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Method for determining total proton reaction cross sections Hojvat, Carlos Federico 1967

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THE U N I V E R S I T Y OF B R I T I S H COLUMBIA FACULTY OF GRADUATE STUDIES PROGRAMME OF THE F I N A L ORAL EXAMINATION FOR THE DEGREE OF DOCTOR OF PHILOSOPHY o f CARLOS FEDERICO HOJVAT L i c e n c i a d o e n F i s i c a , U n i v e r s i d a d N a c i o n a l de C u y o , 1962 TUESDAY, AUGUST 1, 1967 AT 3:30 P.M. IN ROOM 3 0 1 , HENNINGS BUILDING COMMITTEE I N CHARGE C h a i r m a n : .': - J . H. G. S m i t h P. W. M a r t i n E. W. V o g t P. S t e p h a s B. R. James M. K. C r a d d o c k R e s e a r c h S u p e r v i s o r : G. J o n e s E x t e r n a l E x a m i n e r : G e o r g e I g o , L o s A l a m o s S c i e n t i f i c L a b o r a t o r y , U n i v e r s i t y o f C a l i f o r n i a , L o s A l a m o s , New M e x i c o . A METHOD FOR DETERMINING TOTAL PROTON REACTION CROSS SECTIONS ABSTRACT Measurements, of t o t a l proton reaction cross sections by the beam-attenuation method involve determinations of the number of protons removed from the incident beam by an absorber compared to those transmitted. This work presents an adaptation of the associated p a r t i c l e technique to enable t o t a l reaction cross section measurements for the 15.8 MeV protons from the 3He(d,p) 4He reaction. A thick heavy ice target i s bombarded with 600-kev ^He p a r t i c l e s . The 4He p a r t i c l e s are detected in a s i l i c o n surface-barrier detector, and the protons, after traversing the absorber, i n a Csl s c i n t i l l a t i o n counter. Both the s p a t i a l collimation and the time of a r r i v a l of the proton are defined by the detection of the associated 4He p a r t i c l e . Thus, removal of a proton from the proton "beam" i s i d e n t i f i e d by an anticoincidence between the 4He and proton counters, whereas proton transmission i s i d e n t i f i e d by a coincidence. The l i m i t a t i o n s and applications of the technique are presented, as well as a discussion of the c r i t i c a l portions of the experimental'' design. AWARDS 1959-1962 Comision Nacional de Energxa Atomica, Inst i t u t o de F i s i c a de S.C. de Bariloche (Argentina) Scholar-ship. 1962 Comision Nacional de Investiga-ciones C i e n t i f i c a s y Tecnicas. (Argentina) Travel Grant. GRADUATE STUDIES F i e l d of Study: Experimental Nuclear Physics. Quantum Mechanics J.A. Balseiro Nuclear Physics CA. Mallmann Electro n i c s for Nuclear Physics W. Orvedahl Theoretical Nuclear Physics F. Morey Terry Health Physics J.M. Feola S t a t i s t i c a l Mechanics J.A. Balseiro Nuclear Physics E.W. Vogt Theory of Measurements J . Williamson PUBLICATIONS C. F. Hojvat and Garth Jones, Method for determining Total Proton Reaction Cross Sections, Using an Associated P a r t i c l e Technique, B u l l . Amer.Phys. S o c , 11 (1966) 724. C. Hojvat, Proton Reaction Cross Sections at 15 MeV, presented at the Western Regional Nuclear Conference , February 1967 A METHOD FOR DETERMINING TOTAL PROTON REACTION CROSS SECTIONS by CARLOS FEDERICO HOJVAT Licenciado en F i s i c a I n s t i t u t o de F i s i c a de S.C. de Bariloche, Universidad Nacional de Cuyo, • 1962 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in the Department of PHYSICS We accept t h i s thesis as conforming to the required standard, THE UNIVERSITY OF BRITISH COLUMBIA August, 1967 In p re sen t i ng t h i s t he s i s in p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e fo r re ference and Study. I f u r t h e r agree that permiss ion f o r ex ten s i ve copying of t h i s t he s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h.iJs r e p r e s e n t a t i v e s . It i s understood that copying or p u b l i c a t i o n of t h i s t he s i s f o r f i n a n c i a l gain s h a l l not be a l lowed wi thout my w r i t t e n pe rmi s s i on . Department of Physics  The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8 , Canada August, 1967 ACKNOWLEDGMENTS To Dr. Garth Jones whose patience i n overcoming the language b a r r i e r , guidance and understanding made t h i s work poss i b l e . To Dr. Ian McTaggart-Cowan, Dean of Graduate Studies, and other a u t h o r i t i e s of the Unive r s i t y of B r i t i s h Columbia who made possible the t r a n s f e r of my studies to the Ph.D. program of t h i s U n i v e r s i t y . To the technicians and"students i n the Nuclear Physics group who aided i n the maintenance of the accelerator. A l Consejo Nacional de Investigaciones C i e n t i f i c a s y Tecnicas de l a Republica Argentina que p o s i b i l i t o mi v i a j e a esta Universidad. A mis padres. To S a l l y . ABSTRACT Measurements of t o t a l proton reaction cross sections by the beam-attenuation method involve determinations of the number of protons removed from the incident beam by an absorber compared to those transmitted. This work presents an adaptation of the associated p a r t i c l e technique to enable t o t a l reaction cross section measurements f o r the 15.8 MeV protons from 3 4 the He(d,p) He reaction. A thick heavy i c e target 3 4 i s bombarded with 600-keV He p a r t i c l e s . The He p a r t i c l e s are detected i n a s i l i c o n s u r face-barrier detector, and the protons, a f t e r traversing the absorber, i n a C s l s c i n t i l l a t i o n counter. Both the s p a t i a l c o l l i m a t i o n and the time of a r r i v a l of the proton are defined by the detection of the associated 4 . He p a r t i c l e . Thus, removal of a proton from the proton "beam" i s i d e n t i f i e d by an anticoincidence . 4 between the He and proton counters, whereas proton transmission i s i d e n t i f i e d by a coincidence; The l i m i t a t i o n s and applications of the technique are presented, as well as a discussion of the c r i t i c a l portions of the experimental design.-- i i i -TABLE OF CONTENTS ACKNOWLEDGMENTS.- i ABSTRACT.- i i TABLE OF CONTENTS.- i i i LIST OF FIGURES.- v i i i LIST OF TABLES.- x i INTRODUCTION.- x i i CHAPTER I.- THEORY 1. - General introduction 1 2. - Early models 1 3. - The o p t i c a l model 3 4. - The terms of the p o t e n t i a l 6 4.1. - Real term 7 4.2. - Imaginary term 9 4.3. - Spin-orbit term 10 5. - The o p t i c a l model c a l c u l a t i o n s 11 6. - The f i t t i n g of experimental data 13 7. - The importance of experimental uncertainties 16 8. - Computer c a l c u l a t i o n s 17 CHAPTER I I . - TOTAL REACTION CROSS SECTION MEASUREMENTS 1. - General introduction 19 2. - The reaction channels 19 2.1. - The compound e l a s t i c channel 20 2.2. - The i n e l a s t i c s c a t t e r i n g channel 22 2.3. - The charged p a r t i c l e s channels 23 2.4. - The neutron channel 23 3. - The i n d i r e c t method 24 - i v -4.- The d i r e c t methods 25 4.1. - The beam attenuation method 26 4.1.1. - S t a t i s t i c a l considerations 28 4.1.2. - Geometry considerations 34 4.1.3. - Total reaction cross sections measurements 37 4.2. - Basic attenuation method as.applied to t o t a l reaction cross section measurements f o r protons 39 4.3. - The charge method 39 4.4. - The o p t i c a l theorem 41 4.5. - The range ;method 43 4.6. - The coincidence method . 44 4.6.1. - The basic coincidence method 45 4.6.2. - The r e c o i l method 48 4.6.3. - The associated p a r t i c l e method 49, CHAPTER I I I . - EXPERIMENTAL DESIGN 1. - General introduction.. 50 2. - The associated p a r t i c l e technique 50 2.1. - Production of associated beams 50 2.2. - Limitations of the technique 51 2.3. - Production of associated beams of charged p a r t i c l e s 53 2.4. - Requirements f o r an attenuation experiment 54 3 4 3. - The He(d,p) He. reaction- . 56 3;1.- Reaction kinematics 58 3.2. - Kinematical c o l l i m a t i o n of the associated proton beam 66 3.3. - Source target angle, 70 - V -3.4.- Expected y i e l d s 72 4. - Corrections . 75 4.1. - Target corrections 75 4.1.1. - E l a s t i c s c a t t e r i n g 75 4.1.2. - I n e l a s t i c s c a t t e r i n g 76 4.1.3. - L a t t i c e e f f e c t s 77 4.2. - The attenuation background 79 4.2.1. - Background due to the backing f o i l 80 4.2.2. - Background due to the proton detector 85 4.2.3. - Background due to energy degraded protons 96 4.2.4. - Background due to.source target thickness 98 5. - E l e c t r o n i c requirements 99 CHAPTER IV,- THE EXPERIMENTAL SET-UP 1. - General introduction 108 2. - The chamber 108 2.1. - The col l i m a t o r assembly 110 2.2. - The s o l i d state detector assembly 111 2.3. - The deuterium target 113 2.4. - The f i n a l target assembly. 117 2.5. - The rotary assembly 119 2.6. - The proton detector assembly 120 3. - E l e c t r o n i c s 121 3.1. - The s o l i d state detector channel 122 3.2. - The photomultiplier channel 124 3.3. - Coincidences and anticoincidences 126 3.4. - The paralysable dead time generator 127 - v i -4.- E l e c t r o n i c s performance. 131 4.1. - The paralysable dead time generator 131 4.2. - Proton channel threshold t r i g g e r i n g and c a l i b r a t i o n 133 CHAPTER V.- PERFORMANCE AND CONCLUSIONS 1. - General introduction 136 2. - The associated beam.profile;.:- 136 3. - The anticoincidence .background.. 138 3.1. - The primary beam parameters 138 3.2. - The heavy i c e t h i c k n e s s 1 3 9 3.3. - The p l a s t i c s c i n t i l l a t o r : 139 3.4. - The C s l detector 140 3.4.1.- L a t t i c e e f f e c t s 146 4. - The measurements of t o t a l proton reaction cross sections 146 4.1. - Summary of r e s u l t s f o r gold 150 4.2. - Results f o r copper and iron 151 4.3. - "Difference" measurements 154 5. - Conclusions, 157 APPENDIX I.- CONSIDERATIONS IN THE DESIGN OF THE HEAVY ICE TARGET 1. - The target 163 2. - Power d i s s i p a t i o n 164 3. - Energy s t r a g g l i n g and.multiple s c a t t e r i n g 169 3.1. - Energy st r a g g l i n g 169 3.2. - M u l t i p l e : s c a t t e r i n g 171 4 4. - Anticoincidence background due to He s c a t t e r i n g 172 - v i i -APPENDIX I I . - NATURAL FOCUSING 177 APPENDIX I I I . - ELECTRONIC CIRCUITS 181 BIBLIOGRAPHY.- 190 - v i i i .-LIST OF FIGURES Figure number T i t l e Page 2.1 The reaction channels ; 20 2.2 Relative error as. a.function of the sample transmission 30 2.3 Relative error as a function of the sample attenuation 31 2.4 T y p i c a l attenuation experiment ................... 34 2.5 Schematic of,charge; method experiment 40 2.6 Schematic diagram, of ...the Basic Coincidence method ................ . .. 45 2.7 Schematic diagram of.the Low Energy Basic Coincidence method 47 3.1 Schematic diagram of.an."Associated p a r t i c l e " attenuation experiment 54 3 4 i-n 3.3 He(d,p) He reaction.kinematics 59 3 4 , _ 3.4 He(d,p) He reaction kinematics........... 60 3 4 3.5 He(d,p) He reaction kinematics 61 3 4 3.6 He(d,p) He . reaction-kinematics 62 3 4 3.7 He(d,p) He reaction.-kinematics................... 63 3 4 , A 3.8 He(d,p) He.reaction kinematics 64 3.9 3He(d,p) 4He reaction-kinematics ................... 68 3 4 rr. 3.10 He(d,p) He. reaction-kinematics ................... 69 3.11 Source target angle .............................. 72 - i x -Figure number T i t l e Page 3.12 Attenuation background-due to the backing f o i l thickness, as a function of the thickness and the angle subtended:by.the proton detector. 83 3.13 Counting rate at the proton detector as a function of subtended angle 84 3.14 Energy loss curves f o r d i f f e r e n t detectors 90 3.15 Proton t o t a l reaction.cross.sections, coulomb b a r r i e r s and (p,n) thresholds, f o r n u c l e i o f d i f f e r e n t detectors ........ 91 3.16 Calculated attenuation-per MeV of energy loss i n d i f f e r e n t detectors 92 3.17 Calculated attenuation.in CsI as a function of the discrimination, l e v e l .... 94 3.18 Block diagram of e l e c t r o n i c requirements .......... 107 4.1 Schematic diagram of..:the. chamber . 109 4.2 Attenuation as a function of the h o r i z o n t a l 4 p o s i t i o n He detector^....,. 112 4.3 Attenuation as.a.function of the v e r t i c a l 4 p o s i t i o n He. detector-........... 112 4.4 T y p i c a l s o l i d state:detector.spectrum ,.. 114 4.5 C a l i b r a t i o n of heavy .-ice thickness ......... 116 4.6 Stopping power of ^O-.f or ..different p a r t i c l e s . . 1 1 6 4.7 Schematic diagram of the f i n a l target assembly ... 118 4.8. Schematic diagram of the rotary assembly .... 118 4.9 Block diagram of the e l e c t r o n i c s 123 - X -Figure number T i t l e Page 4.10 The paralysable deacLtime generator (e s s e n t i a l components) . 128 4.11 C i r c u i t diagranuof..the.-paralysable dead time generator ................................. 129 4.12 Paralysable dead time generator performance, 134 4.13 Time p i c k o f f unit c a l i b r a t i o n .................... 134 5.1 Associated proton beam p r o f i l e 137 5.2 Attenuation background..as a' function of the disc r i m i n a t i o n l e v e l -........................... 143 5.3 Comparison of the.results -for iron and copper with other measurements i n the same energy range.. 158 A l . 1 Source target power ^ d i s s i p a t i o n 166 AI.2 Energy deposited in.backing f o i l 166 AI.3 Temperature r i s e at.the center of the heavy i c e target 170 4 AI.4 Anticoincidence background due to He s c a t t e r i n g . . 175 A I I . l Natural focusing e f f e c t 178 All.-2 Natural f6cusing in-conjunction with kinematical c o l l i m a t i o n 178 A I I I . l C i r c u i t diagram of the low noise charge s e n s i t i v e p r e a m p l i f i e r 182 - x i -Figure number T i t l e . Page AIII.2 C i r c u i t diagram, of J. pulse shaper .... .. 183 AIII.3 C i r c u i t diagram: of.*zero, crossover t r i g g e r ........ 185 AIII.4 C i r c u i t diagram of f a s t t r i g g e r c i r c u i t 185 All1.5 C i r c u i t diagram.of photomultiplier preamplifier... 186 AIII.6 C i r c u i t diagram.of fast AC gates 187 A l l I. 7 C i r c u i t diagram.-of fast C gate 188 AIII.8 C i r c u i t diagram of double slow C gates 189 , LIST OF TABLES Table number T i t l e Page 3.1 Values f o r backing f o i l background calculations.... 82 5.1 Char a c t e r i s t i c s , of .the .different targets ......... 149 5.2 Experimental r e s u l t s ............... .-............'. . 152 . 5.3 Measured differences .........'.................... 156 5.4 Total reaction cross sections generated from :. differences 156 - x i i -INTRODUCTION From the phenomelogical p o i n t of view, the most s u c c e s s -f u l method of d e s c r i b i n g the average I n t e r a c t i o n between a nucleus and an incoming p a r t i c l e has, without doubt, been the o p t i c a l model d e s c r i p t i o n . In t h i s d e s c r i p t i o n the p r o p e r t i e s f o r the p o t e n t i a l d e s c r i b i n g the i n t e r a c t i o n are assumed on p h y s i c a l b a s i s and expressed i n terms of a number of parameters. By s o l v i n g the/'."' wave equation w i t h t h i s p o t e n t i a l a c e r t a i n number of observa-b l e s are c a l c u l a t e d and compared to experimental r e s u l t s . The parameters are then a d j u s t e d i n order to o b t a i n a good des-c r i p t i o n of the experimental data. Values obtained f o r these parameters are not n e c e s s a r i l y unique, s i n c e t h e i r ambiguity depends on the amount and accuracy of the experimental data with which the comparison i s made. In Chapter 1 , a simple d e s c r i p t i o n of the o r i g i n of the O p t i c a l Model, the p a r a m e t e r i z a t i o n - o f i t s complex p o t e n t i a l , the method of c a l c u l a t i o n and the importance of experimental r e s u l t s i n determining the uniqueness of the parameters Is presented. Of s p e c i a l i n t e r e s t f o r our work i s the r e s t r i c -t i o n i n the parameters t h a t a r i s e s from I n c l u d i n g i n the e x p e r i -mental data values f o r t o t a l r e a c t i o n c ross s e c t i o n s f o r protons measured w i t h e r r o r s of the order of 3 $ . I n a d d i t i o n , measure-ments of the d i f f e r e n c e s between t o t a l r e a c t i o n c ross s e c t i o n s f o r neighbouring n u c l e i , w i l l p r o v i d e v a l u a b l e i n f o r m a t i o n on the i n t e r a c t i o n s of the incoming p a r t i c l e w i t h a few nucleons. Chapter 2 i s a review of the d i f f e r e n t methods emp-- x i i i -loved In proton t o t a l r e a c t i o n c r o s s s e c t i o n measurements. Proton r e a c t i o n c ross s e c t i o n s at energies of the order of the Coulomb b a r r i e r energies (approximately.10 Mev i n medium weight n u c l e i ) are expected t o be p a r t i c u l a r l y dependent on the c h a r a c t e r i s t i c s of the n u c l e a r p o t e n t i a l . Accurate measurements at these energies are made d i f f i c u l t by the l i m i t imposed on the sample t h i c k n e s s by the energy l o s s by the proton beam In i t . T h i s r e s u l t s In a t t e n u a t i o n s t o be measured of the order of