BORON INDUCED TRANSFER REACTIONS by James E. Poth (B.S

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BORON INDUCED TRANSFER REACTIONS by James E. Poth (B.S

Transcript Of BORON INDUCED TRANSFER REACTIONS by James E. Poth (B.S

BORON INDUCED TRANSFER REACTIONS by
James E. Poth ( B. S . , Miami U niversity, 1955) ( M . A . , Miami U niversity, 1960) ( M. S . , Yale University, 1962)
A D issertation Presented to the Faculty of the Graduate School of Yale University in Candidacy fo r the D egree of D octor of Philosophy 1966

T o my m other and father and to A lice

ABSTRACT
Single-nucleon and deuteron transfer reactions induced by 115. 9-M eV B beam s have been observed on C 12 , C , N14, N15, O1 6 , and Ne20 targets, with the prim ary objectives of elucidating the reaction m echanism s and extracting inform ation o f a sp ectroscop ic nature relevant to the interacting nuclear system s. For each target, data on the (B^^.B^®) and (B ^ .B e^ ® ) neutron and proton trans­ fer reactions and the (B ^ .B e® ) deuteron transfer reaction are presented, consisting of forw ard-angle energy spectra of the beryllium and boron products of these reactions and absolute differential cro ss section measurements for states appearing in the spectra.
All transfer reactions are observed to exhibit highly selective population o f a relatively sm all number of final states, and evidence is presented that direct transfer represents the dominant m echanism . These reactions are further charac­ terized by a preferential population of certain of these states, whose yields are large relative to all others in the same spectrum .
The ( B ^ , B * 9) and ( B ^ , Be^9) single-nucleon tran sfer reaction data are consistent with the preferential population o f states of a c o r d o n sin gle-particle configuration. The levels preferentially populated in the (B , Be ) deuteron transfer reactions are the previously observed giant excitations of the deuteron tran sfer reaction and are associated with high angular momentum states of extrem ely pure tw o-particle configuration. The giant excitations of the reactions studied are interpreted on the basis o f sim ple angular momentum arguments in term s o f the capture o f the tran sferred nucleons into d^ 2 and fy^ 2 sin gle-p article states.
A system atic com parison of equivalent ( a , d ) and (B11 , Be 9) reactions reveals a high degree o f sim ilarity regarding both selective and preferential population of final states, including an unexpected sim ila rity o f the is o b a r ic -s p in configurations. The consistency o f the integrated c r o s s sections o f the giant excitations of the two reactions and the equivalence o f the correspon din g angular distributions indicate an identical direct transfer m echanism. The m ass dependence of the cro ss sections can be interpreted in term s o f the shell structure of the respective target nucle
Ratios of neutron and proton transfer c ro s s sections to analog states in the final system s of the (B11, BlO) and (B H , Be10) reactions are utilized in the extrac­ tion of relative spectroscop ic factors for the incident system s, and these data are used to obtain the (B^O+n) and (Be-^+p) parentage o f the B ^ ground state. Calcul­ ations of the corresponding ratios and parentage based on available m odel wave] unc­ tions are in good a ccord with the experim ental results.
A particle identification system developed for this work based on the dE /dx and E method and a m ultiparameter analyzer is described. A sem iem pirical method fo r the calculation o f energy loss for heavy ions has been developed and is show i to be in agreement with available stopping power data. Suggested experim ental extensions of these studies are given.

