, does not account for

such a p o s s i b i l i t y . The predicted maximum fus ion cross sect ion fo r th i s

system i s ~1000 mb, which is about what one would expect.

We have, in t h i s chapter, presented evidence fo r the observation of

charge and mass e q u i l ib r a t io n in the 28Si + ^ N in te ra c t io n . Our model

has been app lied to descr ibe , in q u a n t ita t iv e fa sh ion , the o rb i t in g

y ie ld s fo r the 28Si + 12C in te ra c t io n , and, in q u a l i t a t i v e fa sh ion , the

y ie ld s fo r the 28Si + 14N in te rac t io n . We sh a l l conclude t h i s chapter

with an est im ation of the magnitudes of e rrors in the experimental data

fo r the 28Si + l l fN in te ra c t io n . The f in a l chapter w i l l present a

d is c u s s io n of our re su lt s in the context o f other o r b i t in g measurements,

and a lso suggest p o s s ib le avenues fo r future experimental and th e o re t i

cal in v e s t ig a t io n in these and re lated f i e ld s .


FIGURE 48

O rb it in g cro ss se c t io n s fo r the C, N, and 0 channels in the 28Si +

1**N in te ra c t io n p lo tted as funct ion s of center of mass energies.

The curves are the p re d ic t io n s , in c lu d in g 'p a i r in g c o r r e c t io n s ' ,

of the model.

y f *?

MIL

LIB

AR

NS

2 8 S i + 14N ORBITING100.0

10.0

1.0

0.1

3 0 . 0 3 5 . 0 4 0 . 0 4 5 . 0 5 0 . 0 5 5 . 0 6 0 . 0

C E N T E R OF MASS E N E R G Y (MeV)

A CARBON ■ NITROGEN • OXYGEN “

a CARBON b NITROGEN C OXYGEN

RESULTS: ESTIMATION OF EXPERIMENTAL ERRORS 153

S t a t i s t i c a l :

The to ta l counts in the spectra used in a determ ination of the

cro ss se c t io n s shown in f i g . 44 vary from about 1500 counts for the

n itrogen e x it channel (see f i g . 40) to over 28000 counts fo r the carbon

( f i g . 38). The s t a t i s t i c a l error in the cross se c t io n est im ation is

there fore of the order of 2%.

System atic :

1. The HIC detect ion e f f ic ie n c y v a r ie s with p o s i t io n along the fron t

wire as determined through a study of the e l a s t i c y i e ld of 28Si from the

28Si + 14N in te ra c t io n . This error i s le s s than 10% and inc ludes any

e rro rs in the current in te g ra t io n procedure. For a lpha p a r t ic le s

however, t h i s e f f ic ie n c y i s f a i r l y constant, with a s t a t i s t i c a l e rror of

around 2%, and no system atic e rro r (see f i g . 28). For reaction products

o f intermediate mass, we can assume th a t , because o f an intermediate

kinem atic s h i f t , these errors are somewhere in between (about 5%).

2. E rro rs are introduced by the pressure and f i e l d l im i t a t io n s

d iscu ssed in f i g . 33. These e rrors are minimized fo r the e x it channel

fo r which the magnetic f i e ld and detector pressure have been optim ized.

In p a r t i c u la r , these errors are small fo r the 12C and 160 e x it channels

and s l i g h t l y la r g e r for the 1I+N. The information fo r the 11+N channef^'

was obtained mostly from s e t t in g s optimized fo r the 12C and 160 channels

re sp e c t iv e ly . From the shape o f the 11+N spectra , one can estimate the

magnitude of these e rrors to be le s s than 10% fo r both cross sec t io n and

average k in e t ic energy determ inations.

RESULTS: ESTIMATION OF EXPERIMENTAL ERRORS 154

The to ta l error on the experimental q u an t it ie s can be obtained by

adding these var ious errors in quadrature. The number we get i s at the

leve l of 11%. Comparisons between several independent measurements of

the k in e t ic energies and cross sec t ion s show mutual agreement at around

the 10% le v e l.

FROM FACT TO FICTION

Th is chapter w i l l be devoted to a comparison of the conclusions

arr ive d at in t h i s work with those of other s im i la r works. A lso , avenues

fo r future experimental and th e o re t ica l in v e s t ig a t io n w i l l be suggested.

Some of the ideas presented in t h i s chapter are sp e cu la t iv e in nature

and should be treated accord in g ly .