a. few p a r t s i n 10~^. The d e s c r i p t i o n of a new method t o measure t o t a l p r oton r e a c t i o n c ross s e c t i o n s , based on the " a s s o c i a t e d p a r t i c l e t echnique", i s the aim of t h i s t h e s i s . The.method i s i n t r o d u c e d In Chapter 2 S e c t i o n 4 .6.3 as a m o d i f i c a t i o n to the c o i n c i d e n c e method th e r e d e s c r i b e d . A d e t a i l e d d i s c u s s i o n of the de s i g n of the experiment i s presented i n Chapter 3 t o g e t h e r w i t h a d e s c r i p t i o n of the "a s s o c i a t e d p a r t i c l e t echnique" i n g e n e r a l . S p e c i a l a t t e n t i o n was placed on a n a l y s i n g the p o s s i b l e sources of background. As a r e s u l t of the de s i g n c o n s i d e r a t i o n s , the e x p e r i -mental set up was c o n s t r u c t e d i n order t o I n v e s t i g a t e the u s e f u l n e s s o f . t h e method. The set up i s d e s c r i b e d i n d e t a i l i n Chapter 4. The performance of the system i s presented i n Chapter 5 t o g e t h e r with r e s u l t s f o r r e a d i l y a v a i l a b l e t a r g e t s of n a t u r a l copper, i r o n and g o l d . These measurements obtained with e r r o r s i n the order of lh% are i n good agreement with values measured by other authors i n the same energy range. P o s s i b l e methods of - xiv -improving the technique i n order t o decrease these e r r o r s are presented i n S e c t i o n 5 of Chapter 5. In S e c t i o n 4.3 of Chapter 5 the method of performing., accurate measurements, of d i f f e r e n c e s between t o t a l proton r e a c t i o n cross sections., w i t h our technique, i s presented. The references c i t e d i n Chapter 2 are not intended as a complete review of the d i f f e r e n t methods or t h e i r o r i g i n , but merely to provide examples complementing the e x p o s i t i o n of the s u b j e c t . NOTE: E f f o r t has been made throughout the t h e s i s to be c o n s i s t e n t w i t h the nomenclature, symbols and u n i t s according to the "INTERNATIONAL UNION OF PURE AND APPLIED.PHYSICS" published i n NUCLEAR PHYSICS 81(1966)677. - 1 -1. THEORY 1. General i n t r o d u c t i o n . The aim of t h i s Chapter Is to b r i e f l y Introduce the . n u c l e a r " O p t i c a l Model". Emphasis w i l l be put on the i n f l u e n c e of the experimental data i n determining the phenomenological parameters of the model, the a m b i g u i t i e s i n these parameters, and the importance of the t o t a l r e a c t i o n c ross s e c t i o n measure-ments. There are a v a i l a b l e a l a r g e number of good review a r t i c l e s and books d e d i c a t e d to the t h e o r e t i c a l aspects and the f i t t i n g of experimental data by. means of the " O p t i c a l Model". See f o r example (Pe 54), (Br 58), (Bu 60), (Pr 62), (Ho 63), (Ho 6 4 ) . 2. E a r l y models . The d e s c r i p t i o n of a simple event such as the e l a s t i c s c a t t e r i n g of a nucleon: by a n u c l e u s , becomes extremely d i f f i c u l t i f d e t a i l e d account i s to be taken of the i n t e r a c t i o n s of the p r o j e c t i l e , with each one of the nucleons In the t a r g e t n u c l e u s . The use of a s i m p l i f i e d d e s c r i p t i o n i s necessary, and normally i n v o l v e s approximation of the many-body i n t e r a c t i o n s i n terms of a s i n g l e p a r t i c l e p o t e n t i a l , which r e p r e s e n t s the average e f f e c t of the many t a r g e t nucleons on the incoming p a r t i c l e . For i n c i d e n t neutrons, the average p o t e n t i a l i s an a t t r a c t i v e one of n u c l e a r dimensions. .For i n c i d e n t charged p a r t i c l e s , the net p o t e n t i a l i s considered as the sum .of such a n u c l e a r p o t e n t i a l and the Coulomb p o t e n t i a l of a f i n i t e n u c l e a r charge d i s t r i b u t i o n . The f i r s t attempt i n t h i s d i r e c t i o n i n v o l v e d the use - 2 -of a p a r t i c u l a r l y simple approximation f o r the n u c l e a r p o t e n t i a l , v i z . , a square w e l l . For t h i s case, a s t r a i g h t forward s o l u t i o n of the Schrodinger equation was p o s s i b l e without the n e c e s s i t y of lengthy numerical i n t e g r a t i o n s . T h i s simple model was used by Bethe i n 1935 (Be 35) .and even though i t y i e l d e d some r e s u l t s i n agreement with experiments, i t f a i l e d to account f o r a number of p a r t i c u l a r l y obvious experimental e f f e c t s . The extremely l a r g e values of the s c a t t e r i n g c r o s s s e c t i o n s obtained at widely spaced resonances (approx. 10 MeV s p a c i n g , 1 MeV width) were i n disagreement with the e x p e r i m e n t a l l y observed sharp resonances separated by a few e l e c t r o n v o l t s c h a r a c t e r i z i n g neutron s c a t t e r -i n g . As an a l t e r n a t i v e approach to the s i n g l e p a r t i c l e d e s c r i p t i o n mentioned above, Bohr proposed i n 1936 (Bo 36) the immediate f o r m a t i o n of a many-body s t a t e a f t e r the i n c i d e n t p a r t i c l e Impinges on the t a r g e t n u c l e u s . T h i s Is j u s t i f i e d on the b a s i s t h a t m a n y - p a r t i c l e s t a t e s are necessary In order to e x p l a i n the c l o s e l y spaced resonances. The incoming p a r t i c l e and the nucleons i n the t a r g e t nucleus w i l l a l l I n t e r a c t s t r o n g l y w i t h each o t h e r , or i n other words, the incoming p a r t i c l e w i l l be absorbed by the t a r g e t nucleus to form a new one: the "Compound Nucleus". Due to t h i s s h a r i n g , by the nucleons i n the Compound system, of the energy brought In by the incoming p a r t i c l e , a much l a r g e r number of quantum s t a t e s are a v a i l a b l e f o r e x c i t a t i o n . T h i s approach accounted f o r the low energy neutron resonances t h a t the s i n g l e p a r t i c l e model f a i l e d t o account f o r . However, subsequent s t u d i e s of t o t a l neutron c r o s s - 3 -s e c t i o n s as a f u n c t i o n of energy u s i n g poor energy r e s o l u t i o n gave r e s u l t s s i m i l a r to those obtained i n the s i n g l e p a r t i c l e model (Fo 50, Ba 5 2 ) . In a d d i t i o n , compound n u c l e i were found, t o decay e m i t t i n g p a r t i c l e s with energies l a r g e r than expected on the b a s i s of complete s h a r i n g of the i n c i d e n t energy by a l l nucleons (Gu 5 ^ ) . T h i s i n d i c a t e d t h a t immediate forma-t i o n of a compound nucleus d i d not n e c e s s a r i l y take p l a c e when the incoming p a r t i c l e reached the n u c l e a r s u r f a c e . A f t e r a l l , the success of the " S h e l l Model", t h a t had been developed i n the i n t e r i m , demonstrated t h a t nucleons could e x i s t w i t h i n the nucleus i n s t a t e s of d e f i n i t e angular momentum and d e f i n i t e o r b i t s , without s h a r i n g t h e i r energy with other nucleons w i t h -i n the nu c l e u s . 3. The o p t i c a l "model. See (Be 4 0 , Fe 5 * 0 As d e s c r i b e d p r e v i o u s l y , n e i t h e r the s i n g l e p a r t i c l e model nor the s t r o n g i n t e r a c t i o n one, could p r o v i d e a complete d e s c r i p t i o n of the experimental d a t a . Both seemed to e x p l a i n q u a l i t a t i v e l y d i f f e r e n t aspects of the data. The s i n g l e p a r t i c l e model e x p l a i n s s a t i s f a c t o r i l y the average trends f o r l a r g e v a r i a -t i o n s of incoming, energy, whereas compound nucleus f o r m a t i o n i s necessary t o e x p l a i n the f i n e s t r u c t u r e present f o r s m a l l energy v a r i a t i o n s . A p o t e n t i a l w e l l model could s a t i s f a c t o r i l y account f o r the l a r g e energy i n t e r v a l e f f e c t s i f proper account Is taken of the p r o b a b i l i t y of forming a compound n u c l e u s . In other words, the p o t e n t i a l w e l l should accommodate a b s o r p t i o n of a c e r t a i n - 4 -f r a c t i o n of the incoming wave. The way t h i s a b s o r p t i o n i s in t r o d u c e d i n t o the s i n g l e p a r t i c l e model, i s by a l l o w i n g the p o t e n t i a l w e l l t o be complex. A complex p o t e n t i a l g i v e s r i s e to a complex wave number f o r the incoming p a r t i c l e i n s i d e the n u c l e a r r e g i o n . Thus the incoming wave i s attenuated i n propagating w i t h i n the complex p o t e n t i a l . T h i s a t t e n u a t i o n , or a b s o r p t i o n , i s d i r e c t l y r e l a t e d t o the i n t r o d u c t i o n of the imaginary term i n the n u c l e a r p o t e n t i a l . When the experimental r e s u l t s e x h i b i t a m a n y - p a r t i c l e s t r u c t u r e , I.e. sharp separated resonances, the model can not be expected t o account f o r i t s s t r u c t u r e . On the other hand, i f the r e s u l t s are "averaged" over a l a r g e number of resonances, the model w i l l e x p l a i n the gross behaviour. The complex w e l l i s r e f e r r e d t o as the "The O p t i c a l Model p o t e n t i a l " due to the analogy with the propa g a t i o n of l i g h t i n a semltransparent medium. An important c o n s i d e r a t i o n f o r the success of the model i s to determine the a c t u a l shape t o be taken i n t o account f o r the p o t e n t i a l . For a s p h e r i c a l l y symmetrical nucleus,' only dependence of the p o t e n t i a l on the n u c l e a r r a d i u s i s t o be expected.- • The s i m p l e s t p o t e n t i a l w e l l w i l l then be a square w e l l . As i n any. wave phenomena, a sharp edge p o t e n t i a l , as the one d e f i n i n g a square w e l l , w i l l produce a l a r g e r e f l e c t i o n of the incoming wave. In the o p t i c a l model d e s c r i p t i o n , t h i s r e f l e c t i o n i s j u s t too l a r g e t o accommodate enough a b s o r p t i o n . I f a smoothly v a r y i n g p o t e n t i a l , at the n u c l e a r bound-ary, i s c o n s i d e r e d , the p a r t i c l e can pe n e t r a t e i n t o the a b s o r p t i o n - 5 -p a r t of the p o t e n t i a l without being r e f l e c t e d beforehand. C e r t a i n l y a smooth v a r i a t i o n of the p o t e n t i a l i s p h y s i c a l l y more reasonable than a sharp boundary. Even when assuming a nucleus w i t h a w e l l d e f i n e d g e o m e t r i c a l boundary, the n u c l e a r i n t e r a c t i o n w i l l be expected to reach beyond i t f o r a d i s t a n c e determined by the range of n u c l e a r f o r c e s . In a d d i t i o n , the a c t u a l p h y s i c a l r a d i u s of the t a r g e t nucleus w i l l not be w e l l d e f i n e d due t o o s c i l l a t i o n s of the c o n s t i t u e n t nucleons. From the O p t i c a l Model p o i n t of view, compound nucleus f o r m a t i o n occurs v i a the a b s o r p t i o n a r i s i n g from the imaginary p a r t of the p o t e n t i a l . We must mention here the case of "Compound E l a s t i c S c a t t e r i n g " , d i s c u s s e d i n d e t a i l i n S e c t i o n 2 . 1 of Chapter 2 . T h i s i s the decay of the compound nucleus i n t o the same p a r t i c l e and energy t h a t gave r i s e t o i t . Such processes can complicate the experimental i d e n t i f i c a t i o n of simple p o t e n t i a l s c a t t e r i n g as compared t o compound nucleus f o r m a t i o n . We must emphasise here the phenomenological nature of the model. The g e n e r a l form of the p o t e n t i a l i s chosen u s i n g some t h e o r e t i c a l guidance, but the numerical values are then v a r i e d t o o b t a i n a "good f i t " to the experimental data. U n f o r t u n a t e l y , the vast amount of f i t t i n g of experimental data which has been accomplished t o date has f a i l e d t o d e f i n e a unique shape f o r the components of the complex p o t e n t i a l , ( p r o v i d -i n g a smooth boundary i s used). The shape of the imaginary p a r t i s p a r t i c u l a r l y i l l - d e f i n e d by the experimental data. T h i s i s perhaps expected from simple c o n s i d e r a t i o n s , the d i f f e r e n t types of mechanisms i n v o l v e d In the process of a b s o r p t i o n can vary - 6 -i n importance from the n u c l e a r c e n t r e t o the n u c l e a r s u r f a c e . As extreme cases we have the p o s s i b i l i t y of volume a b s o r p t i o n , where the imaginary p a r t of the p o t e n t i a l extends a c r o s s the n u c l e a r I n t e r i o r u n i f o r m l y , f o l l o w i n g the shape of the r e a l p o t e n t i a l ; and a l t e r n a t i v e l y , s u r f a c e a b s o r p t i o n , where the imaginary p o t e n t i a l i s assumed to be l o c a l i z e d on the n u c l e a r s u r f a c e . An i n c r e a s e of a b s o r p t i o n i n the r e g i o n o f . t h e n u c l e a r s u r f a c e , w i t h r e s p e c t t o the n u c l e a r i n t e r i o r , , i s suggested by the p o s s i b i l i t y of a b s o r p t i o n of the Incoming wave by e x c i t a t i o n of some of the t a r g e t nucleons i n t o neighbouring quantum s t a t e s . These s t a t e s w i l l be a v a i l a b l e In the s u r f a c e r e g i o n , whereas i n the n u c l e a r i n t e r i o r the P a u l i p r i n c i p l e w i l l f o r b i d t r a n s i t i o n s i n t o them. The r e l a t i v e values of the Coulomb b a r r i e r s and the i n c i d e n t energy, f o r the case of charged p a r t i c l e s , w i l l a l s o determine how much of the n u c l e a r I n t e r i o r i s exposed to the incoming wave. 4. The terms of - t h e ^ p o t e n t i a l . ' , In t h i s s e c t i o n we w i l l d e s c r i b e the d i f f e r e n t terms g e n e r a l l y used f o r the o p t i c a l model p o t e n t i a l and t h e i r p a r a -m e t e r i z a t i o n . The p o t e n t i a l can be w r i t t e n as the sum o f : U(r) = V ( r ) + i W(r) + V g p ( r ) + V c where V ( r ) i s the r e a l term, W(r) i s the imaginary term, V ( r ) the s p i n - o r b i t term and V c i s the Coulomb p o t e n t i a l f o r i n c i d e n t charged p a r t i c l e s . - 7 -4.1. The r e a l term. The r e a l term can be w r i t t e n as: V ( r ) = V . f ( r ) where f ( r ) d e f i n e s the r a d i a l dependence of the term. The r a d i a l form commonly used i s the so c a l l e d "Saxon-Woods" p o t e n t i a l o r : _ l for") = j 1 + ex^Cr-R.VeO I ( l . l ) where i / » h O. * Suc&ace dc^-foseness (1.2) A - A+o^i'c vjec^Mr The two parameters governing the r a d i a l .shape are 'r''* and ' a ' j ' r d e t e r m i n e s d i r e c t l y the n u c l e a r r a d i u s by the r e l a t i o n (1.2), and due to the.assumptions of the model, Is expected to be constant f o r a l l n u c l e a r s p e c i e s except the l i g h t n u c l e i where a constant d e n s i t y of n u c l e a r matter i n the core i s not a good assumption. The constant 'a' determines how d i f f u s e the n u c l e a r r a d i u s i s . The i n t e r v a l , centered about the average n u c l e a r r a d i u s , where the f u n c t i o n f ( r ) f a . l l s from .9 to .1 of the value at r = 0 i s g i v e n by: D = 4 a l n 3 = 4.40 a ( 1 . 3 ) The v a r i a t i o n s of these two parameters w i t h energy i s not so simple t o p r e d i c t . One would not expect the t a r g e t nucleus to change with the i n c i d e n t p a r t i c l e energy, but the parameters d e s c r i b e the average p o t e n t i a l and not the a c t u a l nucleus I t s e l f . With i n c r e a s i n g energy the r e s u l t can f o r example become more i n s e n s i t i v e t o the d e t a i l s of the n u c l e a r - 8 -s u r f a c e and the e f f e c t i v e i n t e r a c t i o n could appear t o be r e s t r i c t -ed to s h o r t e r r a d i i . We w i l l see t h a t the e x i s t e n c e of a m b i g u i t i e s between the e f f e c t s of d i f f e r e n t parameters makes i t d i f f i c u l t to o b t a i n phenomenological evidence f o r such changes. The t h i r d parameter a s s o c i a t e d with the r e a l p a r t of the p o t e n t i a l i s the amplitude or s t r e n g t h V whose v a r i a t i o n between d i f f e r e n t n u c l e a r s p e c i e s i s not expected to be s t r o n g . The model c o n s i d e r s each nucleus as an amount o f . u n i f o r m n u c l e a r matter with a s i z e determined by i t s r a d i u s (or mass number). T h i s i s j u s t i f i e d q u a l i t a t i v e l y by f i t t i n g e l a s t i c s c a t t e r i n g data f o r d i f f e r e n t n u c l e i at the same energy. On the other hand, the model t u r n s out to be s e n s i t i v e t o the i n c i d e n t energy and the p o t e n t i a l s must be changed to o b t a i n even q u a l i t a t i v e agreement. T h i s can be I n t e r p r e t e d In terms of. both the i n c i d e n t p a r t i c l e and the p o t e n t i a l being extended i n space and at l e a s t the r e a l i n t e r a c t i o n i s n o n - l o c a l In c h a r a c t e r . The f o r m u l a t i o n of the problem i s r e l a t i v e l y easy i n terms of a l o c a l p o t e n t i a l . By f i t t i n g data f o r d i f f e r e n t n u c l e i at d i f f e r e n t energies the dependence of the r e a l p a r t of the l o c a l p o t e n t i a l can be expressed as (Pe 63): V = 53.3 - .55 E + .4 Z A " 1 ^ + 27 (N-Z) A - 1 (1.4=) and g e n e r a l l y r e f e r r e d to as the "Perey p o t e n t i a l " (obtained from proton e l a s t i c s c a t t e r i n g data i n the range of 9 to 12 MeV and f o r n u c l e i from Pe to Au. The t h i r d term a r i s e s from the energy dependence of the r e a l p o t e n t i a l I n the presence of a Coulomb f i e l d (La 57). The f o u r t h term, depending on the nucleon symmetry number, (N-Z) A - 1 , c h a r a c t e r i z i n g , t h e t a r g e t nucleus i s expected t h e o r e t i c a l l y on the b a s i s of i s o s p i n dependence of n u c l e a r - 9 -i n t e r a c t i o n (La 62). For a rec e n t re,view concerning these two l a s t terms see (Ho 67). 