ACKNOWLEDGEMENTS
I am deeply grateful to my advisor, P rofessor D. A. B rom ley, for his guidance and active participation in all phases of this investigation. The advice, encouragement, and assistance given to me by P rofessor Brom ley throughout my graduate training at Yale will be gratefully rem em bered.
It is a pleasure to thank Dr. J. Birnbaum for his many contributions to all aspects o f this work and for sharing in the long hours of data collection. I also thank Dr. K. Nagatani fo r aid in the record in g o f the data.
Ia m indebted to P rofessor C. K. Bockelman, Dr. I. K elson, Dr. F. B. Malik, and Dr. J. C. O verley for their critica l reading o f the manuscript. The interest and assistance o f Dr. O verley during the experimental stages of this work is gratefully acknowledged. I am also grateful to Dr. L. C. Northcliffe for many helpful discussions and for the use of his unpublished data.
Thanks are extended to P rofessor E. R. B eringer and the staff o f the Yale Heavy Ion A cce le ra to r fo r their courtecus and com petent assistance during the cou rse o f these experim ents, and to Dr. M. S. Davis and the staff o f the Yale Computer Center.
I am sincerely grateful to Miss Catherine Barton for preparation of the figures and to M isses Mary Anne Thomson, Marilyn G izzi, Donna Zyskowski, and M rs. Monica Byrnes for typing the m anuscript.
Finally, gratitude is expressed to the United States A tom ic Energy Com m ission for financial support o f this research.

TABLE OF CONTENTS

ABSTRACT...................................................................................................... i

AC K N O W LED G E M E N TS....................................................................................... ii

TABLE OF C O N T E N T S .............................................................................................iii

LIST OF FIGURES ................................................................................................ v

I.

IN T R O D U C T IO N ..................................................................................... 1

A. The Heavy Ion T ran sfer R e a c t i o n ........................................... 1

B. Single Nucleon T r a n s f e r ............................................................ 4

C. Two Nucleon T r a n s f e r ................................................................. 12

D. Scope o f This S t u d y ..................................................................... 18

H.

EXPERIM ENTAL EQUIPMENT AND P R O C E D U R E ................... 25

A. A cce le ra to r and ExternalBeam F a c i l i t i e s ........................... 25

B. Scattering C h a m b e r ..................................................................... 27

C. Target System .................................................................................. 31

D. D etector A ssem b lies ................................................................. 36

1. P a rticle T e le s c o p e .................................................................. 36

2. C ollim ation System...... ............................................................ 41

3. M onitor A s s e m b l y .................................................................. 44

E. E le c t r o n ic s ...................................................................................... 46

F. P article Identification S y stem .................................................... 49

1. T h e o r y ....................................................................................... 49

2 . A p p l i c a t i o n ............................................................................... 51

3. In s tr u m e n ta tio n ...................................................................... 54

4. P rocedure ............................................................................... 56

5. Data R e d u c t i o n ...................................................................... 59

6 . D i s c u s s i o n ............................................................................... 64

G. Energy C a l i b r a t i o n ..................................................................... 65

H. E rro r A n a l y s i s .............................................................................. 70

1. Absolute C ross S e c t io n ......................................................... 70

2. Excitation E n e r g y .................................................................. 72

HI.

SINGLE NUCLEON TRANSFER R E A C T IO N S ................................ 75

A. Presentation o f R e s u l t s ............................................................ 75

1. Energy S p e c t r a ...................................................................... 75

2. C ro s s S e c t i o n s ...................................................................... 79

B. Angular Momentum T r a n s f e r ................................................... 79

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_ , 1 1 1 0 , , /T,1 1 _ 1 0 , C. (B ,B ) and (B ,B e ) Energy S p e c t r a ................................. 82

1 . C 1 2 (B1 1 ,B e 1 0 )N1 3 )C 1 2 (B1 1 ,B 1 °)C 1 3 ................................. 83 2. C1 3 (B1 1 JB e1 °)N 14)C 1 3 (Bn , B 1 0 )C 1 4 ................................. 86

3. N1 4 (B1 1 ,B e 1 ° ) 0 1 5 !N1 4 (BU , B 1 0 )N1 5 ................................. 87

4. N1 5 (BU B e ' V 6 ,n ' ^ b ' L b ' V 6 ................................. 99

5. 0 1 6 (B1 1 , B e1 0 )F 17,O1 6 (B1 1 , B1 ° ) 0 1 7 ................................. 91

_ __ 20 11 _ 10X14T 21 XT 20 11 _10.__ 21

Q.