We had concluded in the previous chapter that o r b i t in g reactions

l a s t long enough fo r the e q u i l ib r a t io n of energy, angu lar momentum,

charge, and mass to occur. The measurements of (Ray85) however seem to

demonstrate a strong entrance channel dependence in the r e la t iv e y ie ld s

o f the 160 and 12C nuclei emitted from the 2**Mg + 160 and 28S i + 12C

in te r a c t io n s . Th is i s not what one would na ive ly expect based on an

assumption of such e q u i l ib r a t io n in o r b i t in g react ion s. In the 28Si +

ll*N measurement reported herein, the s ign a tu re s fo r charge and mass

e q u i l ib r a t io n are observed over a wide range of energies (100-170MeV).

Th is i s in co n tra d ic t io n to the c la im s of (Ray85) based on a measurement

at a s in g le energy. In our op in ion , at the cm energy of 31.8 MeV and

correspond ing angu lar momentum i = 20fi, the energy a v a i la b le for theI

i n t r i n s i c combined e x c ita t io n o f the 160 and 2i|Mg nuclei in a d inuc lear

c o n f ig u ra t io n i s , on the average, about 10 MeV. The r e la t iv e o rb i t in g

y ie ld s , fo r both entrance channels at these low e x c ita t io n energies, we

there fore expect to be very s e n s i t iv e to the a v a i la b i l i t y , of DMC le v e ls* f " r-

fo r e x c i t a t io n , with appropriate energies and angu lar momenta. F igures

14 and 20 contain the necessary inform ation needed to re in fo rce th is

argument. An a l t e rn a t iv e re so lu t io n of t h i s apparent d iscrepancy invokes

155

FROM FACT TO FICTION 156

d if fe re n ce s in the dominant modes of energy and angu lar momentum d i s s i

pation in the 2ltMg + 160 and 28Si + ll;N in te ra c t io n s . I t i s -q u i t e

p o s s ib le that while d i s s ip a t io n v ia p a r t i c le exchange may be the domi

nant process in the 23Si + 1I+N in te ra c t io n , v ib ra t io n a l and ro ta t ion a l

exchanges without p a r t i c le exchange ( Bet77) may dominate the 2**Mg + 160

in te ra c t io n . Such a d i s t in c t io n w i l l be s i g n i f i c a n t p a r t i c u la r ly at the

low energies where the 2**Mg + 160 measurement was made, because of a

lack o f p a r t i c le channels e n e rg e t ic a l ly acce ss ib le to t h i s in te ra c t io n .

The 2lvMg + 160 system therefore m erits sc ru t in y at h igher energ ies,

where data are a v a i la b le for the 28Si + 12C system (Sha84b). As

d iscu ssed in the chapter e n t it le d MOTIVATION, the 28Si + ll|N in te rac t io n

has several e x it channels e n e rg e t ic a l ly a c c e ss ib le , even at low

ene rg ie s , making the phase space determination o f e x it channel y ie ld s

and a study of charge and mass e q u i l ib r a t io n meaningful.

The emission of massive nuclear fragments, in c o l l i s i o n s between

heavier ions (Heu85, Tok85), has been a t tr ibu ted to a process ca l le d

f a s t - f i s s i o n . This process i s d is t in g u ish e d from f i s s i o n by i t s non

i s o t r o p ic angu lar d i s t r ib u t io n . As with o r b i t in g , f a s t - f i s s i o n i s

characterized by the e q u i l ib r a t io n of energy, angu lar momentum, charge,

and mass. I t i s my opinion that these processes are re la ted . In l i g h t

nuclear systems, the o rb i t in g co n f igu ra t io n i s such that there i s not a

very la rge overlap between the two nuclei forming the DMC. In such a

s i t u a t io n , the o r b i t in g y ie ld s are emitted from a quasi-bound d inuc lear

co n f igu ra t io n that can be assumed to be 'frozen ' with respect to the

shape degree of freedom. In the case of heavy d inuc lear systems, the

fo rces o f coulomb repu ls ion dominate the in te ra c t io n , and more compact


c o n f ig u ra t io n s are required in order to keep the DMC bound. In such a

scenar io , we are no longer j u s t i f i e d in making the assumption of a ' f r o

zen' d in u c le ar co n f ig u ra t io n . The e f fe c ts of deformation become impor

ta n t . The o r b i t i n g - l i k e y ie ld s can now be emitted both from quasi-bound

d in u c le a r c o n f igu ra t io n s as well as from those DMCs that become unbound

as a re su lt o f excess ive Coulomb repu ls ion . This l a t t e r process i s f a s t -

f i s s i o n . The experimental s ign a tu re fo r the observation of f a s t - f i s s i o n

i s a broad mass d i s t r ib u t io n of the product y ie ld s , with a cut o f f at a

mass asymmetry where the e f fe c ts o f Coulomb-induced fragm entation become

important. Such systems a lso do not l i v e long enough fo r there to be a

su b s ta n t ia l y ie ld at backward ang les.