4.2. The imaginary term. The imaginary term can be w r i t t e n as: W ( r ) = W . g ( r ) I f the r a d i a l shape i s assumed t o be the same as the r e a l term the onl y parameter s p e c i f i c a l l y a s s o c i a t e d w i t h i t i s the s t r e n g t h W . E x t r a parameters are i n t r o d u c e d when a shape d i f f e r e n t than t h a t of the r e a l term i s c o n s i d e r e d . In the case of s u r f a c e a b s o r p t i o n u s u a l l y a Gaussian shape Is used. T h i s i s d e s c r i b e d by: g ( r ) = exp [ - ( r - £ ) 2 / b 2 ] (1-5) The n u c l e a r r a d i u s R can be taken as equal t o t h a t d e f i n e d f o r the r e a l term and one more parameter e l i m i n a t e d . The parameter 'b', somewhat analogous t o d i f f u s n e s s , d e f i n e s t h e - " s u r f a c e t h i c k n e s s " f o r a b s o r p t i o n . Much e f f o r t has been expended i n the past i n t r y i n g to determine the nature of the a b s o r p t i v e Imaginary p o t e n t i a l , i n p a r t i c u l a r , whether i t i s p r i m a r i l y a s u r f a c e or volume term. I f a constant volume a b s o r p t i o n w i t h s u r f a c e peaking i s used, then at l e a s t another parameter must, be i n t r o d u c e d . See f o r example (Lu 63). Another f r e q u e n t way of I n t r o d u c i n g a s u r f a c e p l u s volume a b s o r p t i o n i n v o l v e s a decomposition of the imaginary term of the p o t e n t i a l i n t o two terms: W ( r ) = W v f ( r ) + 4 a t W s d [ f ( r ) ] / dr (1.6) each term with i t s own s t r e n g t h . The volume p a r t i s normally - 10 -assigned the same r a d i a l dependence as the r e a l p a r t and the surface, c o n t r i b u t i o n the d e r i v a t i v e of the volume. The 4 a^ f a c t o r i s i n t r o d u c e d t o make the peak value of the r a d i a l d i s t r i b u t i o n equal t o u n i t y . As b e f o r e another parameter, W , s i s i n t r o d u c e d . 4 .3. The s p i n - o r b i t term. P o l a r i z a t i o n of the incoming p a r t i c l e s occurs when they are e l a s t i c a l l y s c a t t e r e d by n u c l e i (Ox 5 3 , WI 64). As had been proposed by •Fermi (Fe 5^a) t h i s e f f e c t can be taken i n t o account In the o p t i c a l model by i n c l u d i n g a " S p i n - O r b i t " term i n the p o t e n t i a l . Thus, an e x t r a term w i l l be i n t r o d u c e d , of the form: V S Q ( r ) = - C ' ( l . <T ) ( 1 . 7 ) where C 1 determines the s t r e n g t h of the I n t e r a c t i o n , & i s the s p i n of the I n c i d e n t p a r t i c l e , and 1_ i t s angular momentum. T h i s a l s o accounts f o r the asymmetrical d i s t r i b u t i o n of p o l a r i z e d p a r t i c l e s e x p e r i m e n t a l l y observed (Fe 5 5 ) . The shape of the S p i n - O r b i t p o t e n t i a l has been c a l c u l a t e d In d e t a i l from nucleon-nucleon i n t e r a c t i o n and Is found t o be of the form; V S Q ( r ) = - C (1 . 9) (d ? / dr) / r ( 1 . 8 ) where Is the n u c l e a r d e n s i t y , assumed t o be onl y a f u n c t i o n of the n u c l e a r r a d i u s . T h i s term has the same form as the Thomas term f o r the Atomic S p i n - O r b i t i n t e r a c t i o n (Fe 5 5 a , Br 5 7 ) . From t h i s f o l l o w s the form commonly used f o r the S p i n - O r b i t p o t e n t i a l , vso'(r) = " V S 0 (I • (b / r) d f d r ^-9) where f ( r ) i s the r a d i a l form of the r e a l p o t e n t i a l , and b i s a -26 2 constant equal to 10 cm i n t r o d u c e d t o keep h ( r ) dimensionless and to normalize V to f e r m i s (10~ cm). The n e g a t i v e s i g n i s i n t r o d u c e d so t h a t h ( r ) i s always p o s i t i v e . Some authors take the constant 'b' to be s i m i l a r i n form to the one appearing i n the Thomas term i n atomic p h y s i c s i n v o l v i n g , i n t h i s case, the mass of the p i o n or the proton. T h i s l a c k of s t a n d a r d i z a t i o n i n the d e f i n i t i o n s must be taken i n t o account when comparing d i f f e r e n t c a l c u l a t i o n s . The o n l y parameter to be determined e x p e r i m e n t a l l y i s the s t r e n g t h VgQ, i n energy u n i t s , P o l a r i z a t i o n measurements are v a l u a b l e mainly because i t a r i s e s from the i n t e r f e r e n c e between d i f f e r e n t p a r t i a l waves. I t i s reasonable t o expect t h a t i t depends to a g r e a t e r extent on the p a r t i a l wave s c a t t e r i n g amplitudes than the e l a s t i c d i f f e r e n t i a l s c a t t e r i n g cross s e c t i o n , and i s more s e n s i t i v e to the n u c l e a r s u r f a c e s t r u c t u r e . S i m i l a r i n t e r a c t i o n s I n v o l v i n g t a r g e t s p i n s are i n g e n e r a l n e g l e c t e d . These f o r c e s w i l l be expected t o a f f e c t the p o l a r i z a t i o n r e s u l t s . E x p e r i m e n t a l l y , n u c l e i with t o t a l l y d i f -f e r e n t s p i n s are found to y i e l d almost i d e n t i c a l p o l a r i z a t i o n r e s u l t s . [ See f o r example: Co(I = 7/2) and Ni ( 1 = 0 ) i n the work.of Rosen et a l (Ro 65)2« T h i s j u s t i f i e s the l a c k of c o n s i d e r a t i o n of t a r g e t s p i n s . An imaginary s p i n - o r b i t term W had been proposed but t h e r e i s no s t r o n g experimental evidence r e q u i r i n g i t and so i t i s g e n e r a l l y not c o n s i d e r e d . 5. The o p t i c a l model c a l c u l a t i o n s . In this, s e c t i o n we w i l l b r i e f l y d e s c r i b e the c a l c u l a t i o n of observable from an assumed p o t e n t i a l . For a d e t a i l e d - 12 -d e s c r i p t i o n of the c a l c u l a t i o n s the. reader should r e f e r , f o r example, t o the a r t i c l e by Buck et a l (Bu 60) or the book by Hodgson (Ho 6 3 ) . Prom the d e s c r i p t i o n of the d i f f e r e n t terms of the p o t e n t i a l w e l l of the pre v i o u s s e c t i o n , the. i n t e r a c t i o n poten-t i a l can be w r i t t e n as: U(r) = V . f ( r ) + iW . g ( r ) -f V S Q . h ( r ) + V Q (I. 1 0 ) where ' r ' i s the r e l a t i v e c o o r d i n a t e between the t a r g e t nucleus c e n t e r and the incoming p a r t i c l e . With t h i s p o t e n t i a l , the, r a d i a l p a r t of the wave equation can be w r i t t e n down f o r each p a r t i a l wave c o n s i d e r e d . Due to the complex nature of the p o t e n t i a l used, the s o l u t i o n of the,wave equation w i l l a l s o have r e a l and imaginary components. The s o l u t i o n s t o the wave equation a re obtained by d i v i d i n g the r a d i u s T ' i n t o two r e g i o n s , one w i t h i n the p o t e n t i a l w e l l and extending to a r a d i u s ' r ^ 1 where the n u c l e a r p o t e n t i a l can be n e g l e c t e d ; the other one frorn'r^' t o i n f i n i t y , a r e g i o n where the equation can be sol v e d a n a l y t i c a l l y . The s o l u t i o n f o r the r e g i o n w i t h i n the n u c l e a r p o t e n t i a l may be obtained by performing a step by step numerical I n t e g r a t i o n . The s o l u t i o n f o r the r e g i o n o u t s i d e the p o t e n t i a l , i . e . the asymptotic form of the r a d i a l wave f u n c t i o n , i s a n a l y t i c a l l y known (Sc 5 5 ) . A l l the e f f e c t s of the I n t e r a c t i o n are contained i n the complex p a r t i a l wave s c a t t e r i n g amplitudes S^. The matching of the l o g a r i t h m i c d e r i v a t i v e s of the i n t e r i o r and asymptotic s o l u t i o n s a t the r a d i u s 'r^' p r o v i d e s a continuous wave f u n c t i o n over the boundary r e g i o n . T h i s matching - 13 -c o n d i t i o n permits the d e t e r m i n a t i o n of S^. The s c a t t e r i n g amplitude f ( 0 ) Is then found, u s i n g the r e l a t i o n ^ ( P O T VG*Q)I f ( 0 ) = ' £ (aU-L) C 5 e - i ) 9 e c ^ e ) ( i . n ) 2IK £st> The d i f f e r e n t i a l c r o s s s e c t i o n f o r e l a s t i c s c a t t e r i n g 0"' ( © ) , the t o t a l e l a s t i c s c a t t e r i n g cr,6ss s e c t i o n (TL, the E a b s o r p t i o n c r o s s s e c t i o n 0"^ , and the t o t a l c r o s s s e c t i o n ( 0 " T =. CT^+O^') are g i v e n by: cr e t©) * Two equations t h a t w i l l be mentioned d u r i n g chapter 2 are deduced from the s e t ( 1 . 1 2 ) and ( 1 . 1 1 ) One i s the Wick's l i m i t : tfF(0°) >y ( &Sz)* ( 1 . 1 3 ) and the other t h e . o p t i c a l theorem: b crT = 4 7 i zWco°; ( 1 . i 4 ) 6 . The f i t t i n g of experimental d a t a . The problem of. determining a p o t e n t i a l U(r) from experimental data i s the i n v e r s e one to the c a l c u l a t i o n s d e s c r i b e d In the p r e v i o u s s e c t i o n . E x t e n s i v e work went i n t o s o l v i n g the mathematical problem a s s o c i a t e d w i t h i t , with the r e s u l t t h a t * i n - 14 -the g e n e r a l case, a unique d e t e r m i n a t i o n of U(r) can not be obtained (Ba 49). When the p o t e n t i a l U ( r ) has some s p e c i a l p r o p e r t i e s , only then, i s t h i s p o s s i b l e . A review of these r e s u l t s can be obtained i n T.WU and T.OHMURA "Quantum theory of s c a t t e r i n g " (1962) S e c t i o n G.2. Here we s h a l l j u s t mention the r e s u l t s f o r a short range a t t r a c t i v e p o t e n t i a l , i . e . o f . t h e type of the n u c l e a r p o t e n t i a l . In t h i s case the exact and complete energy spectrum of phase s h i f t s f o r a g i v e n angular momentum are to be known. I f t h i s angular momentum i s not one corresponding t o a d i s c r e t e e i g e n v a l u e , f o r the p o t e n t i a l , the de t e r m i n a t i o n of U(r) i s unique. I f f o r . t h e angular momentum value chosen e x i s t s 'm' d i s c r e t e eigenvalues of the energy, then the d e t e r m i n a t i o n of U(r) w i l l g i v e r i s e t o an m-fold p o t e n t i a l . Each p o t e n t i a l of t h i s s et w i l l be c o n s i s t e n t w i t h the phase s h i f t s and energy e i g e n v a l u e s . T h e r e f o r e , the l a r g e amount of acc u r a t e experimental data necessary, which f o r most cases i s extremely d i f f i c u l t to o b t a i n , makes t h i s procedure of determining the p o t e n t i a l U ( r ) i m p r a c t i c a b l e at pr e s e n t . The technique used to o b t a i n an approximation of the p o t e n t i a l i n v o l v e s assuming a form f o r i t c o n t a i n i n g e m p i r i c a l parameters which are assumed to change s l o w l y , i n a uniform f a s h i o n from one nucleus t o another. With t h i s p o t e n t i a l the set of observables i s c a l c u l a t e d as d e s c r i b e d i n the pre v i o u s s e c t i o n . The p o t e n t i a l parameters are then v a r i e d so t h a t a good f i t t o the experimental data i s obt a i n e d . We have used the word "good f i t " and not "optimum f i t " t o the experimental data d e l i b e r a t e l y . The parameters are chosen to correspond as much as p o s s i b l e to r e a l i s t i c p h y s i c a l q u a n t i t i e s (such as n u c l e a r r a d i u s , edge d i f f u s e n e s s , e t c . ) . The model does not take i n t o account the s t r u c t u r a l d e t a i l s of each nucleus and so s m a l l d i v e r g e n c i e s from i t s r e s u l t s are to be expected. From the p h y s i c a l p o i n t of view the p o t e n t i a l parameters t h a t enable a reasonable f i t to a l a r g e amount of. data are more v a l u a b l e than those s e l e c t e d to f i t s p e c i a l cases, w e l l . I f the v a r i a t i o n s of the parameters are done by "hand" a c o n t r o l of the c o r r e l a t i o n s can be done. In the case of automatic f i t t i n g by computer, r e s t r i c t i o n s In the multiparameter space are i n t r o d u c e d so t h a t the f i t t i n g Is made "good" and not o p t i m i z e d . The comparison between theory and experimental data 2 2 i s normally done u s i n g the X t e s t . The q u a n t i t y X i s d e f i n e d where (J ® X P corresponds to the experimental v a l u e s ; and CT ^heo to the t h e o r e t i c a l values obtained as d e s c r i b e d i n the p r e v i o u s s e c t i o n . For a d e r i v a t i o n of t h i s f o r m u l a r see (Ho 63, page 62). The "optimum f i t " can then be d e f i n e d as the set of 2 parameters' t h a t minimizes X . When experimental values f o r d i f f e r e n t types of data are f i t t e d (as e l a s t i c d i f f e r e n t i a l c r oss s e c t i o n s , p o l a r i z a -t i o n s as f u n c t i o n of angle, a b s o r p t i o n cross s e c t i o n , e t c . ) the sum over ' i 1 i n e q u a t i o n ( 1 . 1 5 ) i s understood to i n c l u d e a l l of them. - 16 -7. The importance of experimental u n c e r t a i n t i e s . See (1) (Di 66a); (2) (Ho 64); (3) (Me 64) When a set of experimental data i s used t o determine the parameters of a p o t e n t i a l of g i v e n form, the r e s u l t s are not normally unique. How w e l l the parameters can be d e f i n e d i s c l e a r l y a f u n c t i o n of the q u a l i t y of the experimental data. Q u a l i t y i s understood to r e f e r to completeness as w e l l as accuracy. Other a m b i g u i t i e s Inherent i n the model, are those. 2 l i k e the V.R = c o n s t a n t . T h i s ambiguity i s p l a u s i b l e t h e o r e -t i c a l l y , s i n c e two p o t e n t i a l s w i t h d i f f e r e n t v a l u e s of V and R, the values being s e l e c t e d o n l y t o m a i n t a i n the requirement of 2 VR mentioned, g i v e r i s e t o the same number of waves w i t h i n the nucleus (No 59). T h i s ambiguity i s a l s o r e p o r t e d t o d i s -appear with improved experimental data (Ho 63, p. 69'). In r e f e r e n c e ( l ) a d e t a i l e d study of the I n f l u e n c e of the d i f f e r e n t experimental u n c e r t a i n t i e s i n e l a s t i c s c a t t e r -i n g data i s presented. I t i s found t h a t parameter s e n s i t i v i t y t o Change i n experimental data Is i n v e r s e l y p r o p o r t i o n a l to the amount of d e f i n i t i o n of the d i f f r a c t i o n p a t t e r n i n the e l a s t i c s c a t t e r i n g c ross s e c t i o n as a f u n c t i o n of a n g l e . Reference (2) i s a g e n e r a l review of the success of the o p t i c a l model c a l c u l a t i o n s . The model i s a b l e t o account f o r a l l neutron s c a t t e r i n g data and r e a c t i o n c ross s e c t i o n s from the resonance r e g i o n to around 25 MeV. S u b s t a n t i a l d i f f i c u l t i e s are expected to appear i f the e r r o r s of the experimental cross sections, were decreased to about 3$ and i f measurements could be extended over the whole angular range. The p o t e n t i a l s obtained from f i t t i n g the d i f f e r e n t i a l c r o s s s e c t i o n s g i v e , In g e n e r a l , - 17 -a good f i t t o the t o t a l r e a c t i o n c ross s e c t i o n s (to about k%) r e g a r d l e s s of the d e t a i l e d shape assumed f o r the imaginary p a r t . In r e f e r e n c e ( 3 ) the I n f l u e n c e t h a t more ac c u r a t e measurements of t o t a l p roton r e a c t i o n c r o s s s e c t i o n s could have, i n some cases, f o r r e d u c i n g the a m b i g u i t i e s f o r o p t i c a l model parameters i s c l e a r l y p ointed out by Melkanoff et a l . In Chapter 2 the experimental d i f f i c u l t i e s i n v o l v e d i n o b t a i n i n g a c c u r a t e measurements of t o t a l r e a c t i o n c r o s s s e c t i o n s f o r protons are d e s c r i b e d . Only d u r i n g the l a s t few years methods capable of y i e l d i n g measurements wi t h e r r o r s i n the 5$ o r d e r , f o r reasonable measuring times, have been p u b l i s h e d . Accurate a b s o l u t e measurements of these t o t a l r e a c t i o n c ross s e c t i o n s p l u s the i n c r e a s i n g data a v a i l a b l e on p o l a r i z a t i o n , see f o r example (Ro 65), w i l l make