6 . Ne (B ,B e )Na, Ne (B ,B )Ne ........................... 92

7. D i s c u s s i o n ................................................................................... 93

D. The T ran sfer C ross S e c t i o n ...........................................................97

E. Calculation o f S p ectroscop ic F a c t o r s .......................................104

F. (B10+n) and (Be1 0 +p) S p ectroscop ic F a c t o r s .......................... 109

1. C ross Section Ratios ...........................................................109

2. B 11 Ground State P a r e n t a g e ..............................................116

IV.

DEUTERON TRANSFER R E A C T IO N S ................................................121

A. Presentation o f R e s u l t s ................................................................. 121

1. Energy S p e c t r a ........................................................................ 121

2 . C ro s s S e c t i o n s ........................................................................ 123

B. (B-U-, B e9) Energy S p e c t r a ............................................................. 128

1 . c ' V ' . B e V " ....................................................................130 2. N1 4 (BU , B e 9 ) 0 1 6 ....................................................................133

3. N1 5 (B1 1 , B e 9 )0 ; l 7 ....................................................................134

4. 0 1 6 (B1 1 , B e 9 )F 1 8 ....................................................................136

5. Ne2 0 (B1 1 , B e 9 )Na2 2 ............................................................... 138

6 . C 1 3 (BU ,B e 9 )N1 5 ....................................................................139 7. D i s c u s s i o n .................................................................................140 C. P referential Population o f Final S t a t e s ...................................143 D. C om parison o f ( B ^ , B e9) and (a , d) R e a c t io n s ..................... 146

V.

S U M M A R Y .................................................................

155

APPENDIX. SEM3EMPIRICAL CALCULATION OF ENERGY. LOSS

FOR HEAVY IONS ...................................................................................................160

A. I n t r o d u c t io n ....................................................................................... 160

B. The Stopping Pow er Form ula .................................................... 161

C. Sem iem pirical Stopping Pow er fo r Heavy I o n s ......................164

D. Range Energy R e la t io n s ................................................................. 169

E. A p p l i c a t i o n .......................................................................................170

F. Summary

............................................................................ 174

REFERENCES

175

LIST OF FIGURES

Figure 2.1. Schematic diagram of the Yale Heavy Ion A ccelera tor. . . .

26

Figure 2. 2. Schem atic drawing o f scattering c h a m b e r ..................................28

Figure 2. 3. Photograph o f experim ental target a r e a ..................................30

Figure 2. 4. d E /d x -E p article counter t e l e s c o p e ...........................................37

Figure 2. 5. D etector r e s p o n s e ..............................................................................40

Figure 2 . 6 . Schem atic diagram o f detector and collim a tor assem bly . . . 45

Figure 2. 7. B lock diagram of electron ic s y s t e m .......................................... 47

Figure 2. 8 . P a rticle separation by m ass and c h a r g e ..................................52

Figure 2. 9. Block diagram o f m ultiparam eter analyzer l o g i c ......................... 55

Figure 2.10. Photograph o f experim ental control a re a ..............................................55

Figure 2.11. Multiparameter analyzer contour and isom etric displays, b 11+n ! 5 reaction s ................................................................................. 57

Figure 2.12. Multiparameter analyzer contour and isom etric displays, Bn +C1 2 , Bu +N14, and B44+ 0 46 re a ctio n s.......................................57

Figure 2 .1 3 . P a rticle identification system response to boronio n s .......................60

Figure 2 .1 4 . M ultiparam eter analyzer energy c a lib r a t io n s .................................. 67

Figure 2.15. Figure 3.1. Figure 3.2.

Multiparameter analyzer excitation energy calibrations

X 2

X 3

X4 9

C and C angular distributions, N +Be reactions

10

12 11 „ 10,XT13

Be energy spectrum , C (B ,B e )N

B49 energy spectrum , C4 2 (B44, B4 0 )C48

. . . 67 . . . 76
78

Figure 3. 3.