What do we need to do in order to understand the connections bet

ween these two p rocesses? We need to make system atic measurements on the

mass y ie ld s from fully-damped nuclear c o l l i s i o n s as a function of angle

and lab o ra to ry bombarding energy from in te ra c t io n s between nuclei of

mass interm ediate between those described in t h i s work and in (Tok85).

Th is i s the region where I would expect to see the in c re a s in g importance

o f Coulomb forces and deformation in determing the outcome of an

in te r a c t io n . While a th e o re t ica l d e sc r ip t io n of the so r t d iscussed in an

e a r l i e r chapter should be adequate fo r a d e sc r ip t io n of an in te rac t io n

between l i g h t nuclear c o l l i d in g partners, the assumption of coupling

on ly between d in u c le a r co n f igu ra t io n s having the same mass r a t io w i l l

have to be relaxed i f the model has to succeed fo r a d e sc r ip t io n of

c o l l i s i o n s between heavier n u c le i. Add it iona l r e s t r i c t i o n s on the

a lready l im ite d a c c e s s ib le phase space w i l l have to be app lied to

account fo r the fac t that some d inuc lear c o n f igu ra t io n s may become

FROM FACT TO FICTIONi! 158

unbound as a re su lt of excessive Coulomb repu ls ion . These unbound chan

nels could e ith e r be treated in the same foo t in g as the fragmentation

channels, or e lse introduced as a ' s i n k ' term in eq. 4 (chapter on

th e o ry ) , which descr ibes the coupling between d inuc lear co n f igu ra t ion s.

A bound DMC can a lso become unbound in the case of co n f igu ra t ion s

with a very la rge mass asymmetry as a re su lt o f excess ive cen tr ifuga l

rep u ls ion . Data may a lready e x is t to demonstrate t h i s conjecture. The

way to id e n t i f y such a process would invo lve the populat ion of a DMC

v ia a symmetric channel. Such a ce n tr i fu g a l l im ita t io n would mani fe st

i t s e l f as a decreasing y ie ld in the asymmetric channels, with increasing

bombarding energy. One has to be c a re fu l, in such a measurement, in

d i s t in g u i s h in g the o r b i t in g y ie ld s from those from compound nucleus

decay.

What needs to be done in order to enhance the knowledge we have

gained from a study of the 28Si + 1JtN system?

At the ou tse t, i t would be of in te re s t to measure the fus ion cross

se c t io n s , fo r the same system, over an energy range s t a r t in g below, and

extending over the range fo r which o rb i t in g data are a v a i la b le . This

would f a c i l i t a t e an in te rp re ta t io n of the data in a fa sh ion s im i la r to

that done fo r the 28Si + 12C system.

In the previous chapter, the model we had developed was unable to

provide a d e sc r ip t io n , in q u a n t ita t ive fa sh ion , fo r the absolute

o r b i t in g y ie ld s fo r the 28Si + 14N system. An improved leve l density

c a lc u la t io n , and an incorporat ion of entrance channel sp in into the fo r -


mulation might r e c t i fy th i s problem. We could take two approaches to the

leve l de n s ity c a lc u la t io n . Both require the ta b u la t io n , from a knowledge

of the e x c ita t io n energies (E) and angu lar momenta (J) of le v e ls in

n u c le i , o f the leve l density p (E ,J ) fo r each nucleus. The level density

in the DMC can then be ca lcu la te d as

p (E .J ) = 0/ J0/ E p i (E - 6E, J - 6J) p2 (6E,5J) dE dJ (17)

Th is approach w i l l , in my op in ion , not conform to the s t i c k in g l im i t .