complete s e t s of data f o r the same nucleus and a t the same energy a v a i l a b l e f o r l a r g e numbers of n u c l e a r s p e c i e s . T h i s completeness In the experimen-t a l data w i l l d e f i n e more a c c u r a t e l y the phenomelogical p a r a -meters d e s c r i b i n g the p o t e n t i a l s . The experiment d e s c r i b e d i n the present t h e s i s , i s a new technique developed t o enable the measurements of values f o r t o t a l r e a c t i o n c r o s s s e c t i o n s f o r protons, with e r r o r s of a few per cent f o r running time of a few hours. ft. Computer c a l c u l a t i o n s . A complete, d e t a i l e d d i s c u s s i o n of the computational methods c u r r e n t l y used f o r O p t i c a l model c a l c u l a t i o n s i s presen-ted i n "Nuclear o p t i c a l model c a l c u l a t i o n s " by Melkanoff, - 18 -T. Sawada and J . Raynal i n Volume 6 of "Methods i n computa-t i o n a l p h y s i c s " (Academic Press 1 9 6 6 ) . In t h i s s e c t i o n we w i l l mention the programs a v a i l a b l e at the U n i v e r s i t y of B r i t i s h Columbia. Most of the c a l c u l a t i o n s connected w i t h the present T h e s i s were performed w i t h a v e r s i o n of the SCAT-4 program £ Melkanoff et a l "A f o r t r a n program f o r e l a s t i c s c a t t e r i n g a n a l y s i s with the o p t i c a l model" U n i v e r s i t y of C a l i f o r n i a Press ( 1 9 6 1 ) J . The program c a l c u l a t e s i n the c e n t e r of mass system the d i f f e r e n t i a l e l a s t i c s c a t t e r i n g c r o s s s e c t i o n 0^9), the p o l a r i z a t i o n P ( 9 ) , and the t o t a l r e a c t i o n c r o s s s e c t i o n 0 * R . Incoming p a r t i c l e s of s p i n 0 or §• and s p i n l e s s t a r g e t s are c o n s i d e r e d . The program compares the c a l c u l a t i o n s with ex-2 p e r i m e n t a l data by c a l c u l a t i n g the value f o r X but does not c o n t a i n automatic s u b r o u t i n e f o r v a r y i n g the parameters to 2 minimize the X v a l u e . M o d i f i c a t i o n s i n the Input - Output statements were i n t r o d u c e d to make i t more v e r s a t i l e , and simple programs f o r i n t e g r a t i o n of angular d i s t r i b u t i o n s and p l o t t i n g of output data were added. L a t e r on, the program ABACUS-2 [ E.H. AVERBACH BROOKHAVEN NAT.LAB. B N L 6 5 6 2 ( 1 9 6 2 ) ] became a v a i l a b l e . I t i s more v e r s a t i l e than SCAT-4 i n the sense t h a t i t can a u t o m a t i c a l l y 2 search f o r a minimum on the X i n a 5-parameter space. - 19 -2. TOTAL REACTION CROSS SECTION MEASUREMENTS. 1. General I n t r o d u c t i o n . The importance of the t o t a l r e a c t i o n c r o s s s e c t i o n s i n determining the o p t i c a l model parameters was d i s c u s s e d In the prev i o u s chapter. In the present chapter i t i s intended t o review the d i f f e r e n t techniques used i n measuring them, and t o i n t r o d u c e the method developed i n t h i s l a b o r a t o r y . F i r s t we w i l l d i s c u s s the d i f f e r e n t decay mechanisms of the compound nucleus c l a s s i f i e d a c c o r d i n g t o the f i n a l p r o d u c t s , as they are important i n the e v a l u a t i o n of the experimental d a t a . Secondly we w i l l d e s c r i b e the d i f f e r e n t experimental techniques used t o o b t a i n the t o t a l r e a c t i o n c r o s s s e c t i o n s . 2. The r e a c t i o n channels. The compound n u c l e u s , formed when an incoming p a r t i c l e i s absorbed by a t a r g e t n u c l e u s , w i l l e v e n t u a l l y decay t o one of a number of p o s s i b l e f i n a l s t a t e s of the r e a c t i o n . The process that gave r i s e t o the compound^ nucleus i s r e f e r r e d t o as the "INPUT CHANNEL". The f i n a l s t a t e s are r e f e r r e d t o as the "OUTPUT CHANNELS" of the r e a c t i o n . The number of such channels p o s s i b l e and t h e i r „ r e l a t i v e occurrence, w i l l depend on the p a r t i c u l a r s of the r e a c t i o n i n v o l v e d . " P a r t i a l r e a c t i o n c r o s s s e c t i o n s " are d e f i n e d f o r each of the p o s s i b l e output channels, w h i l e the " t o t a l r e a c t i o n c r o s s s e c t i o n " i s the sum of a l l the p a r t i a l ones. As we w i l l see l a t e r on, t h i s adding of p a r t i a l c r o s s s e c t i o n s i s one of the methods used t o e v a l u a t e the t o t a l one. Gross f l u c t u a t i o n s i n the p a r t i a l r e a c t i o n c r o s s s e c t i o n s - 20 -can be expected both as a f u n c t i o n of energy f o r a p a r t i c u l a r t a r -get, and f o r d i f f e r e n t n u c l e a r s p e c i e s f o r f i x e d bombarding energy. The t o t a l r e a c t i o n c r o s s s e c t i o n , on the other hand, i s expected, on the b a s i s of the o p t i c a l model of n u c l e a r r e a c t i o n s , t o be a smoothly v a r y i n g f u n c t i o n of those parameters. P a r t i a l c r oss s e c t i o n s w i l l depend on the p a r t i c u l a r s of the.output channels, such as presence of resonances, neutron t h r e s h o l d s , Q values and so on. The t o t a l c r o s s s e c t i o n , however, i s onl y r e l a t e d t o the p r o b a b i l i t y of forming a compound n u c l e u s . i n P i g . 2 ( 1 ) . In the f o l l o w i n g d i s c u s s i o n the output channels are d i v i d e d i n t o : r e - e m i s s i o n Into the i n p u t channel, I n e l a s t i c s c a t t e r -i n g , e mission of charged p a r t i c l e s and neutron e m i t t i n g channels. The c l a s s i f i c a t i o n of the d i f f e r e n t channels i s i n d i c a t e d INPUT : CHANNEL ABSORPTION or COMPOUND NUCLEUS FORMATION OUTPUT CHANNELS - DIRECT PROCESSES COLLECTIVE EXCITATION t a r g e * Q - INELASTIC -SGATTEM-NS-ELASTIC SCATTERING / CHARGED PARTICLE EMISSION NEUTRON EMISSION COMPOUND ELASTIC SCATTERING Figure 2,1 The reaction channels 2 . 1 . The compound e l a s t i c channel. Compound e l a s t i c events a r i s e from compound n u c l e i t h a t decay through the in p u t channel, i . e . e m i s s i o n of the same p a r t i c l e - 21 -and energy as the i n c i d e n t one. T h i s process i s , at f i r s t s i g h t , s i m i l a r t o t h a t of e l a s t i c s c a t t e r i n g , except t h a t I t invokes the Intermediate f o r -mation of a compound nu c l e u s . The two p r o c e s s e s , e l a s t i c s c a t t e r i n g and compound-elastic s c a t t e r i n g , are e x p e r i m e n t a l l y i n d i s t i n g u i s h a b l e , at p r e s e n t , f o r most experimental s i t u a t i o n s . ( E i 60). R e c e n t l y i n d i r e c t t e c h -niques such as t h a t of " f l u c t u a t i o n a n a l y s i s " (Er 65), have y i e l d e d a d e t e r m i n a t i o n of the compound e l a s t i c f o r a s p e c i a l case. The t e c h n i q u e however, r e q u i r e s s p i n 0 t a r g e t n u c l e i and a very complete angular d i s t r i b u t i o n d a t a . As seen i n the p r e v i o u s chapter u s i n g the o p t i c a l model one i s a b l e to c a l c u l a t e the a b s o r p t i o n of the Incoming wave, r e p r e s e n t i n g the removal of p a r t i c l e s from t h e i n p u t channel, without d e t a i l e d c o n s i d e r a t i o n of the decay of the system so formed. S i n c e compound-elastic s c a t t e r i n g cannot be r e s o l v e d from t h a t of d i r e c t e l a s t i c s c a t t e r i n g , t h i s c o n t r i b u t i o n rndst be estimated i n order t o compare experimental n o n - e l a s t i c c r o s s s e c t i o n s w i t h t h e o r e t i c a l values of the t o t a l r e a c t i o n c r o s s s e c t i o n s . In the h i g h energy, r e g i o n , or when the continum of the compound system e x c i t e d s t a t e s i s reached, the c o m p e t i t i o n between the many open channels f o r decay makes the p r o b a b i l i t y of r e -e m i s s i o n i n t o the entrance channel n e g l i g i b l e . For low e n e r g i e s , where l e v e l d e n s i t y i s lower, fewer open channels are p o s s i b l e f o r decay so t h a t the r e - e m i s s i o n p r o b a b i l i t y may no l o n g e r be s m a l l . When neutron emission i s a c o m p e t i t i v e channel,; r e - e m i s s i o n of " charged p a r t i c l e s i s g e n e r a l l y f u r t h e r i n h i b i t e d by Coulomb/barrier c o n s i d e r a t i o n s . - 22 -One way of r e s o l v i n g compound-elastic from d i r e c t e l a s t i c s c a t t e r i n g t h a t may e v e n t u a l l y be p o s s i b l e would i n v o l v e r e c o g n i z i n g the! d i f f e r e n t t i m i n g c h a r a c t e r i s t i c s . A time dependent treatment (Fr 6 2 ) , shows t h a t r e - e m i s s i o n should take p l a c e l a t e r than the d i r e c t e l a s t i c s c a t t e r i n g , even.when e x p e r i m e n t a l l y they a r e not d i s t i n g u i s h a b l e by the present t i m i n g t e c h n i q u e s . ( E l a s t i c s c a t t e r -i n g : 1 0 " 2 3 seconds, compound-elastic: lO'" 1^ seconds). In a d d i t i o n , c a l c u l a t i o n s of compound-elastic c r o s s s e c t i o n s seems t o be p o s s i b l e f o r some simple cases u s i n g s t a t i s t i c a l t heory f o r zero s p i n t a r g e t and no p o s s i b l e e l a s t i c channels (Ca 6 0 ) . For a s m a l l number of I n e l a s t i c channels Hauser-Fesbach type c a l c u l a t i o n s c ould be employed (Ha 5 2 ) . 2 . 2 The i n e l a s t i c s c a t t e r i n g channel. These are compound n u c l e i t h a t decay hy emission of the same i n c i d e n t p a r t i c l e but of d i f f e r e n t energy> l e a v i n g the t a r g e t n u c l e i i n an e x c i t e d s t a t e . When the energy d i f f e r e n c e between these and the e l a s t i c s c a t t e r e d p a r t i c l e s i s g r e a t e r than the r e s o l u t i o n o f the pr o t o n energy d e t e c t i o n system, these channels can be e x p e r i m e n t a l l y r e s o l v e d . A c c o r d i n g t o whether the energy spread of the i n c i d e n t beam i s much l e s s than the energy s e p a r a t i o n between t h e e x c i t e d s t a t e s or not, the energy d i s t r i b u t i o n of the i n e l a s t i c s c a t t e r e d p a r t i c l e s w i l l have d e f i n i t e peaking (corresponding t o each p o s s i b l e i n e l a s t i c c h a n n e l ) , or w i l l be a.continum. For the same t a r g e t and I n c r e a s i n g i n c i d e n t energy, f i r s t we w i l l f i n d separated i n e l a s t i c peaks l o c a t e d a t an energy equal t o the I n c i d e n t energy minus the e x c i t a t i o n e n e r g i e s of the r e s p e c t i v e i n e l a s t i c channels, or low energy r e g i o n ; then more and more i n e l a s t i c channels w i l l - 23 -become e n e r g e t i c a l l y p o s s i b l e and t h e s p e c t r u m w i l l become a c o n t l n u m , o r h i g h e n e r g y r e g i o n . The i n e l a s t i c s c a t t e r i n g a r o u n d 15 Mev has been t h e s u b j e c t o f e x t e n s i v e e x p e r i m e n t a l w o r k on a w i d e v a r i e t y o f t a r g e t s (Co 59, Be 61). F o r some t a r g e t n u c l e i , e s p e c i a l l y de formed t y p e s as i n t h e r a r e e a r t h r e g i o n , r o t a t i o n a l and c o l l e c t i v e s t a t e s c a n be e x c i t e d and " i n e l a s t i c l i k e " s c a t t e r i n g p r o d u c e d . The c a s e i s now t h e o p p o s i t e t o t h e " c o m p o u n d - e l a s t i c " s i t u a t i o n . H e r e we have a n e l a s t i c p r o c e s s , n o t i n v o l v i n g a b s o r p t i o n o f t h e i n c o m i n g w a v e , a p p e a r i n g as a compound n u c l e u s d e c a y . T h i s c o n t r i b u t i o n c a n be t a k e n i n t o a c c o u n t by e n e r g e t i c a l l y r e c o g n i z i n g t h e l e v e l s i n v o l v e d o r s i m p l y by s e l e c t i n g t a r g e t n u c l e i where t h e s e e f f e c t s a r e . n e g l i g i b l e . . 2.3. The c h a r g e d p a r t i c l e s c h a n n e l s . T h e s e a r e compound n u c l e i d e c a y i n g v i a open c h a n n e l s i n v o l v i n g t h e e m i s s i o n o f a c h a r g e d p a r t i c l e , o t h e r t h a n t h e i n c i d e n t one.. C h a r g e d p a r t i c l e s a r e e a s i l y d e t e c t a b l e w i t h 100$ e f f i c i e n c y . F u r t h e r m o r e s i m p l e d E / d X c o u n t e r t e c h n i q u e s a l l o w t h e i r I d e n t i f i c a t i o n . 2.4. The n e u t r o n c h a n n e l . These a r e compound n u c l e i t h a t w i l l d e c a y w i t h t h e e m i s s i o n o f a n e u t r o n . O n l y t h e c a s e o f i n c i d e n t c h a r g e d p a r t i c l e s w i l l be c o n s i d e r e d , ; s i n c e f o r I n c i d e n t , n e u t r o n s t h i s w i l l be I n c l u d e d i n t h e t y p e s o f s c a t t e r i n g a l r e a d y d i s c u s s e d i n s e c t i o n s 2.2 and 2.1. - 24 -Threshold measurements f o r neutron production are available for more than 40 reactions including, protons, deuterons, He^ and alpha as incident p a r t i c l e s (Ma 63 P. 1 8 6 5 ) . As mentioned before, above the neutron threshold the compound n u c l e i are .generally expected to decay mainly through t h i s channel as the Coulomb b a r r i e r i n h i b i t s the p r o b a b i l i t y of emitting a charged p a r t i c l e . The behaviour of the p a r t i a l . c r o s s section near thres-hold can be approximately described f o r l i g h t and medium n u c l e i , as proportional to A E^/2 (Ma 63 p. 1 8 1 1 ) , where A E i s the energy above the threshold. (When mainly s- wave emission Is important). This description i s not correct when the threshold energy i s close to a resonance of the compound nucleus, but i l l u s t r a t e s the f a s t r i s e of the p a r t i a l cross section f o r neutron production above the threshold energy. When higher angular momentum components are^involved, then the dependence on A E i s even stronger and neutron emission r a p i d l y becomes the major contribution to the absorption cross section f o r increasing Incident energy. Accurate measurements of p a r t i a l cross sections f o r neutron production had been hindered by d i f f i c u l t i e s involved i n determining absolute e f f i c i e n c i e s f o r neutron detection. 3 . The i n d i r e c t method. The sum of the p a r t i a l cross sections f o r a l l the open channels i s a measure of the absorption pf the incoming beam, the formation of compound n u c l e i or the t o t a l reaction cross section. Obtaining the value of CTR by adding up the p a r t i a l reaction cross sections f o r a l l the possible open channels i s - 25 -r e f e r r e d t o as t h e " I n d i r e c t m e t h o d " . Prom t h e e x p e r i m e n t a l p o i n t o f v i e w a b s o l u t e c r o s s s e c t i o n d a t a . i s . n e c e s s a r y f o r a l l t h e r i e l e v a n t open c h a n n e l s . T h i s summation i s o n l y p r a c t i c a l f o r bombard ing e n e r g i e s s u f f i -c i e n t l y l ow so t h a t o n l y a few decay c h a n n e l s a r e e n e r g e t i c a l l y p o s s i b l e . The l i m i t o f a c c u r a c y i s s e t by t h e d i f f i c u l t i e s i n d e t e r m i n i n g a b s o l u t e n e u t r o n f o r m a t i o n c r o s s s e c t i o n s a b o v e - t h e r e s p e c t i v e n e u t r o n t h r e s h o l d . . When f i s s i o n becomes an i m p o r t a n t c o n t r i b u t i o n , t y p i c a l l y 80$ t o 90% o f t h e . t o t a l a b s o r p t i o n , t h e method can be a p p l i e d a g a i n (Fu 59). F o r a p p l i c a t i o n s o f t h e " i n d i r e c t method " see (SfL59, Me 60). 4. The d i r e c t methods . D i r e c t methods a r e t h o s e a imed a t measur ing - t o t a l r e a c t i o n c r o s s s e c t i o n s w i t h o u t d e t a i l e d c o n s i d e r a t i o n o f t h e r e a c t i o n p r o d u c t s . T h i s i s e q u i v a l e n t t o m e a s u r i n g t h e a t t e n u a -t i o n o f an i n c o m i n g beam i n g o i n g t h r o u g h t h e t a r g e t under s t u d y . As a who le t h e s e methods; i n v o l v e t h e c o m p a r i s o n o f a p a r t i c l e f l u x w i t h and w i t h o u t t h e t a r g e t . They t h e r e f o r e have t h e advan tage t h a t o n l y a s i n g l e measurement i s i n v o l v e d r a t h e r t h a n t h e measurement o f a number o f p a r t i a l c r o s s s e c t i o n s . F o r r e a s o n s o f c o n v e n i e n c e i n I n t r o d u c i n g ou r method we w i l l f u r t h e r c l a s s i f y t h e D i r e c t methods a c c o r d i n g t o t h e t e c h -n i q u e i n v o l v e d , n o t n e c e s s a r i l y i n c h r o n o l o g i c a l o r d e r . - 26 -4.1. The beam a t t e n u a t i o n method. I f one can r e l y on the i n c i d e n t beam i n t e n s i t y b e i n g constant over some time ' t a d i r e c t comparison of f l u x e s can be made by a l t e r n a t e l y p u t t i n g the t a r g e t i n and out of the beam f o r pe r i o d s of time much s h o r t e r than ' t 1 . The beam constancy can be checked by m o n i t o r i n g some secondary e f f e c t such as e l a s t i c s c a t t e r i n g from the t a r g e t or some oth e r c h a r a c t e r i s t i c of the p a r t i c l e source dependent on beam I n t e n s i t y . T h i s method i s e s p e c i a l l y a t t r a c t i v e f o r neutron beam a t t e n u a t i o n d e t e r m i n a t i o n s s i n c e the r e l a t i v e nature of the measurement means t h a t d e t a i l e d knowledge of the a b s o l u t e counter e f f i c i e n c y i s not r e q u i r e d . The expected i n t e n s i t y change ,f or an i n c i d e n t beam of I n t e n s i t y I, for* a t a r g e t of .thickness dx and N n u c l e i cm-^ , due t o a process w i t h a c r o s s s e c t i o n 0* i s : d l ^ - I N c r d x (2.1) The r e l a t i v e change or beam a t t e n u a t i o n & i s then, d&-^-_dI _ Ncrd% ( 2 . 