B e1 0 energy spectrum , C 4 3 (B4 4 , B e4 0 )N44 B40 energy spectrum , C ^ ( B H , B4 9 )C4 4 ...................................... 78

Figure 3. 4. B e19 energy spectrum , N4 4 (B4 4 , B e4 9 ) 0 48

B4 0 energy spectrum , N4 4 (B4 4 , B4 0 )N48

78

Figure 3.5.

Be1 9 energy spectrum , N4 8 (B4 4 , B e4 0 )O48 B49 energy spectrum , N4 8 (B4 4 , B4 9 )N4 8 ......................................78

Figure 3. 6 . Be49 energy spectrum , 0 4 8 (B4 4 , Be4 9 )F47

B49 energy spectrum , 0 4 8 (B4 4 , B 4 9 )0 47

78

Figure 3. 7.

Be49 energy spectrum , Ne2 0 (B4 4 , Be4 0 )Na34 B4 9 energy spectrum , Ne2 9 (B4 4 , B1 0 )Ne2 4 ......................................78

Figure 3. 8 .

B40 and Be40 energy spectra from (B44 , B45) and (B4 4 , B e 40) single-nucleon transfer r e a c t i o n s ................................. 94

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Figure 3. 9. Dependence of reaction Q value on the m ass number o f the residual nucleus for levels preferentially populated in the (B ^ L b -*9) and (B^^,Be^®) re a ctio n s.................................. 96

Figure 3 . 1 0 . Com parison o f experim ental and calculated ( B H , B-^9) and (B11, Be19) transfer reaction cross section ratios . . . 117

Figure 3 .1 1 . (B-*-9+n) and (Be-^^+p) parentage o f the B ^ ground state . . . 1 19

Figure 4.1. Figure 4. 2.

B e9 energy sp ectru m , C 1 2 (B1 1 , B e9 )N1 4 ......................................... 122 B e9 energy spectrum , C1 2 (B11, Be^JN1^ ......................................... 122

Figure 4. 3. B e9 energy sp ectru m , n 1 4 (b H , B e9 )CJ9 ......................................... 122

Figure 4. 4. B e9 energy spectrum ,

, B e9 ) 0 ^ ......................................... 122

Figure 4. 5. B e9 energy spectrum , 0 1 ®(B1 1 , B e9 )F 1 8 ......................................... 122

Figure 4. 6 . B e9 energy spectrum , Ne2 0 (B1 1 , B e9 )Na2^ ................................... 122

Figure

4. 7. Angular distributions, B11-induced single-nucleon and deuteron tran sfer r e a c t i o n s ....................................................... 124

Figure 4. 8 . B e9 energy spectra, O ^ B -*^ , B e9 )F -*-8 ............................................127

Figure 4. 9. Deuteron energy spectra from ( 0/, d) r e a c tio n s ...............................129

Figure 4.10.

B e9 energy spectra from (B1 :1- , B e 9) deuteron transfer r e a c t i o n s ................................................................................................... 142

Figure 4.11.

Dependence of reaction Q value on the m ass number of the residual nucleus fo r levels o f p roposed ^ 5 / 2 )$ and (d5 / 2f7/ 2 )6 configurations preferen tially populated in (B1 1 , B e9) r e a c t i o n s .........................................................................145

Figure 4.12.

B ^ energy spectra, N*4 ( B ^ , B^^)N^4 and

, B-*-^)0^ 8

r e a c t i o n s ...................................................................................................147

Figure 4.13.

Comparison of absolute total cro ss sections for ( B H .B e 9) and ( a , d ) giant excitation s.............................................. 150

Figure 4.14.

B e9 and deuteron angular distributions, B^1+ 0 ^8 and a+ O * 9 r e a c t i o n s ..................................................................................... 153

Figure A. 1.