An a l t e r n a t iv e approach i s to d iv id e the a v a i la b le e x c ita t io n energy and

angu lar momentum between the two nuclei in accordance with the s t i c k in g

l im i t and c a lc u la te the leve l density of s ta te s in the DMC as

p(E,J) = p i (E i ,J!) x p2(E2,J2) (18)

Spin can be incorporated in to a c a lc u la t io n in one of several ways. *

For each incoming p a r t ia l wave £, we could couple to the entrance chan

nel sp in and a r r iv e at d i f fe re n t values fo r the to ta l angu lar momentum

J in the DMC. We could then c a lc u la te e x it channel y ie ld s based on the

phase space a c c e s s ib le fo r a l l the channels, fo r a l l J allowed with a

s in g le incoming o rb i t a l angu lar momentum £. A l te r n a t iv e ly , we could

c a lc u la te the y i e ld from a s in g le £ as the ar ithm etic average of the

y ie ld s from the d i f fe re n t m-substates corresponding to the entrance cha-i t

nel sp in . ^

With the modified level density c a lc u la t io n , and entrance channel

sp in incorporated in to the model, we should expect a better d e sc r ip t io n

o f the o r b i t in g data.

FROM FACT TO FICTION 1 160

An a l te rn a t iv e in te rp re ta t io n of the e q u i l ib r a t io n of energy and

angu lar momentum in heavy-ion in te ra c t io n s i s based on the d iv i s io n of

e x c ita t io n energy between the reaction partners with a r a t io equal to

that of th e i r masses. This corresponds to a co n s t ra in t of equal tem

perature, in con tra st to the l im i t of no re la t iv e motion as has been

app lied in t h i s work. The relevance of these and other approaches to a

d e sc r ip t io n of nuclear in te ra c t io n s m erits in v e s t ig a t io n .

I t would be of in te re s t to in v e s t ig a te the entrance channel depen

dence of the o rb i t in g process by popu lat ing a DMC v ia entrance channels

that have several a c c e s s ib le e x it channels fo r decay. The 26A1 + 160

could be such a system fo r comparison with the 28S i + ^ N measurement.

Such a measurement would be a meaningful a p p l ic a t io n o f the ideas

in v e s t ig a te d in (Ray85).

Measurements of the alignment of the reaction products of o rb i t in g

in 2l*Mg + 12C (Dun85, Gla86) and 28Si + 12C (Ray86) have ind icated

alignm ents in excess of the 90% le v e l . Th is needs fu r th e r in v e s t ig a t io n ,

perhaps with 4n gamma detection systems, for DMCs w ith both zero and

non-zero entrance channel sp in . This would be a way to in v e s t iga te

p o s s ib le dealignment e f fe c ts that a non-zero entrance channel spin may

have. I t would a lso be of in te re s t to measure the alignment in channels

other than the entrance channel to shed some l i g h t on the nature of the

react ion dynamics in in te rac t io n s of the o rb i t in g type.

S tu d ie s of the duration of the o r b i t in g process in the 2I+Mg + 12C

system have ind icated o rb i t in g l i fe t im e s o f the order of 2 x 10"21 secs

(Dun85, G la86). I t would be in te re s t in g to make s im i l a r measurements in


other systems to in v e s t ig a te whether there is a co re la t io n between the

number of p a r t i c le s exchanged and the o rb i t in g l i fe t im e . In order to do

t h i s , we would have to measure the f u l l mass and charge d i s t r ib u r io n of

o r b i t in g products from an in te rac t io n between two n u c le i. For l i fe t im e s

exceeding 10“19 s e c s . , c ry s ta l b lock ing techniques (Gom83) may prove

u s e f u l .

D eta i led angu lar d i s t r ib u t io n s o f o rb i t in g y ie ld s corresponding to

the ground s ta te and lo w - ly in g excited s ta te s need to be in ve st iga te d to

id e n t i f y the angu lar momenta co n tr ib u t in g to the o r b i t in g process. Such

phenomena have been in v e s t iga te d fo r the ground s ta te under the rubr ic

of molecular resonances (Erb85). How i s the process we observe re lated

to molecular resonances seen in l i g h t nuclear systems? I t i s p o s s ib le

th a t , fo r l i g h t systems, the nucleus-nucleus potentia l has sha llow

pockets and i t i s ju s t a few modes of i n t r i n s i c e x c ita t io n of the DMC

that s a t i s f y the con d it ion s required fo r trapp ing . In such a case, the

in te ra c t io n s may be dominated by a few s ta te s of d e f in i t e sp in and

p a r i t y . The fu s io n process a lso proceeds through these few doorway s t a

te s and hence shows the s ign a tu re s of a resonance. The to ta l o rb i t in g

in te ra c t io n in heavier systems invo lves the overlap of several p o s s ib le

modes of DMC e x c i ta t io n allowed because of deeper p o ten t ia l pockets. The

to ta l c ross sec t ion there fore shows no resonant behavior.