2 ) I For a sample of t h i c k n e s s L c e n t i m e t e r s , we can I n t e g r a t e ( 2 . 2 ) a n d o b t a i n : o=fnIo-fT)I=H f C r d % ( 2 „ 3 ) ; o For charged p a r t i c l e s , the mean energy of the i n c i d e n t beam i n the t a r g e t w i l l be l e s s than the i n c i d e n t energy because of the energy l o s t i n I o n i z a t i o n and i n e l a s t i c c o l l i s i o n s w i t h the t a r g e t atoms. In g e n e r a l Q* w i l l be a f u n c t i o n of energy. I f the t a r g e t i s t h i n enough so t h a t CT can be c o n s i d e r e d constant (a reasonable approximation f o r measurements of neutron a t t e n u a t i o n s ) &n ( i ^ - N cr L (2.4) The " t r a n s m i s s i o n " of the sample i s d e f i n e d as, T_ _JL_ = exp (-NcrL) = exp (- &) (2.5) Io By measuring the t r a n s m i s s i o n as a f u n c t i o n of the t a r g e t t h i c k n e s s , by the method d e s c r i b e d above, the e x p o n e n t i a l law can be checked, ( f o r 95 Mev neutrons, Ju 50). Expanding the e x p o n e n t i a l i n ( 2 . 5 ) j T = 1 - S + JL2 - • • • - (2.6) 2 and f o r T = l - £ (2.7) Thus, I o " 1 (2.8) I o By measuring the f l u x e s w i t h and without t a r g e t the t r a n s m i s s i o n T can be measured; w h i l e . f o r t a r g e t s w i t h t r a n s -m i s s i o n s c l o s e t o u n i t y , <£ can be determined d i r e c t l y by u s i n g (2.8). The value of the c r o s s s e c t i o n O" i n v o l v e d w i l l be g i v e n by e i t h e r : 0- = ( N L ) " ' & (2.9) a - - ( N L ) " 1 t n { L T H ) (a .9 . , When the assumption of the c r o s s s e c t i o n being constant i s not v a l i d , then the O" of equations ( 2 . 9 )and ( 2 . 9 a )should be 28 r e p l a c e d by the mean value or = L j Q- (%) d% (2.10) where GCt) = 0" (. E - 6 d.% ) (2.11) and € i s the sample s t o p p i n g power. When c r y s t a l l i n e s t r u c t u r e i s present i n the sample equations (2.9) and (2.9a) which are based on the assumption t h a t the t a r g e t i s i s o t r o p i c i n nature, should be used with c a r e . The e f f e c t of c r y s t a l l i n e s t r u c t u r e i s d e s c r i b e d i n s e c t i o n 4 .1 .3. of Chapter 3. 4.1.1. S t a t i s t i c a l c o n s i d e r a t i o n s . I f the " t a r g e t i n " and " t a r g e t out" measurements are performed f o r the same time ' t 1 , then - (2.12) X 0 M o where M r e p r e s e n t s the t o t a l number of counts d e t e c t e d . The c o n t r i b u t i o n of s t a t i s t i c a l f l u c t u a t i o n s i n M and M Q to the e r r o r a s s o c i a t e d with a d e t e r m i n a t i o n of O* are r e a d i l y determined. The assumption of equal times f o r " t a r g e t i n " and " t a r g e t out" measurements i n v o l v e d i n ( 2 . 1 2 ) i s used f o r convenience i n the f o l l o w i n g d i s c u s s i o n . I f a f i x e d time i s a v a i l a b l e f o r the measurement, the e r r o r i n the c r o s s s e c t i o n can be reduced by u s i n g unequal time i n t e r v a l s f o r " t a r g e t i n " and " t a r g e t out" measurements. By d i f f e r e n t i a t i n g ( 2 . 9 ) and (2.9a) we f i n d f o r the r e l a t i v e e r r o r , - 29 -and from 2 . 5 , A & = T ~ ' A T (2.14) Prom the d e f i n i t i o n of T ( 2 . 5 ) , u s i n g 2.12 and the standard d e v i a t i o n s f o r the P o i s s o n d i s t r i b u t i o n s of M and M Q, we get f o r the v a r i a n c e of T, ( z r r ) 2 = T M " 0 ' (X + T) where the c r o s s or q u a d r a t i c terms are put equal t o z e r o . Prom here we o b t a i n the r e l a t i v e s t a t i s t i c a l e r r o r on the t r a n s m i s s i o n as, - i .1/2 , - Ve A T T = ( I f T ) ' C M 0 T ) (2 . 1 5 ) And f r o m ( 2 . 1 3 ) f o r the r e l a t i v e e r r o r s on the c r o s s s e c t i o n we get, r,. ( l + T ) ' ^ (M 0T)"'^(fnT)-' vieKi.)* M . - ^ r ' ( 2 - 1 6 ) Equations (2.16)permit c a l c u l a t i o n of the s t a t i s t i c a l accuracy l i m i t f o r a sample of t r a n s m i s s i o n T, or a t t e n u a t i o n , when the t o t a l number of counts without t a r g e t i s M Q. F i g u r e s 2.2 and 2 . 3 are a p l o t of ( M Q ) 2 ^ as a f u n c t i o n of the t r a n s m i s s i o n T and the a t t e n u a t i o n Q as d e s c r i b e d by(2.16). I t i s c l e a r t h a t the lower the t r a n s m i s s i o n , or the h i g h e r the a t t e n u a t i o n , of the sample the b e t t e r the accuracy on the measurement f o r the same number of i n c i d e n t p a r t i c l e s . T h i s , i n t u r n means b e t t e r accuracy I n the same beam time. The l i m i t t o how t h i c k & t a r g e t can be i s s e t by the secondary e f f e c t s so introduced.. In the case of charged p a r t i c l e s , due t o t h e i r h i g h s p e c i f i c energy l o s s , c o r r e c t i o n s due t o the - 3 0 -Figure 2,.2 : Relative error as a function of the sample transmission. S A M P L E A T T E N U A T I O N Figure 2.3 : Relative-error as a function of the sample attenuation. - 32 -averaging i n d i c a t e d i n (2 .7) are Important u n l e s s the energy l o s s i n the t a r g e t i s very s m a l l compared with the I n c i d e n t energy, or t h i n t a r g e t s . T h i c k e r t a r g e t s , on the other hand, can be used i f the trend of the c r o s s s e c t i o n w i t h energy i s w e l l known. For example,for a 1 Mev t h i c k copper t a r g e t w i t h 16 Mev protons, the expected a t t e n u a t i o n of the i n c i d e n t beam w i l l be only a few p a r t s i n 10"^ . For a value of 1 x 10"^ and a d e s i r e d s t a t i s t i c a l a ccuracy of ^ = 5 x 1 0 " 2 , then from F i g . 2 .2 we f i n d , \ . = 1.4 * 104" or a t l e a s t M c± M Q = 8 x 1 0 1 0 protons should be a n a l y s e d . Such l a r g e protons counts l e a d to severe experimental d i f f i c u l t i e s . For proton c o u n t - r a t e s of even 10 s" , at l e a s t 25 hours would be r e q u i r e d f o r a s i n g l e measurement. For I n c i d e n t neutrons a d d i t i o n a l c o m p l i c a t i o n s such as " m u l t i p l e s c a t t e r i n g " p l a c e a p r a c t i c a l upper l i m i t t o t a r g e t t h i c k n e s s , much b e f o r e energy l o s s c o n s i d e r a t i o n s are important ( M a 63 p. 992) . We w i l l c o n s i d e r how, i n more d e t a i l , the case f o r i n c i d e n t charged p a r t i c l e s i n v o l v i n g & < K l ( T ~ l ) . From (2.8) and (2 .12 ) , we g e t : 4 = ( V \ 0 - M ) M ~ ' (2.17) We can envisage two types of experiments. As d e s c r i b e d b e f o r e , we can measure d i r e c t l y M and M 0, t h i s we r e f e r t o as the "ATTENUATION BASIC METHOD". On the other hand i f the aim of the experiment i s to measure d i r e c t l y the d i f f e r e n c e : ' M C = M 0 - ^ ( 2 . i 8 ) - 33 -such an experiment w i l l be r e f e r r e d t o as the "COINCIDENCE ATTENUATION METHOD". T h i s technique w i l l be d i s c u s s e d • i n d e t a i l i n S e c t i o n 4 . 6 . At t h i s time we want o n l y t o compare both methods from the s t a t i s t i c a l p o i n t of view. For the b a s i c method w i t h T— I we get from (2.16):. T£= ^ f C S M j * ) " 1 (2.19) For the c o i n c i d e n c e method, we can r e w r i t e (2.17) as: h> = L M c M~' (2.20) The s t a t i s t i c a l e r r o r on S w i l l be determined mainly by the d i s t r i b u t i o n on M c, by d i f f e r e n t i a t i n g (2.20) 2. (2.21) The va l u e f o r the v a r i a n c e Is then, assuming t h a t the c r o s s terms average out: and f o r Po i s s o n s t a t i s t i c s : The r e l a t i v e e r r o r ; g i v e n by the r a t i o of the a t t e n u a t i o n standard d e v i a t i o n and the a t t e n u a t i o n I t s e l f , I s : And f o r the case of c» C< 1 we can w r i t e : 1/2 f [ c = (. Ho)" (2.22) The r a t i o of the r e l a t i v e e r r o r s f o r the two methods i s then g i v e n by: -y? c}l2 -±c_ _ d . d (2.23) where we assume the same number of i n c i d e n t counts i n both type of - 34 -measurements. The coincidence method thus offers at least an order of magnitude "better accuracy than the basic method fo r the copper example mentioned e a r l i e r , f o r the same number of incident counts. 4.1.2. Geometry considerations. In a l l previous discussions i t was assumed that: a) f o r target out measurements: a l l detected p a r t i c l e s belong to the Incident beam. b) f o r target i n measurements: a l l incident p a r t i c l e s s u f f e r i n g nuclear i n t e r a c t i o n were not detected. Incident beam Sample t a r g e t Transmitted p a r t i c l e s d e t ector Figure 2. 4 : T y p i c a l a t t e n u a t i o n experiment Figure 2.4 shows a schematic of a t y p i c a l attenuation experiment. A possible background f l u x of p a r t i c l e s , not o r i g i n a t i n g i n the incident beam and not depending on whether the target i s i n or out, w i l l be designated by 1^. During the time of measuring - 35 M and MQ, I b w i l l g i v e r i s e t o a number of counts Mg. The r e a l values f o r M and M Q w i l l then be: M Q = - Mfi ; M = M' - M B ; T' = M' / M Q (2.24) where the primes i n d i c a t e the measured v a l u e s . We can assume t h a t w i l l be p r o p o r t i o n a l t o the detec t e d number of - p a r t i c l e s without t a r g e t , i f both f l u x e s arose o r i g i n a l l y from the same source. Thus, M B = (3'M'o (2.25) Then the t a r g e t t r a n s m i s s i o n w i l l be g i v e n by: Here we are c o n s i d e r i n g o n l y those events Mg t h a t are not d i s t i n g u i s h a b l e , a t the d e t e c t o r , from those forming p a r t of M and M . o S i m i l a r events produced by s c a t t e r i n g of i n c i d e n t p a r t i c l e s i n t o the f i n a l d e t e c t o r by the t a r g e t assembly could be present and w i l l i n g e n e r a l be dependent on the t a r g e t p o s i t i o n . fi> can be measured by s t o p p i n g the d i r e c t f l u x . The second type can be minimized by s u i t a b l e mechanical d e s i g n . These c o n s i d e r a t i o n s a re important f o r neutron experiments due t o the room-scattered background. In the case of i n c i d e n t charged p a r t i c l e s , i n g e n e r a l , fd can e a s i l y be made n e g l i g i b l e by proper g e o m e t r i c a l d e s i g n . Let us c o n s i d e r the case of the experimental arrangement i l l u s t r a t e d i n F i g u r e 2.4. Besi d e s the d i r e c t a b s o r p t i o n events l e a d i n g t o measurements of the r e a c t i o n c r o s s s e c t i o n , a number of secondary processes may occur. These processes can have s u f f i c i e n t - 36 -magnitude t o r e q u i r e e s t i m a t i o n i n order t o c o r r e c t the measured a t t e n u a t i o n . I f the a t t e n u a t i o n of the beam i s due t o a combination of processes o c c u r r i n g i n the t a r g e t each one w i t h a cross s e c t i o n , then from (2 .1) the change In beam I n t e n s i t y i s given by: d !=• Z ; dlL ^ H. JHcr. d% (2.27) and f o r the r e l a t i v e change: c (2.28) Assuming t h a t the t a r g e t i s t h i n enough f o r each Q"£ to be considered constant: £ = N L ^_LQ-L (2.29) We can then.define an a t t e n u a t i o n r e l a t e d to each process Q"/ as: S . ^ N L O - ^ . S = ^ ^ (2.30) i n terms of t r a n s m i s s i o n t h i s means: T— exp (- = ex p (- ) (2.31) and d e f i n i n g f o r each process a t r a n s m i s s i o n T^: 1"^ = exp(-*0 ; T ^ T I T ^ (2.32) Then the cross s e c t i o n c a l c u l a t e d from the measurement of S or T w i l l be given by: <r= ° J (2.33) R e f e r r i n g back to Figu r e 2 .4 we can, then, decompose the t o t a l measured cross s e c t i o n Into s e v e r a l terms: • cr =. 0-0 + f" cr (e) d 0 - ( cr (e)di © _ cr ox) (2. j E C N M S ' V ,34) - 37 -where i s the h a l f .angle subtended by-the d e t e c t o r . The f i r s t term i s the t r u e t o t a l r e a c t i o n cross s e c t i o n ; the second term takes care of the a t t e n u a t i o n c o n t r i b u t e d by e l a s t i c s c a t t e r i n g of i n c i d e n t p a r t i c l e s o u t s i d e of the f i n a l d e t e c t o r acceptance angle; the t h i r d term takes care of the p a r t i c l e s which s u f f e r e d some n u c l e a r i n t e r a c t i o n (e.g. compound-e l a s t i c s c a t t e r i n g ) but which are s t i l l d e t e c t e d as t r a n s m i t t e d ones. The f o u r t h term takes care of m u l t i p l e i n t e r a c t i o n s . T h i s w i l l i n c l u d e c o r r e c t i o n s t o the e l a s t i c s c a t t e r i n g term due t o m u l t i p l e s c a t t e r i n g i n t o the d e t e c t o r and to the t h i r d term due to m u l t i p l e s c a t t e r i n g o u t s i d e t h e d e t e c t o r . I f one assumes t h a t a l l products of the r e a c t i o n can 1 be d i s t i n g u i s h e d a t the d e t e c t o r , then t h i s term w i l l be o n l y r e l a t e d ,to the e l a s t i c s c a t t e r i n g . I t i s r e f e r r e d t o , then, as the " i n - s c a t t e r i n g " c o r r e c t i o n term. 4 . 1 . 3 . T o t a l r e a c t i o n cross, s e c t i o n measurements. Prom ( 2 . 3 4 ) , ^ « o• = cr - f a-Ec©) c i©+ ce)cLe+cr M6x)(2.36) J c< ^ 0 The " m u l t i p l e s c a t t e r i n g " term accounts f o r p a r t i c l e s t h a t a f t e r b e i ng e l a s t i c a l l y s c a t t e r e d o u t s i d e the d e t e c t o r a n g l e , as c o n s i d e r e d by the second term, are r e s c a t t e r e d i n t o I t '•' by a second or m o r e - s c a t t e r i n g . In order to o b t a i n the order of magnitude of the m u l t i p l e s c a t t e r i n g term we can estimate the c o r r e c t i o n a r i s i n g from double s c a t t e r i n g . We w i l l assume t h a t t o get " i n - s c a t t e r i n g " of a p a r t i c l e f i r s t s c a t t e r e d i n t o an angle 0 ( g r e a t e r t h a n O d ) , a second s c a t t e r i n g i n t o 0 i s n e c e s s a r y . We can then w r i t e f o r - 38 -the double s c a t t e r i n g c o n t r i b u t i o n : o- 2 = H\_.aD [e-gCe)] de (2.37) o r : ^ c r * ^ N l _ r 2 0 L ^ ( « ) 3 & 2 T I 0 ^ ^ ) ( 2 . 3 8 ) where J Q d Is the s o l i d angle subtended by the d e t e c t o r . The f i r s t o rder of s c a t t e r i n g , O"*, i s the second term of (2.36) and can be w r i t t e n as: CT1 ±_ <J~ECoO 2T1 O + C o s e x ) (2.39) Then: ' c r 2 / ^ ' L H L n D e £ C o < ) (2.4o) An order of magnitude f o r < T 2 i s then g i v e n by the pr o -duct of the a t t e n u a t i o n due t o s i n g l e s c a t t e r i n g i n t o ©< by the s o l i d angle subtended by the d e t e c t o r . T y p i c a l v a l u e s f o r the r a t i o ( 2 . 