Effective charge param eter, y , as a function of ion atom ic number and e n e r g y ................................................................166

Figure A. 2. R ange-energy relations fo r heavy ions in aluminum....................171

Figure A. 3. Stopping power for heavy ions in various materials . . . . 173

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1
I. INTRODUCTION
A. The Heavy-ion Transfer Reaction The heavy-ion transfer reaction is that in which a nucleon or clu ster of
nucleons is exchanged during the scattering of two com plex nuclei. These reactions w ere fir s t observed experim entally a little over a decade ago^ 1 and have since been the subject of extensive theoretical and experim ental study.(2) Reviews of this work have been presented during this period by a number of authors/ 3-71
Transfer reactions have traditionally been considered a part of the broader field of heavy-ion physics. However, theanergence of the general properties of heavy-ion interactions from an e v e r-in cre a sin g body of experim ental and theoretical information and the establishment of the qualitative ch a racteristics of many of these reaction s have resulted in a gradual integration of heavy-ion studies into the general field of nuclear structure and reaction physics. Present studies of transfer re a ctio n s, in com m on with companion studies involving lighter p r o je c t ile s , share the separate but related ob jectives o f elucidating the reaction m echanism s and of providing inform ation on the structure of the nuclei involved.
There are a number of advantages inherent in the utilization of heavy p ro ­ je c tile s in nuclear reaction studies. Because o f their short mean fr e e path in nuclear m atter, heavy-ion reaction s are lo ca lize d in the nuclear surface and are highly selective in populating collectiv e states strongly coupled to the ground state in scattering and particularly sim ple single or m ulti-particle or hole states in transfer reactions. Large angular momenta are ch aracteristic of heavy p ro je ctile s , thus providing a mechanism fo r the form ation of otherwise in accessible states of high angular momentum. Evidence will be adduced later that an additional sp ecific m echanism exists leading to an enhanced population of these high-spin states in transfer reaction s. The com plexity of the reaction produ cts p aradoxically enables a reasonably accurate specification of the reaction m echanism to be made in many c a s e s , and the p ossib ility of tra n sfer-* ring several nucleons allow s the examination of m ulti-nucleon correla tion s in

2
the nuclei involved. F inally, the features of many heavy-ion interactions may be ea sily understood in term s of cla s sic a l analogs, which, although not detailed, furnish the physical insight required fo r the proper assessm ent of m ore com plete theories.
It should be noted that there are attendant lim itations associated with the use of heavy projectiles. The lack of detailed nuclear structure calculations for heavy nuclei has resulted in the absence of a general m icro s co p ic procedure for the extraction of absolute sp ectroscop ic fa ctors from experim ental data. Recent evidence, both experim ental and th eoretica l, suggests that only v e r y restricted nuclear structure information is derivable from transfer angular distributions, at least when studied at relatively high energies. The ch aracteristically large number of open reaction exit channels resu lts in a general depletion of the c r o s s section fo r any given p r o c e s s , and the resultant large number of reaction products p oses form idable p roblem s in the experim ental isolation of a particular nuclear species fo r analysis. The high energy loss rates of com plex nuclei often demand correction fo r energy lo sse s in absorbing m aterials which are present experimentally and, m ore fundamentally, make it difficult to achieve adequate resolution to separate individual residual energy states. There is often an am biguity, ch a ra cteristica lly not present fo r light p r o je c tile s , in the assignment of observed final state excitations for reactions involving binary exit channels wherein both nuclei p ossess low -lying stable excited states.
Even in the sim plest approxim ation, the transfer reaction rem ains a com plicated theoretical problem which involves a nuclear system com prising at least three m em bers, the two heavy nuclear co re s and the transferred nucleon or nucleon cluster. General techniques for solving three-body nuclear problem s have not as yet been developed to such an extent that they a re useful in these situations. H owever, studies of transfer reactions have shown that these reactions a re, nevertheless, often describable in term s of rather sim plified nuclear reaction m odels. This w ork has a lso indicated that the nature of the
ReactionsPopulationTransfer ReactionsDistributionsData