I t i s my contention that fo r a la rge body of fu s ion data in

e x is tence , y ie ld s that could have been a t tr ibu te d to o r b i t in g may have

been included in to what was considered as fus ion y ie ld . Th is may be a

problem p a r t i c u la r l y fo r systems populated via symmetric entrance chan-

FROM FACT TO FICTION ‘ 162

nels where the error introduced by the in c lu s ion of such y ie ld s could be

as la rge as 30%. O rb it in g s tud ie s in systems populated v ia -a symmetric

channel s u f fe r in that the y ie ld s of reaction products are dominated by

secondary y ie ld s . The primary products often have enough energy to decay

before they are detected. The a n a ly s i s o f experimental data have then to

be supplemented by evaporation c a lc u la t io n s to account fo r the secondary

em ission.

On the b a s is of th i s work i t seems appropriate to speculate on the

dynamics o f the fus ion process. Does fu s ion occur through a process of

continua l p a r t ic le exchange whereby one nucleus i s g r a d u a l ly consumed by

the other, or does i t occur by a change of shape of a d inuc lear system

that re ta in s i t s mass asymmetry? On the b a s is of the 28Si + 1I+N measure

ment, the l a t t e r mode appears to be the favored. S ince both the 160 and

12C o r b i t in g y ie ld s exceed the 11*Nf i t appears that there i s no favored

d ire c t io n fo r mass flow between the in te ra c t in g n u c le i . These ideas bear

fu r th e r in v e s t ig a t io n .

In conc lu s ion , there are a wide spectrum o f phenomena covering the

sub f i e ld s o f d i s s ip a t iv e c o l l i s i o n s , fus ion react ion s and molecular

resonances that come under the purview of o rb i t in g heavy ion react ion s.

On a p h i lo so p h ica l note, th i s th e s is has been an attempt to id e n t ify and

u n ify some of the observations in these d if fe re n t s u b f ie ld s . *

SYNOPSIS

Let me summarize what has been accomplished in t h i s work. I have

measured the o r b i t in g y ie ld s from 28Si + 1I+N re a c t io n s. From the ra t io

o f e x it channel y ie ld s I have concluded that o r b i t in g in te ra c t io n s la s t

long enough to permit the constra ined e q u i l ib ra t io n o f charge and mass.

The measurement i s unique in i t s experimental content. I t takes

f u l l advantage of a contaminant free superson ic g a s - j e t ta rge t , the mass

and charge re so lu t io n provided by a spectrograph based detector system,

and inverse kinematics in the use of an acce le ra tor th a t i s capable of

a c c e le ra t in g the heavier of two in te r a c t in g nuc le i.

I have developed a model that accounts fo r s im u ltaneous ly , in quan

t i t a t i v e fa sh ion , the o r b i t in g and fu s ion y ie ld s in 28S i + 12C in te ra c

t io n s and, in q u a l i t a t i v e fa sh ion , the o rb i t in g y i e ld s in 28Si + 14N

in te r a c t io n s .

In co n c lu s ion , I have shown that the o rb i t in g and the fu s ion y ie ld s

from the in te ra c t io n between r e la t i v e ly l i g h t heavy ions can be

understood q u a n t i t a t i v e ly as the consequence of the e vo lu t ion of a

d in u c le a r molecular complex formed in the e a r l ie s t phase of the in te ra c

t io n . The o r b i t in g y ie ld s are emitted from some such complexes during

the course of th e i r f i r s t ro ta t ion and show the s ig n a tu re s fo r the

constra ined e q u i l ib r a t io n of energy, angu lar momentum, charge, and mass.

The su rv iv in g ro ta t in g complexes then undergo an e q u i l ib r a t io n of shape

to form a compound nucleus.

163

This appendix l i s t s some of the information re levant to Bass model and

i t s parameters as relevant to the c a lc u la t io n s presented in the chapter

e n t it le d THEORY.