3 8 ) are i n the 10"^ order f o r common experimental c o n d i t i o n s . S i n c e s i m i l a r r a t i o s are expected between each order of s c a t t e r i n g and the next, the c o n t r i b u t i o n s t o . t h e m u l t i p l e s c a t t e r i n g term w i l l decrease r a p i d i l y w i t h . i n c r e a s i n g o r d e r . I t i s c l e a r then t h a t the m u l t i p l e s c a t t e r i n g c o r r e c t i o n term can be ne g l e c t e d f o r t o t a l r e a c t i o n c r o s s s e c t i o n measurements. As i s c l e a r from (2.36) the accuracy i n the d e t e r m i n a t i o n of 0"R w i l l be a f u n c t i o n of the c h o i c e of the angle oi . T h i s w i l l determine the r e l a t i v e importance of the e l a s t i c c o r r e c t i o n and the C r C M terms compared t o the experimental value of 0" . The accuracy of the experimental angular d i s t r i b u t i o n data w i l l determine, then, the e r r o r i n t r o d u c e d i n crl by these c o r r e c t i o n terms. - 39 -4 .2. B a s i c attenuatlon.method as a p p l i e d t o t o t a l r e a c t i o n cross s e c t i o n .measurements f o r ..protons . An example of the b a s i c a t t e n u a t i o n method i s the measurement of t o t a l r e a c t i o n c r o s s s e c t i o n f o r 9 MeV protons on copper by GREENLESS and JARVIS (Gr 6 l ) . The beam i n t e n s i t y i s assumed t o be constant over short time i n t e r v a l s and the t a r g e t i s c y c l i c a l l y i n t e r p o s e d i n the beam w i t h a frequency of twice a second. The t r a n s m i t t e d beam i n t e n s i t y i s , t h u s measured with and without t a r g e t . The use of a beam monitor makes the-beam constancy not so c r i t i c a l . The r e s u l t quoted i s 930 * 70 mb. The experimental raw value of 1530 i 70. mb i s c o r r e c t e d by a number of terms adding up to 3^05 1 76 mb. 4.3. The charge method See (Be 65) T h i s method i s . a p p r o p r i a t e o n l y f o r I n c i d e n t charged p a r t i c l e s . The schematic of the experiment i s shown i n F i g u r e 2 .5. In t h i s method, the a t t e n u a t i o n of the beam i s found by comparing the t o t a l charge t r a n s p o r t e d by the beam t o t h a t t r a n s f e r r e d t o the .target system due t o the a b s o r p t i o n of charged p a r t i c l e s by r e a c t i o n s i n i t . I f an i n c i d e n t beam c u r r e n t of 1 x 10- A i s being used f o r example, then an a t t e n u a t i o n of a -4 few p a r t s i n 10 w i l l mean a c u r r e n t t r a n s f e r r e d t o the t a r g e t of the order of 10"^° A, a va l u e r e a d i l y measured u s i n g an e l e c t r o m e t e r . T y p i c a l l y s r u n n i n g times of l e s s than f i v e minutes are quoted as adequate f o r such a t t e n u a t i o n measurement. B a s i c a l l y i f 'q' i s the charge d e p o s i t e d on the t a r g e t , and 'Q' the t o t a l - 40 - • charge conveyed by the beam, then the uncorrected a t t e n u a t i o n i s given by: q. Q~ (2.4i) The expression(2.41)assumes the presence of n e g l i g i b l e background, i . e . q = 0 f o r targe t - o u t measurements. Due to the s c a t t e r i n g pf the Incident beam from the c o l l i m a t i n g s l i t edges, i o n i z a t i o n of the r e s i d u a l gas by the i n c i d e n t beam and emission of secondary e l e c t r o n s from the t a r g e t assembly, t h i s assumption i s not v a l i d . entry-port target sample ex i t port I I electrometer Incident beam Target chamber Faraday cup Figure 2.5 :.Schematic of charge method experiment The a t t e n u a t i o n f o r t a r g e t - o u t , S 0UT* h a s t o b e c o n s i d e r e d ' T n e n the r e a l t a r g e t a t t e n u a t i o n i s given- by: IN O U T (2.42) - 41 - . The c o r r e c t i o n s i n v o l v e d f o r the t a r g e t - i n measurements a r e : a) secondary e l e c t r o n s emitted from the t a r g e t f o i l s ; b) p a r t of the t r a n s m i t t e d beam s u f f e r s e l a s t i c s c a t t e r i n g i n t o the t a r g e t assembly, c o n t r i b u t i n g t o the t r a n s f e r r e d charge; c) decay channels i n v o l v i n g charged p a r t i c l e s t h a t escape the t a r g e t assembly v i a the en t r y and e x i t p o r t s . C o r r e c t i o n c) can be p a r t i c u l a r l y s e r i o u s I f the decay products are m u l t i p l e charged, e.g. (p, C<) r e a c t i o n s . I f the secondary e l e c t r o n s a re stopped from l e a v i n g the t a r g e t , e.g. by u s i n g a magnet, then the r e a c t i o n c r o s s s e c t i o n can be w r i t t e n as: c r R = J L _ c r E 4- f o - c©)dr2 4./'c r p ^©)Jn ( 2 . 4 3 ) N L- JEMTA*' + J B X I T POBT- PORT where the terms are the same as those r e f e r r e d t o i n s e c t i o n 4.1 . 3 . The 0" t o_ terms are l a r g e r than those i n experiments u s i n g counters due.to the l a c k of energy d i s c r i m i n a t i o n on the beam t r a n s m i t t e d t o the Faraday cup, but the -main c o r r e c t i o n i s r e p r e s e n t e d by the e l a s t i c s c a t t e r i n g term, CT^ , which can c o n t r i b u t e up t o 70$ of the measured t r a n s f e r r e d charge. Although quoted e r r o r s are of the order of yfo, the method i s very s e n s i t i v e t o experimental e r r o r s i n the angular d i s t r i b u t i o n s f o r e l a s t i c s c a t t e r i n g and f o r charged p a r t i c l e y i e l d . 4 . 4 . The o p t i c a l theorem. See (Ho 65 , Ho 65a) The I n t e r f e r e n c e between Coulomb and n u c l e a r s c a t t e r i n g at forward angles permits the measurement of magnitude and phase - 42 - . of the nuclear s c a t t e r i n g amplitude. I f i t i s known, by applying the o p t i c a l theorem: CT_ = A~nk~] 2m Ko°) ( 2 . 4 4 ) where f ( 0 ° ) i s the forward s c a t t e r i n g amplitude, the t o t a l r e a c t i o n cross s e c t i o n can be determined. We. w i l l b r i e f l y d e s c r i b e the theory behind the method. The e l a s t i c s c a t t e r i n g amplitude f o r an i n c i d e n t charged p a r t i c l e can be w r i t t e n as two separate terms; ^ 0 ) = ^COULOMB W + ^RESIDUAL. (©> ( 2 . 4 5 ) The o r i g i n of the two terms i s s e l f explanatory. Now we apply the o p t i c a l theorem, even when the t o t a l r e a c t i o n cross s e c t i o n i s i n f i n i t e due t o the Coulomb s c a t t e r i n g : a - ; — " - = t T T - < ° ^ o u s ) = 4 n If 1 3 W Then, i s obtained f o r the t o t a l r e a c t i o n cross s e c t i o n the expression: c - e - - 4 ^ ' W R E S , D u a u ( o > ) - < r E — ( 2 . 4 6 ) where: - _ £ ^ S \ D U * U f . , . C O U L O M B , v , , ^ = J I V e ) - cr_ (e)Jci-Q-Por very small angles f R E s i D U A L ^ ^ c a n t e taken as a constant equal t o f ( 0 ° ) , meanwhile fnnT„Mim ( 0 ) i s RESIDUAL COULOMB ' r a p i d l y v a r y i n g , i n a w e l l known form.' Measurements of the e l a s t i c s c a t t e r i n g at two s m a l l angles can then be used t o determine f R E S I D U A L ( 0 ° ). This method has r e c e n t l y been a p p l i e d t o 17.5 Mev protons on A l and Cu, by measuring $ * E O ) from 4° to 1 5 ° t o Vfo accuracy. The. forward s c a t t e r i n g amplitude was determined t o 10$ :•  - 43 -accuracy (Po 6 7 ) . The authors do not quote the r e a c t i o n cross s e c t i o n s r e s u l t s , but they are " i n agreement w i t h the a t t e n u a t i o n method". The u n c e r t a i n t y i n these r e s u l t s i s expected to be of the same order as the one i n the determination of the forward r e s i d u a l s c a t t e r i n g amplitude. 4.5. The range method. See (Bu 59) This method allows measurements of the r e a c t i o n cross s e c t i o n s of e l e m e n t s . c o n s t i t u t i n g p a r t i c l e d e t e c t o r s , by d e t a i l e d a n a l y s i s of the shape of the pulse height spectrum of the p a r t i c l e s stopped i n the d e t e c t o r . I f the number of i n c i d e n t p a r t i c l e s i n t o the detector i s known and compared w i t h those d e t e c t e d - i n the f u l l energy peak, an a t t e n u a t i o n can be observed. I t w i l l a r i s e from n o n - e l a s t i c c o l l i s i o n s and r e a c t i o n s t a k i n g place i n the d e t e c t o r . An in c r e a s e i n the i n c i d e n t energy w i l l have the same e f f e c t as adding a t a r g e t made of the dete c t o r m a t e r i a l , as t h i c k as the increase i n range. The a t t e n u a t i o n w i l l then Increase. The energy dependence of t h i s a t t e n u a t i o n , i n the d e t e c t o r , can be used as a measurement of the r e a c t i o n cross s e c t i o n f o r the detec t o r m a t e r i a l . The method depends on the a n a l y s i s of the low energy r e g i o n of the energy spectrum. Here, the c o n t r i b u t i o n w i l l o r i g i n a t e from those p a r t i c l e s t h a t l o s t energy due t o a nuclear i n t e r a c t i o n or where completely removed ( v i a neutron emission) from the beam, a f t e r l e a v i n g only a f r a c t i o n of t h e i r energy i n the d e t e c t o r . - 44 -The d i f f i c u l t i e s a r i s i n g from the assignment of p u l s e s to the t a i l of the f u l l energy peak may c o n t r i b u t e with e r r o r s comparable to or h i g h e r than, s t a t i s t i c a l u n c e r t a i n t i e s . The method does not seem to be s e n s i t i v e enough to measure s m a l l a t t e n u a t i o n s , corresponding to v a r i a t i o n s i n the i n c i d e n t energy of the order of 10$. The r e s u l t s w i l l then be an average of the t o t a l r e a c t i o n c r o s s s e c t i o n over a wide energy range. As an example, quoting from 1?he work by E. Burge (Bu 5 9 ) ,the r e s u l t s f o r t o t a l proton r e a c t i o n c r o s s s e c t i o n s i n Carbon are g i v e n as: 376 1 40 mb at 25 ± 15 Mev and 355 - 50 mb a t 54 ± 14 Mev. T h i s Is not, by any means, the lower l i m i t of the method, but r e s u l t s f o r an energy average comparable t o t h a t of the a t t e n u a t i o n methods seem d i f f i c u l t t o o b t a i n . 4 . 6 . The c o i n c i d e n c e method. The t r a n s m i s s i o n , or a t t e n u a t i o n measurements f o r charged p a r t i c l e s d e s c r i b e d i n s e c t i o n 4.1 i n v o l v e d the measure-ment of s m a l l d i f f e r e n c e between two l a r g e numbers. T h i s problem Is worse at low e n e r g i e s where t a r g e t s w i t h t r a n s m i s s i o n s c l o s e to u n i t y must be used t o keep the r e l a t i v e energy l o s s i n the t a r g e t , at a r e a s o n a b l e magnitude. As a r e s u l t , the number of events t h a t have to be analysed i s extremely l a r g e , as t h e r e f o r e i s the beam time i n v o l v e d (See S e c t i o n 4.1.1.) B a s i c a t t e n u a t i o n methods can be m o d i f i e d so t h a t each I n d i v i d u a l proton i s a n a l y s e d . By t h i s Is meant t h a t s i g n a l s I n d i c a t i n g both the i n c i d e n c e of a p a r t i c l e i n the t a r g e t , and the emergence of the p a r t i c l e from the t a r g e t are o b t a i n e d . I f now c o i n c i d e n c e measurements between these s i g n a l s are made, the f a t e of each proton, whether absorbed or t r a n s m i t t e d , can be determined. - 45 -In the f o l l o w i n g s e c t i o n s a c l a s s i f i c a t i o n of coincidence methods i s made according to the method of determining when a proton i s i n c i d e n t . Coincidences and a n t i c o i n c i d e n c e s between d i f f e r e n t s i g n a l s w i l l be i n d i c a t e d w i t h the f o l l o w i n g n o t a t i o n : A coincidence between s i g n a l s A, B and C as ABC The same ABC i n a n t i c o i n c i d e n c e w i t h s i g n a l D as.. ABCD The n o t a t i o n M(ABCD) i s used t o i n d i c a t e a c e r t a i n i number of events of the kind Indicated between brackets. 4.6 . 1 . The b a s i c coincidence method. See (Ca 54) Incident A B C D beam Figure 2.6 : Schematic diagram o f the Basic Coincidence method A s e r i e s of t h i n t r a n s m i s s i o n detectors on the i n c i d e n t beam path define when a proton i s i n c i d e n t on the t a r g e t . For example, i n the schematics i l l u s t r a t e d i n Fi g u r e 2.6, two t h i n d e t e c t o r s , A and B, are lo c a t e d on the beam path to the t a r g e t C. - 46 -The t r a n s m i t t e d p a r t i c l e s are detected i n the f u l l energy d e t e c t o r D. S i g n a l s from d e t e c t o r s A and B t r i g g e r e d i n c o i n c i d e n c e d e f i n e the Incidence of a p r o t o n . Transmitted p a r t i c l e s w i l l g i v e r i s e to ABB events. Absorbed p a r t i c l e s w i l l g i v e r i s e to ABD events. The u n c o r r e c t e d a t t e n u a t i o n i s then g i v e n by: where the two kind of events are recorded i n the same g i v e n time. A necessary c o r r e c t i o n i s i n t r o d u c e d by the f a c t t h a t , even with no t a r g e t i n the beam, a s i g n i f i c a n t number of ABD are d e t e c t e d , mainly due t o n o n - e l a s t i c events i n counter D. Let us c a l l S j N and % 0UT the a t t e n u a t i o n s f o r t a r g e t - i n and t a r g e t -out r e s p e c t i v e l y . The' t a r g e t a t t e n u a t i o n i s then g i v e n by: ® T T N O U T A number of c o r r e c t i o n s must s t i l l be a p p l i e d to t h i s v a l u e . Those a r i s i n g from g e o m e t r i c a l c o n s i d e r a t i o n s were d e s c r i b e d i n s e c t i o n 4;1.2. S p e c i a l c o n s i d e r a t i o n must be made f o r the f a c t t h a t the energy of the protons, i n c i d e n t on the f u l l energy d e t e c t o r , changes between the t a r g e t - i n and the t a r g e t - o u t measurements due to the energy l o s s i n the t a r g e t . The method as d e s c r i b e d i s u s e f u l at energies h i g h enough, s-uch t h a t t h e s t r o n g forward s c a t t e r i n g makes the d i s p e r s i o n of the beam by the t h i n d e t e c t o r s n e g l i g i b l e ' a n d thus reduces the g e o m e t r i c a l c o n t r i b u t i o n , t o the ABD,events c o n s t i t u t i n g & OUT" For lower I n c i d e n t e n e r g i e s the c o l l i m a t i o n of the i n c i d e n t beam Is l o s t due to Coulomb s c a t t e r i n g i n the dE/dx d e t e c t o r s . More complex t e l e s c o p i c arrangements have had to be used to d e f i n e the i n c i d e n t beam of p a r t i c l e s (Wi 62). F i g u r e 47 -2.7 i s the schematics f o r such a t e l e s c o p i c arrangement of d e t e c t o r s . 1 Incident A beam B C Figure 2 . 7 : Schematic diagram of the Low Energy Basic Coincidence method Coincidences and a n t i c o i n c i d e n c e s a g a i n d e f i n e t r a n s -m i t t e d or absorbed p a r t i c l e s . Thus: Transmitted ... A B C D E Absorbed A,.B~ C D E S i n c e the r u n n i n g s time r e q u i r e d f o r t h i s type of measurement i s l i m i t e d by the "instantaneous" c o u n t - r a t e s p e r m i t t e d i n the f i r s t ' d e t e c t o r s of the t e l e s c o p e , namely A and B, i t i s c l e a r t h a t DC a c c e l e r a t o r s present s i g n i f i c a n t advantages over pulsed, machines. We'can then c l a s s i f y t h i s type of measurement i n t o two-c a t e g o r i e s , a c c o r d i n g t o the energy of the i n c i d e n t p a r t i c l e . The low energy one, where the t a r g e t - o u t a t t e n u a t i o n i s determined by the s c a t t e r i n g and r e a c t i o n s on the d e f i n i n g counters, p l u s the - 48 f u l l energy d e t e c t o r . The h i g h energy one, when the t a r g e t - o u t a t t e n u a t i o n i s determined l a r g e l y by the n o n - e l a s t i c c o l l i s i o n i n the f u l l energy counter. In the low energy type of : measurement the a n t i c o i n c i d e n c e d e t e c t o r can f a i l t o t r i g g e r , due to n o n - e l a s t i c c o l l i s i o n s , i n i t , and p a r t i c l e s b e i n g considered as i n c i d e n t on the t a r g e t , when they had a c t u a l l y been removed from the beam. The f r a c t i o n of beam i n c i d e n t on the a n t i c o i n c i d e n c e a n u l a r d e t e c t o r i s determined by the s c a t t e r i n g - s u f f e r e d on the p r e v i o u s dE/dx detector,-which Is l a r g e In t h i s energy range. The work f o r 134 Mev protons by C a s s e l s and Lawson (Ca 54) r e p o r t s e r r o r s on the r e a c t i o n c r o s s s e c t i o n s of the order of 10$ wit h t a r g e t - o u t c o r r e c t i o n s of the order of 30$ the t a r g e t - i n v a l u e s . The work f o r 10 Mev protons by W i l k i n s and Igo (WI 62) r e p o r t s r e a c t i o n c r o s s s e c t i o n s w i t h u n c e r t a i n t i e s between 2$ and 10$. The t a r g e t - o u t a t t e n u a t i o n s are r e p o r t e d i n a r a t i o ' of 4/5 of the t a r g e t - i n v a l u e s . A more r e c e n t work at a proton energy of 14.5 Mev (-M 66) uses a m o d i f i e d t e l e s c o p i c arrangement of d e t e c t o r s , and a combination of p l a s t i c s c i n t i l l a t o r and a l i t h i u m d r i f t e d d e t e c t o r i n s t e a d of a s i n g l e f u l l energy counter. The t o t a l r e a c t i o n cross s e c t i o n s are r e p o r t e d w i t h e r r o r s of the order of 2$. The r a t i o of t a r g e t - o u t to t a r g e t - I n a t t e n u a t i o n s i s reduced t o 1/2.2 from the value i n the pre v i o u s work. 4.6.2. The r e c o i l method. See (Bu 61) (Ar 64) In t h i s method the i n c i d e n t beam i s a c t u a l l y the secondary beam produced by a primary s c a t t e r i n g p r o c e s s . S i n c e - 49 -t h e d i r e c t i o n a n d k i n e t i c e n e r g y o f t h e r e c o i l p a r t i c l e s p r o d u c e d i n t h e p r i m a r y s c a t t e r i n g a r e k i n e m a t i c a l l y r e l a t e d t o t h e p a r t i c l e s o f t h e i n c i d e n t b e a m , t h e p r e s e n c e o f a n i n c i d e n t p a r t i c l e c a n b e d e t e r m i n e d b y d e t e c t i n g t h e r e c o i l p a r t i c l e a t a n a p p r o p r i a t e a n g l e a n d w i t h a p p r o p r i a t e e n e r g y . T h e n a t t e n u a -t i o n s c a n b e m e a s u r e d u s i n g t h e c o i n c i d e n c e t e c h n i q u e . T h e s y s t e m h a s t h e a d v a n t a g e o f n o t r e q u i r i n g t h e t r a n s v e r s i n g o f m a t e r i a l o b j e c t s b y t h e i n c i d e n t b e a m b e f o r e i t r e a c h e s t h e t a r g e t m a t e r i a l . T h e m e t h o d c a n i n p r i n c i p l e b e a p p l i e d f o r a n y e n e r g y o f i n c i d e n t b e a m s w i t h o n l y g e o m e t r i c a l c h a n g e s n e c e s s a r y . T o t h e a u t h o r ' s k n o w l e d g e t h i s m e t h o d h a d n o t b e e n u s e d f o r p r a c t i c a l m e a s u r e m e n t s u n t i l t h e p r e s e n t . 