The to ta l nuc leus-nucleus potentia l i s a sum of nuclear , Coulomb and

c e n tr i fu g a l co n tr ib u t io n s . In the nuclear potentia l as parametrized by

Bass (Bas74), t h i s proxim ity type poten tia l is expressed as

V„ - — g( x)(R l + R2 )

where the rad ii o f the two nuclei Rj and R2 are parametrized as

R = 1.16 A1/ 3 - 1.39 A”1/ 3

g (x ) = ------------------- 1-------------------A exp(x/a) + B exp(x/b)

The values o f the four parameters are

A = 0.045, B = 0.0061, a = 3.3, b = 0.65

These parameters d i f f e r from those quoted by Bass. They were adjusted to

describe the o r b i t in g data. The same parameters were used fo r a l l the

channels.

APPENDIX 1 '

164

APPENDIX 2

Th is appendix l i s t s magnetic f i e l d , pressure and vo ltage se t t in g s

used in the 28Si + 14N experiment. T y p ic a l ly , two runs were needed at

each energy to detect elements from Boron to F luor ine at one angle

s e t t in g of the spectrograph. These se t t in g s invo lved d i f fe re n t magnetic

f i e l d s and d i f fe re n t pressures in the HIC. Consequently, the electrode

and wire vo ltage s had to be changed too. L isted in t a b le 2 are the

magnetic f i e l d , detector and absorber pressures used to detect the Car

bon and Oxygen iso to pes. The absorber sandwich used with the HIC con

s i s t e d of the HIC window, a second window fo r the gas absorber (GAW),

and a region of gas in between. An ad d it ion a l removable s o l id absorber

(SA) was placed in front of t h i s whole arrangement. The HIC and gas

absorber windows, and the s o l id absorber were made of Mylar of

th ickn e sse s 1, 1, and 0.5 m ils re sp e c t iv e ly (1 mil = 0.0254 mm). Table 2

a ls o in d ica te s the presence or absence o f the GAW and the SA. While the 1

SA can be manipulated from outs ide the spectrograph, removing the GAW

in v o lv e s breaking the magnet vacuum. A lso , i t i s r e l a t i v e l y easy to

remove the GAW and hard to put i t in! Therefore, cau tion should be exer

c ized in p lann ing the sequence of measurements.

F igures 49 and 50 show the vo ltage s used on the HIC wires and the

io n iz a t io n chamber e lectrodes re sp e c t iv e ly .

165

APPENDIX 2 166

TABLE 2

A l i s t o f experimental parameters used in the 28S i + 11+N

experiment fo r the detection of Carbon and Oxygen iso to p e s . These

s e t t in g s are adequate fo r elements one Z away from Carbon or

Oxygen.

Energy i s in MeV, f i e ld in K i lo g a u s s , Pg i s the detector

pressure in t o r r , i s the absorber pressure in t o r r , SA i s the

s o l i d absorber, and GAW the gas absorber window. IN or OUT in d ic a

te s the presence or absence of these elements.

TABLE 2 167

CARBON

ENERGY FIELD PD PA S A GAW

100 8.8 175 0 OUT OUT

110 9.403 185 0 OUT IN

120 9.505 203 50 OUT IN

130 9.999 250 100 OUT IN

140 10.539 262 20 IN IN

150 10.49 312 201 OUT IN

160 10.986 340 130 IN IN

170 11.111 330 162 IN IN

OXYGEN

100 8.0 143 0 OUT OUT

110 8.299 80 0 OUT IN

120 8.81 95 50 OUT IN

130 8.92 120 100 OUT IN

140 9.33 90 24 IN IN

150 9.484 140 82 IN IN

160 10.307 200 145 IN .• IN

170 9.905 185 160 IN IN

APPENDIX 2

FIGURE 49

Optimal vo ltage s e t t in g s fo r wires 1 and 2 p lo tted as a function

o f the pressure in the HIC. The gas used in the counter was isobu

tane.

O R N L - D W Q 8 5 C - 14 9 5 0

DETECTOR PRESSURE (torr)

APPENDIX 2 170

FIGURE 50

Optimal vo ltage s e t t in g s fo r the cathode and anode as a function

of the pressure in the HIC. The gas used in the detector was

isobutane.

VO

LTS

FIGURE 50

CATHODE VOLTAGE VS HIC PRESSURE

-8 0 0

-1000in_jo> -1200

-1400

0 100 200 300 400TORR

•

1I -----

9 V

ANODE VOLTAGE VS HIC PRESSURE400

300

200

TORR

1000 100 200 300 400

■■

■B ■ ■

11

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ABSTRACT EQUILIBRATION IN ORBITING HEAVY ION REACTIONS ... · Balasubramanian Shivakumar Yale University March 1986 On the basis of this work, it seems apt to conclude that available