4 . 6 . 3 . T h e a s s o c i a t e d p a r t i c l e m e t h o d T h i s m e t h o d i s d i s c u s s e d i n d e t a i l i n t h e n e x t c h a p t e r . I t s h o u l d b e m e n t i o n e d h e r e a s a n a l t e r n a t i v e t o t h e r e c o i l m e t h o d . I n s t e a d o f p r o d u c i n g a s e c o n d a r y b e a m b y e l a s t i c s c a t t e r i n g , a n u c l e a r r e a c t i o n i s c h o s e n t h a t g i v e s r i s e t o t w o c h a r g e d p a r t i c l e s . ' D e t e c t i o n o f o n e o f t h e p a r t i c l e s t h u s d e f i n e b y k i n e m a t i c a l r e l a t i o n s t h e d i r e c t i o n a n d e n e r g y o f t h e a s s o c i a t e d o n e . T h e l a t t e r t h e n c o n s t i t u t e s t h e i n c i d e n t b e a m I n w h i c h a t a r g e t f o l l o w e d b y t h e f u l l e n e r g y d e t e c t o r may b e i n s e r t e d . A g a i n c o i n c i d e n c e m e a s u r e m e n t s p e r m i t a t t e n u a t i o n d e t e r m i n a t i o n s t o b e o b t a i n e d . - 50 -3 . EXPERIMENTAL DESIGN.. 1. General i n t r o d u c t i o n . In the pr e v i o u s chapter d i f f i c u l t i e s a s s o c i a t e d w i t h determining the i n c i d e n c e of a charged p a r t i c l e e n t e r i n g an a t t e n u a t i o n apparatus has been p o i n t e d out,. T h i s i s an important c o n s i d e r a t i o n f o r low i n c i d e n t e n e r g i e s , where the c o i n c i d e n c e technique i n v o l v e s the use of complex t e l e s c o p i c arrangements of d e t e c t o r s . The a s s o c i a t e d p a r t i c l e technique p r o v i d e s a new method f o r determining the a r r i v a l of an i n c i d e n t p a r t i c l e . In t h i s chapter we w i l l b r i e f l y d i s c u s s the a s s o c i a t e d p a r t i c l e technique and i t s l i m i t a t i o n s . F i n a l l y the r e a c t i o n used i n the present p r o j e c t w i l l be d i s c u s s e d t o g e t h e r w i t h the d e s i g n of the experiment. " K i n e m a t i c a l c o l l i m a t i o n " of the a s s o c i a t e d beam w i l l be d i s c u s s e d i n c o n n e c t i o n w i t h t h i c k t a r g e t s i n producing the a s s o c i a t e d beam. 2. The a s s o c i a t e d p a r t i c l e t e c h nique. 2.1. P r o d u c t i o n of a s s o c i a t e d beams. As i s i m p l i e d by the technique's name, a l s o r e f e r r e d t o as the MAssoclate ;d' :'particle g a t i n g technique", i t i s the d e f i n i t i o n of the c h a r a c t e r i s t i c s of a p a r t i c l e by the p r o p e r t i e s of a d i f f e r e n t one, a s s o c i a t e d w i t h t h e . f i r s t by a w e l l d e f i n e d k i n e m a t i c a l r e l a t i o n s h i p . In a n u c l e a r r e a c t i o n w i t h two p a r t i c l e s as the f i n a l s t a t e , the p r i n c i p l e s of c o n s e r v a t i o n of energy and momentum permits the c o r r e l a t i o n of the two products i n an unambiguous way. T h i s means t h a t i f one of the products i s dete c t e d at some angle w i t h r e s p e c t t o the d i r e c t i o n of the incoming primary beam the energy and angle of emission of the a s s o c i a t e d product are d e f i n e d by the parameters of the r e a c t i o n . The parameters are the masses of the i n i t i a l and f i n a l products of the r e a c t i o n and the Q-value a s s o c i a t e d w i t h them. K i n e m a t i c a l r e l a t i o n s h i p s can then be w r i t t e n down f o r a p a r t i c u l a r r e a c t i o n , c o r r e l a t i n g the angles and energies of the outcbming p a r t i c l e s u s i n g , f o r example, the i n c i d e n t energy i n the input channel as a parameter. T h i s w i l l be i l l u s t r a t e d i n d e t a i l f o r the r e a c t i o n He(d,p) He used i n the present experiment. Furthermore, d e t e c t i o n of one of the products not only d e f i n e s the s p a c i a l a s p e c t s of the a s s o c i a t e d one but a l s o use-f u l temporal i n f o r m a t i o n . I t p r o v i d e s , f ;or example, a means of knowing when i t was produced or i s expected t o a r r i v e . In what f o l l o w s we w i l l r e f e r t o the a c t u a l a c c e l e r a t o r beam, d e f i n i n g the Input channel, as the "primary beam"; t o the d e f i n i n g beam of p a r t i c l e s as the "secondary beam"; t o the beam used f o r the a t t e n u a t i o n measurements as the " a s s o c i a t e d beam"; and the r e a c t i o n i n v o l v e d as the "source r e a c t i o n " . The " a s s o c i a t e d p a r t i c l e t e c h n i q u e " has been a p p l i e d e x t e n s i v e l y t o neutron work as a source of monoenergetic and w e l l c o l l i m a t e d neutron beams. I t i s a l s o used as a convenient way of d e f i n i n g time zero i n " T i m e - o f - f l i g h t " techniques f o r measuring nevlroT) e n e r g i e s . 2.2. L i m i t a t i o n s of the te c h n i q u e. The a s s o c i a t e d p a r t i c l e . t e c h n i q u e s u f f e r s , i n g e n e r a l , from two disadvantages. The energy can not be v a r i e d as r e a d i l y - 52 - . as f o r the case of ah a c c e l e r a t o r beam, s i n c e here must be taken i n t o account the kinematics of the r e a c t i o n i n v o l v e d . In a d d i t i o n , the beam f l u x a v a i l a b l e i s much l e s s than o b t a i n a b l e i n an a c c e l e r a t o r by the l i m i t set by the maximum a c c e p t a b l e counting r a t e on the secondary beam d e t e c t o r . I f the r e a c t i o n used i s endoenergetic, then above the r e a c t i o n t h r e s h o l d the energy of the r e a c t i o n products w i l l be s t r o n g l y dependent on the primary beam energy. On the other hand, i f the r e a c t i o n used i s e x o e n e r g e t i c , then f o r primary energies much below the Q-value the energy of the r e a c t i o n products w i l l be mainly d e f i n e d by the Q-value i t s e l f . When the primary energy becomes of the order of the Q-value, or h i g h e r , the dependence of the energies of the products on the i n c i d e n t energy r e t u r n s . In f a c t t h i s l a s t c o n s i d e r a t i o n l i m i t s the range of energies a v a i l a b l e i n the secondary and a s s o c i a t e d beams to energies below the Q-value. I t p r o v i d e s thereby a means of o b t a i n i n g h i g h energy p a r t i c l e s w i t h r e l a t i v e low energy a c c e l e r a t o r s . The case i s i l l u s t r a t e d by the % ( d , n ) ^ H e (Q=17.6 Mev) and the ^He(d,p)^He (Q=l8.352 Mev) r e a c t i o n , where with en e r g i e s i n the primary beam below 1 Mev, neutrons or protons above 10 Mev can be o b t a i n e d ^ The f l u x a v a i l a b l e i n the a s s o c i a t e d beam w i l l depend on the cr o s s s e c t i o n f o r the source r e a c t i o n t o take p l a c e . In g e n e r a l , t h i s i s not l i m i t e d by the f l u x e s a v a i l a b l e i n the primary beam from a p a r t i c l e a c c e l e r a t o r as much as i t i s from the problem i n v o l v e d i n the d e s i g n of source t a r g e t s capable of w i t h s t a n d i n g the necessary beam c u r r e n t s without i n t r o d u c i n g unwanted s c a t t e r i n g m a t e r i a l i n the secondary and a s s o c i a t e d - 53 -beam paths. Choice of the source r e a c t i o n depends a l s o on the presence of competing r e a c t i o n s which may a r i s e from the./ same t a r g e t or contaminations on i t . I d e a l l y one should be ab l e t o e i t h e r n e g l e c t their c o n t r i b u t i o n i f s u i t a b l y nrinor, ° r e x p e r i -m e n t a l l y r e s o l v e t h e i r e f f e c t . 2.3. P r o d u c t i o n of a s s o c i a t e d beams of charged p a r t i c l e s . For n e u t r a l beam's i t i s d i f f i c u l t t o o b t a i n v a r i a b l e energy, good c o l l i m a t i o n or energy s e l e c t i o n due to t h e i r l a c k of e l e c t r i c charge. The advantages of producing them by an a s s o c i a t e d p a r t i c l e technique are c l e a r . In the case of charged p a r t i c l e s the s i t u a t i o n i s t o t a l l y d i f f e r e n t . P a r t i c l e a c c e l e r a t o r s can p r o v i d e h i g h f l u x e s of monoenergetic and w e l l c o l l i m a t e d charged p a r t i c l e s of v a r i a b l e energy. I t Is c l e a r t h a t the p r o d u c t i o n of an a s s o c i a t e d beam only i n v o l v e s the ch o i c e of an a p p r o p r i a t e source r e a c t i o n , g i v i n g r i s e t o two charged p r o d u c t s . The a v a i l a b i l i t y of a c c e l e r a t o r beams makes i t not s u r p r i s i n g , then, t h a t the p r o d u c t i o n of a s s o c i a t e d beams of charged p a r t i c l e s has not been pursued up t o the p r e s e n t . Some p r o t o n and deuteron producing r e a c t i o n s have been used as a source of p o l a r i z e d beams (Br 63), but without u s i n g the secondary p a r t i c l e s to d e f i n e the wanted beam. I n t e r e s t i n a s s o c i a t e d charged p a r t i c l e beams w i l l be more l i m i t e d than i n the neutron case. A p p l i c a t i o n of the technique t o the measurements of t o t a l r e a c t i o n c r o s s s e c t i o n s f o r protons i s the o b j e c t of the present work. - 54 - . 2 . 4 . Requirements f o r an a t t e n u a t i o n experiment. The p a r t i c u l a r " a s s o c i a t e d p a r t i c l e t e c h n i q u e " used f o r the measurement of t o t a l r e a c t i o n c r o s s s e c t i o n s f o r protons i s a m o d i f i c a t i o n of the "Coincidence t e c h n i q u e " d e s c r i b e d i n the pre v i o u s chapter. Primary beam Secondary beam Associated beam F i n a l target Figure 3 . 1 : Schematic diagram of an "Associated p a r t i c l e " • attenuation experiment; '  ! • F i g u r e 3.1 i s a schematic diagram of such an experiment. The primary beam, o r i g i n a t i n g from a p a r t i c l e a c c e l e r a t o r , produces r e a c t i o n s i n the source t a r g e t t h a t g i v e r i s e t o the secondary and a s s o c i a t e d beams. The angular c o r r e l a t i o n between the two f i n a l products can be k i n e m a t i c a l l y c a l c u l a t e d . By g a t i n g the d e t e c t o r D2, at angle , wi t h the output of the d e t e c t o r of the secondary beam, s e l e c t e d i n angle ( ^ ) and energy at D l , an a s s o c i a t e d beam i s s e l e c t e d out of the t o t a l f l u x of p a r t i c l e s i i n c i d e n t on D2. N e g l e c t i n g both s c a t t e r i n g e f f e c t s In the source - 55 -t a r g e t and l o s s e s i n the d e t e c t o r s , t o each p a r t i c l e of the secondary beam detected a t D l the corresponding a s s o c i a t e d p a r t i c l e w i l l be det e c t e d on D2. The f i n a l t a r g e t , whose a t t e n u a t i o n i s to be measured ;is p l a c e d j u s t b e f o r e the d e t e c t o r D2. A f r a c t i o n of the t o t a l number of p a r t i c l e s i n the a s s o c i a t e d beam w i l l be removed from i t when p a s s i n g through the f i n a l t a r g e t . A n t i c o i n c i d e n c e as w e l l as c o i n c i d e n c e measurements are obtained between det e c t e d events i n D l and D2. L e t the numbers of such events recorded d u r i n g an a p p r o p r i a t e time i n t e r v a l be M(D1 D~2) and M(D1D2), r e s p e c t i v e l y . For the case when & £ < i l t h e number of a n t i c o i n c i d e n c e s w i l l be much s m a l l e r than the number of c o i n c i d e n c e s , o r : M ( D l 6 1 ) <£<• M (Ol D 2 V so the t o t a l number of p a r t i c l e s i n the a s s o c i a t e d beam i s M (Dl DE) -V-MCDI02) ^ M ( D \ 0 2 ) Using equations (2.8) and (2.12) we o b t a i n : ' & = " <° ' ^> (3.1) (Dl D 2 ) Thus, the d e t e c t i o n of a secondary p a r t i c l e D l i s used t o r e p l a c e the d e t e c t o r t e l e s c o p e employed i n the c o i n c i d e n c e technique i n order t o I n d i c a t e the i n c i d e n c e of a p a r t i c l e i n t o the f i n a l t a r g e t . As d i s c u s s e d i n the pre v i o u s chapter, some a n t i c o i n c i -dence events w i l l be present even when the f i n a l t a r g e t Is removed. In order f o r the a t t e n u a t i o n of the f i n a l t a r g e t t o be measured with p r e c i s i o n , t h i s a n t i c o i n c i d e n c e background should be reduced t o . t h e minimum p o s s i b l e and i t s o r i g i n and. energy - 56 -d e p e n d e n c e w e l l u n d e r s t o o d . C h o i c e o f t h e s o u r c e r e a c t i o n was d e t e r m i n e d " b y . t h e f o l l o w i n g c o n s i d e r a t i o n s : a ) t h e p r o t o n t o t a l r e a c t i o n c r o s s s e c t i o n s s h o u l d b e m e a s u r a b l e t o a n a c c u r a c y o f a f e w p e r c e n t i n a r e a s o n a b l e b e a m t i m e . b ) E n e r g i e s o f l e s s t h a n 1.5 Mev a r e r e a d i l y o b t a i n e d f r o m t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n d e G r a a f f g e n e r a t o r w i t h c u r r e n t s o f t h e o r d e r o f m i c r o a m p e r e s a t t h e s e e n e r g i e s . c ) S e c o n d a r y p a r t i c l e s m u s t b e c h a r g e d p a r t i c l e s ( d e t e c t i o n e f f i c i e n c y 100$) a n d e a s i l y d i s t i n g u i s h a b l e f r o m t h e s c a t t e r e d i n c i d e n t b e a m . d ) C o m p e t i n g . r e a c t i o n s I n t h e s o u r c e t a r g e t m u s t n o t g i v e r i s e t o p a r t i c l e s a t e n e r g i e s s u c h t h a t t h e y c a n n o t b e e x p e r i m e n t a l l y r e s o l v e d f r o m t h e s e c o n d a r y b e a m . e ) T h e d i s p e r s i o n o f t h e a s s o c i a t e d b e a m , a n d i t s a n g u l a r d i v e r g e n c y s h o u l d b e k e p t a t a m i n i m u m . P o i n t s c ) a n d d ) w e r e i m p o r t a n t i n d e t e r m i n i n g t h e a t t e n u a t i o n b a c k g r o u n d . C o n s i d e r a t i o n o f p o i n t e ) i s r e q u i r e d w h e n p e r f o r m i n g t a r g e t c o r r e c t i o n s a n d f o r d e t e r m i n i n g t h e s i z e o f t h e f i n a l t a r g e t . 3. T h e 3 H e ( d , p ) % e r e a c t i o n . T h e p a r t i c u l a r s o f t h i s r e a c t i o n f u l f i l l e d t h e r e q u i r e m e n t s s p e c i f i e d i n s e c t i o n , 2.4. T h e r e a c t i o n c r o s s s e c t i o n h a s a p r o n o u n c e d r e s o n a n c e a t 430 k e v i n c i d e n t d e u t e r o n e n e r g y i n t h e l a b o r a t o r y s y s t e m , o f - 5 7 - : 450 k e v w i d t h ( B o 5 7 ) . F o r i n c i d e n t % e t h e r e s o n a n c e i s o b s e r v e d a t 640 k e v l a b o r a t o r y e n e r g y w i t h a - w i d t h o f 6 7 - O - k e v ; t h e e n e r g y d e p e n d e n c e o f t h e c r o s s s e c t i o n i s s h o w n i n ( K u 52).. [':/"•. ( T h e p e a k v a l u e i s g i v e n a s (695 i 14) m b . T h e h i g h Q - v a l u e o f 18.352 M e v p e r m i t s t h e p r o d u c t i o n o f p r o t o n s w i t h e n e r g i e s b e t w e e n 12 a n d ,18 M e v f o r i n c i d e n t ^>Ee e n e r g i e s n e a r t h a t c o r r e s p o n d i n g t o t h e m a x i m u m i n t h e c r o s s s e c t i o n . T h i s e n e r g y r a n g e i s u s e f u l f o r o p t i c a l m o d e l i n v e s t i g a -t i o n s f o r t h e f o l l o w i n g r e a s o n s . . I t i s j u s t a b o v e t h e C o u l o m b b a r r i e r f o r a l l t h e p o s s i b l e t a r g e t s ; c o n t r i b u t i o n s f r o m c o m p o u n d e l a s t i c s c a t t e r i n g c a n b e e x p e c t e d t o b e s m a l l d u e t o t h e n u m b e r o f . c o m p e t i n g c h a n n e l s ; c o m p a r i s o n w i t h o p t i c a l m o d e l c a l c u l a t i o n s c a n b e m a d e e a s i l y d u e t o t h e d e n s i t y o f l e v e l s a n d t h e n u m b e r o f p a r t i a l w a v e s t h a t m u s t b e c o n s i d e r e d i s s t i l l . r e l a t i v e l y s m a l l . T h e s e c o n d a r y b e a m i s c o m p o s e d o f ^ H e w i t h e n e r g i e s i n t h e 1 t o 7 M e v r a n g e . T h e y c a n b e e a s i l y d e t e c t e d u s i n g s o l i d s t a t e d e t e c t o r s w i t h F . W . H . M . r e s o l u t i o n s o f l e s s t h a n 50 K e v . T h e y c a n b e e a s i l y d i s t i n g u i s h e d e x p e r i m e n t a l l y f r o m t h e i n c i d e n t s c a t t e r e d b e a m . T h e p r e s e n c e o f p o l a r i z a t i o n i n t h e p r o t o n b e a m i s n o t r e l e v a n t f o r t h e t o t a l r e a c t i o n c r o s s s e c t i o n m e a s u r e m e n t s . I f p r e s e n t , i t w i l l g i v e r i s e t o s o m e l e f t - t o - r i g h t a s y m m e t r y i n t h e d i f f e r e n t i a l e l a s t i c c r o s s s e c t i o n s . T h e a v a i l a b l e e x p e r i m e n t a l d a t a ( L a 66), i n d i c a t e s t h a t l e s s t h a n 5$ p o l a r i z a t i o n i s t o b e e x p e c t e d a t t h e e n e r g i e s i n v o l v e d i n t h e p r e s e n t e x p e r i m e n t . T h e c o m p e t i n g r e a c t i o n s a r e ( L a 66): 1) 3 n e ( d , tf)5LI : Q - v a l u e = 16.388 M e v E v =16.6 M e v - -58 -<T = 50 1 10 jxbarns at E D = 450 kev Not only i s the c r o s s s e c t i o n very s m a l l compared with the (d,p) channel but the ^ L i r e c o i l energy i s too low t o be d e t e c t e d . In a d d i t i o n , the d e t e c t o r s a re not very s e n s i t i v e t o gamma, r a d i a t i o n . 2) ^He(d,n)^Li : CT = 3 to 8 x 10~ 3 ^ b a r n s f o r E D from .5 t o 2.3 Mev. Again the cr o s s s e c t i o n i s extremely s m a l l • ,<;•{ compared t o the (d,p) channel. A l s o , the d e t e c t o r s are i n s e n s i t i v e t o neutron d e t e c t i o n . 3) 3He(d,np) 3He : Q-value = -2.225 Mev T h i s r e a c t i o n Is not e n e r g e t i c a l l y p o s s i b l e at the resonance energy f o r the (d,p) channel. 4) 3 H e ( d , p p ) % : Q-value = -1.461 Mev As case 3) above. Thus, no i n t e r f e r e n c e from competing r e a c t i o n s i n the source t a r g e t i s t o be expected. 3.1. R e a c t i o n k i n e m a t i c s . The r e s u l t s of the computations f o r the n o n - r e l a t l v i s t i c two body breakup of 3He(d,p)^He are p l o t t e d i n F i g u r e s 3.3 t o 3 .8. The r e g i o n of the r e a c t i o n c r o s s s e c t i o n resonance was. covered by assuming 3He i n c i d e n t energies of 400, 600 and 800 kev as the f r e e parameter i n the c a l c u l a t i o n s . I t i s evident i n each of the f i r s t f o u r graphs t h a t there i s a r e g i o n i n which the i n f l u e n c e of the i n c i d e n t energy i s minimum. These correspond t o the i n t e r c e p t of the curves c o r r e s p o n d i n g to the t h r e e - d i f f e r e n t i n c i d e n t e n e r g i e s . I8H 0 20 40 60 80 100 120 140 160 180 PROTON ANGLE Figure 3.5 : 3He(d,p) 4He r e a c t i o n kinematics ALPHA ENERGY (MeV) - Z9 ~ - V9 -- 65 T h i s i s u s e f u l b e c a u s e i t p e r m i t s t h e u s e o f t h i c k s o u r c e t a r g e t s ( b y t h i c k i s m e a n t a n e n e r g y l o s s i n t h e t a r g e t c o m p a r a b l e t o t h e i n c i d e n t e n e r g y ) w i t h o u t c o n s i d e r a b l e c h a n g e i n t h e k i n e m a t i c s o f t h e p r o d u c t s o f r e a c t i o n s t a k i n g p l a c e a t d i f f e r e n t d e p t h s . T h e p o s s i b i l i t y o f t h i c k t a r g e t s i s i m p o r t a n t i n o r d e r t o o b t a i n h i g h c o u n t i n g r a t e s i n t h e a s s o c i a t e d b e a m . We w i l l now d e s c r i b e t h o s e p r o p e r t i e s o f f i g u r e s 3 . 4 , 3 .5> 3 . 6 , 3 . 7 * w h i c h a r e o f r e l e v a n c e i n l a t e r d i s c u s s i o n . T h e r a n g e o f p a r a m e t e r s c o r r e s p o n d t o a c h a n g e i n 3 H e i n c i d e n t e n e r g y f r o m 4 0 0 t o 800 k e v . CASE I ( F i g u r e 3 . 4 ) ; ^He a n g l e = 50° CASE I I ( F i g u r e 3 . 5 ) I n t e r c e p t a t E = 14 Mev P R a n g e s E i , = 4 . 7 5 - 5 . 2 Mev; p a n g l e = 1 1 7 ° - 1 1 0 ° T h i s c o n f i g u r a t i o n f a c i l i t a t e s t h e ii p r o d u c t i o n o f a w e l l c o l l i m a t e d He b e a m a s s o c i a t e d w i t h m o n o e n e r g e t i c p r o t o n s . I n t e r c e p t a t Eh = 4 . 0 Mev ;.^He a n g l e = 75° R a n g e s E = 1 4 . 7 5 - 15.15 Mev; p a n g l e = hr 90° - 82° T h i s c o n f i g u r a t i o n f a c i l i t a t e s t h e p r o d u c t i o n o f a w e l l c o l l i m a t e d a n d m o n o -h e n e r g e t i c He b e a m . CASE I I I ( F i g u r e 3 . 6 ) : I n t e r c e p t a t E = 1 4 . 5 Mev. ; p a n g l e = 98° R a n g e s E 4 H e = ^ - 2 5 - ^.65 Mev ; ^He a n g l e = 6 7 ° - 6 1 . 5 ° T h i s c o n f i g u r a t i o n f a c i l i t a t e s t h e p r o d u c t i o n o f a w e l l c o l l i m a t e d , m o n o e n e r g e t i c p r o t o n b e a m . - 66 -CASE IV (Figure 3.7) : Intercept at E4 H e= 3.3 Mev ; p angle = 65° Ranges E p = 15.45 - 15.9 Mev; ^He angle = 92° - 1 0 0 ° This c o n f i g u r a t i o n f a c i l i t a t e s the production of a w e l l c o l l i m a t e d proton beam ass o c i a t e d with monoenergetic ^He. The two i n t e r e s t i n g cases that minimized v a r i a t i o n s of the secondary, and as s o c i a t e d beams at the same time are cases I and IV. In CASE I the d e t e c t i o n of ^He at a " w e l l d e f i n e d " angle defines an ass o c i a t e d beam of "monoenergetic" protons, at around 113.5 » f o r r e a c t i o n s t a k i n g place w i t h i n c i d e n t JHe energies between 400 and 800 kev. The angular divergency on the proton beam w i l l be of 7 ° hut the energy w i l l be defined to b e t t e r than 100 kev f o r the s p e c i f i e d range. The ass o c i a t e d ^He p a r t i c l e s are assumed to be detected i n a counter subtending an angle of 2 ° and span an energy range of 450 kev. In CASE IV the d e t e c t i o n of ^He w i t h i n a "narrow energy" i n t e r v a l of 50 kev permits the " c o l l i m a t i o n " of an ass o c i a t e d beam of 15.7 i .22 Mev protons to the order of 1 ° f o r r e a c t i o n t a k i n g place f o r i n c i d e n t ^>Ee energies between 400 and 800 kev. A The He p a r t i c l e s associated, with the protons would be spread over an angular range of 8 ° „ 3.2. K i n e m a t i c a l C o l l i m a t i o n of the associated proton beam. From the con s i d e r a t i o n s of s e c t i o n 3 . I * Case IV w i l l permit the use of t h i c k source t a r g e t s w i t h t h e i r r e s u l t i n g higher counting r a t e , at the same time as a h i g h l y c o l l i m a t e d - 67 -h proton beam, i f the secondary beam of He i s energy s e l e c t e d with good energy r e s o l u t i o n . The spread i n proton energies of 220 kev i s s u f f i c i e n t l y s m a l l t h a t the c o r r e c t i o n s d i s c u s s e d i n Chapter 2 s e c t i o n 4.1 (eq. 2.10) can be n e g l e c t e d . The p r o p e r t i e s of Case IV amounts t o a "K i n e m a t i c a l  c o l l i m a t i o n " of the a s s o c i a t e d proton beam. F i g u r e s 3.9 and 3.10 present an expanded view of the i n t e r c e p t area f o r Case IV. Here a primary t a r g e t t h i c k n e s s of 100 kev has been c o n s i d e r e d , centred at the peak resonance energy of 650beV. Design of the present experiment represented a com-promise between angular d i s p e r s i o n and p a r t i c l e , f l u x In the a s s o c i a t e d beam. The case f o r an energy window of 100 kev In 4 the He channel- i s I n d i c a t e d i n the.expanded f i g u r e s , . c e n t e r e d 4 at the i n t e r c e p t p o i n t . I t i n v o l v e s He energies between 3.17 and 3.27 Mev and a s s o c i a t e d protons emitted between 6 2 ° and 6 5 ° . . The proton e n e r g i e s i n v o l v e d are from 15.68 to 15.89 Mev and the angles f o r the secondary beam between.9 3 . 7° and 98.6° (center angle 9 6 . 2 ° see f i g u r e 3 . 2 ) . In p r a c t i c e the proton beam w i l l not be as s h a r p l y d e f i n e d as mentioned In the p r e v i o u s paragraph due to the in h e r e n t energy r e s o l u t i o n of the ^ He d e t e c t i o n system. A value of 40 kev F.W.H.M. corresponds t o the energy r e s o l u t i o n t h a t could be r e a d i l y obtained with standard i n s t r u m e n t a t i o n I n our l a b o r a t o r y . The e f f e c t of a 40 kev energy i n t e r v a l i n the ^He energies on the a s s o c i a t e d beam i s i n d i c a t e d by the dotted l i n e s i n f i g u r e s 3.9 and 3.10, centered at the i n t e r c e p t p o i n t j u s t f o r i l l u s t r a t i o n . I t corresponds to an angular divergency i n the - 68 -3 . 3 0 j 450 k«v 63° 64' P R O T O N A N G L E Figure 3.9 : 3He(d,p) 4He r e a c t i o n kinematics - 70 -proton beam of l e s s than 1.2 . •3.3. Source t a r g e t angle. The p a r t i c u l a r s of the source; t a r g e t I t s e l f w i l l be di s c u s s e d i n s e c t i o n 2.3 of Chapter 4. Here we are concerned with choosing the; o r i e n t a t i o n of the source t a r g e t plane. The t a r g e t was chosen to be a deuterium t a r g e t i n the form of s o l i d DgO, formed on a t h i n copper f o i l backing at l i q u i d n i t r o g e n temperatures. For h i g h p a r t i c l e f l u x e s i n the a s s o c i a t e d beam a t h i c k primary t a r g e t i s wanted; the use of k i n e m a t i c a l c o l l i m a t i o n can be used t o o b t a i n n e v e r t h e l e s s , a s m a l l angular d i v e r g e n c y . As seen i n s e c t i o n 3.2 t h i s c h a r a c t e r i s t i c depends on d e t e c t i n g the 4 He secondary beam wit h good energy r e s o l u t i o n and s m a l l s c a t t e r -i n g e f f e c t s on i t s o r i g i n a l angle of em i s s i o n . In oth e r words, as l i t t l e t a r g e t m a t e r i a l as p o s s i b l e is, wanted i n the d i r e c t i o n of the s e l e c t e d ^He p a r t i c l e s ( % = 9 6 . 2 ° ). T h i s w i l l imply a primary t a r g e t angle s m a l l e r than <^  ,,or fb<C 9 6 . 2 ° , . Due to the low thermal c o n d u c t i v i t y of i c e , a low cur r e n t d e n s i t y on the primary beam i s d e s i r a b l e f o r s t a b l e t a r g e t s . At 173°K the value f o r normal i c e can be c a l c u l a t e d to be 8 x 10~3 c a l ° C - 1 s~ 1cm" 1 (Po 65). I f the temperature of the i c e r i s e s above 1 7 3 ° K I t i s v a p o r i z e d a t a f a s t r a t e . For a s e l e c t e d beam c u r r e n t , low c u r r e n t d e n s i t i e s r e q u i r e a l a r g e beam spot. The g e o m e t r i c a l e f f e c t s of a l a r g e beam spot can be minimized by the use of " n a t u r a l f o c u s i n g " as d e s c r i b e d i n Appendix I I . The best angle f o r n a t u r a l f o c u s i n g t o take p l a c e , as shown i n the appendix, i m p l i e s the t r a n s v e r s a l of more t a r g e t - 71 — m a t e r i a l i n the d i r e c t i o n of the secondary beam than i n the d i r e c t i o n of the i n c i d e n t beam. In p r a c t i c e , c h o i c e of the primary t a r g e t angle depends on the ch o i c e between " k i n e m a t i c a l c o l l i m a t i o n " or " n a t u r a l f o c u s i n g " . Let us estimate the s i z e of primary beam necessary. _2 Beam d e n s i t i e s i n the order of 150 JJ<A cm f o r 20G kev deuterium beams on t h i c k heavy Ice l a y e r s (energy l o s s ' i n the t a r g e t comparable t o the I n c i d e n t energy) have been found a c c e p t a b l e a c c o r d i n g t o p u b l i s h e d Information (Ma 63 ) . Prom the s t o p p i n g cross s e c t i o n curves g i v e n In Chapter 4 Section 2 .3* the sto p p i n g power of DgO i c e f o r 650 kev 3He i s a f a c t o r of th r e e l a r g e r than f o r 200 kev deuterons. Thus, a c u r r e n t d e n s i t y of 50 j^k cm" 2 f o r an I n c i d e n t -'He beam w i l l be co n s i d e r e d a c c e p t a b l e . For 1 u.A of p 2 <• i n c i d e n t c u r r e n t a beam spot of a t l e a s t 2 x 10 c cm , 0.16 cm i n diameter, should be used. I t i s c l e a r then, t h a t the e f f e c t s of beam s i z e can be p r a c t i c a l l y minimized by l o c a t i n g the. secondary beam d e t e c t o r at a s u f f i c i e n t l y l a r g e d i s t a n c e from the primary t a r g e t . N a t u r a l f o c u s i n g i s , then, a secondary c o n s i d e r a t i o n i n choosing the primary t a r g e t a n g l e . /The. primary t a r g e t angle can then be chosen s o l e l y on the b a s i s of the energy l o s s i n the t a r g e t by the primary and secondary beams. As i n d i c a t e d b e f o r e , any angle s m a l l e r than 96.2 0 w i l l i n v o l v e a t h i c k e r D^O i c e l a y e r i n the d i r e c t i o n of the primary beam than f o r the secondary beam. The h i g h energy protons w i l l be r e q u i r e d to go through the primary t a r g e t backing metal f o i l , so a convenient angle i s a p e r p e n d i c u l a r t o the - 72 -proton angle ^ , or fi>Cz 30°. Figure 3.11 : Source target angle I f 'L' i s the DgO t a r g e t t h i c k n e s s i n the d i r e c t i o n then t h e . t a r g e t t h i c k n e s s i n the d i r e c t i o n s of the secondary beam and primary beams i s g i v e n by (See F i g u r e 3.11): 4He d i r e c t i o n L g > 6 e * = L / c o s ( 9 o 6 + p > - ^ ) ^  l.l L (3.3) 3He d i r e c t i o n L 0 ° = L / c o S - - ^ ) ^  2 L (3.4) 3.4. Expected y i e l d s . In S e c t i o n 3.2 a t o t a l angular divergency of 3 0 was obtained f o r a t a r g e t 100 kev t h i c k and a 650 kev ^He beam, i f 4 an energy window of 100 kev i s used on the secondary He beam. As w i l l be seen i n S e c t i o n 4.1.1 of t h i s chapter, t h i s value of angular divergency i s q u i t e compatible w i t h the accuracy desired*., i n these experiments. In t h a t s e c t i o n we s h a l l a l s o i n d i c a t e that-. - 73 -the t h i c k n e s s of 100 kev i n the primary t a r g e t i s a l s o compatible with background c o n s i d e r a t i o n s . We w i l l , on t h i s b a s i s , c a l c u l a t e the expected y i e l d s from the source r e a c t i o n . 3 4 The s t o p p i n g power f o r protons, He and He on B^O i c e as a f u n c t i o n of energy i s p l o t t e d i n F i g u r e 4.5 of the next chapter. From i t we obtain:-6 ( 3He) j 6 5 = 64 x 1 0 " 1 5 ev- cm 2 / molecule (3.5) The molecular d e n s i t y of i c e i s : N = 3.35 x 1 0 2 2 molecules cm" 3 (3.6) From (3.5) and (5.6) : dE/dx ( 3He) ^ = 2144 Mev cm" 1 The 100 kev t h i c k n e s s of the DgO i c e t a r g e t w i l l thus be e q u i v a l e n t t o : L = 4.66 x 1 0 " 5 cm L M = I . 5 6 x 10 Molecules cm"^ (3.7) L Q = 5.17 x l O " ^ g cm" 2 We w i l l assume a constant r e a c t i o n c r o s s s e c t i o n of 680 mb f o r the energy range of i n t e r e s t , and t h e y i e l d w i l l be c a l c u l a t e d per ^u.A-second, For s i n g l y i o n i z e d helium 1 LcA = 6.281 x 1 0 1 2 3He s " 1 (3.8) The t o t a l y i e l d of the r e a c t i o n per y.k and per second i s g i v e n 12 -1 -1 2 N cr R L x 6.28] " A 1.33 x 1 0 7 y iA - A " where the f a c t o r 2 takes i n t o account the presence of 2 deuterium atoms per each heavy water molecule. M' = 2 CT0 1 x 10 uA s , 1 r (3.9) M» = . 3 ' u A " 1 a'1 - 74 -Since the r e a c t i o n cross s e c t i o n Is i s o t r o p i c i n center of mass (Ku 52) (Bo 57) the r e a c t i o n y i e l d per u n i t of s o l i d angle (center of mass) i s , M£ = 1.06 x 1 0 6 4He ^ . A " 1 s " 1 s r " 1 (3-10) Some a n i s o t r o p y w i l l be present i n the l a b o r a t o r y system of c o o r d i n a t e s a r i s i n g from the s o l i d angle t r a n s f o r m a t i o n o between them. The r a t i o of s o l i d angles at 9 ° .2 i s , R = 1.1. D i v i d i n g (3.10) we get f o r the l a b o r a t o r y c o o r d i n a t e s a value c l o s e t o : M s = 1 x 1 0 6 4He yoJT1 s " 1 s r " 1 (3.11) From f i g u r e 3.10 the range of He an g l e s , d e f i n e d by an energy range of 100 kev f o r any g i v e n value of the I n c i d e n t energy i n the r e g i o n of i n t e r e s t ; i s l e s s than 3 ° ; t h i s corresponds to a s o l i d angle o f : O J D I - 2 n ( 1 - c o s ) = 2 . 1 5 * io** 5 s r (3.12) From (3.12) and (3.11) the number of ^He p a r t i c l e s In the secondary beam wit h the wanted energy per yjwA of c u r r e n t In the primary beam and per second i s found t o be: M(D1) = M( 4He) = 2.15 x 1 0 3 jj^A'1 s " 1 (3.13) As the number of p a r t i c l e s In the a s s o c i a t e d proton beam i s the same, the number of c o i n c i d e n c e s i s : M(D1 D2) = 2.15 x 1 0 3 ^/.A"1 s " 1 (3.14) -4 I f an a t t e n u a t i o n of 5 x 10 i s to be measured, then the number of a n t i c o i n c i d e n c e s recorded w i l l be: M(D1 D2) = 1.08 J J . A ' 1 s " 1 (3.15) Using the approximation f o r &C< L , (eq. 3.1) £ = M(D1 D2) / M(D1 D2) - 75 -and from (2.22) the r e l a t i v e e r r o r f o r the c o i n c i d e n c e method i s g i v e n by: = j S M ( D I D 2 ) For a 3% r e l a t i v e e r r o r and an a t t e n u a t i o n of 5 x 10 the number of c o i n c i d e n c e counts M(D1 D2) should be at l e a s t 6 2.2 x 10 . Using the r a t e g i v e n by (3.14) the time i n v o l v e d i s of the order of 1 0 3 . jj~A s or approximately 17 min. 4. C o r r e c t i o n s . In t h i s s e c t i o n we w i l l d i s c u s s the c o r r e c t i o n s to be a p p l i e d to the experimental data In the case of c o i n c i d e n c e a t t e n u a t i o n methods. The c o r r e c t i o n s w i l l be d i v i d e d i n t o two c a t e g o r i e s : one i n c l u d i n g , those r e l a t e d to " t a r g e t - i n " or " t a r g e t - o u t " s i t u a t i o n s ; and the other i n c l u d i n g those Independent of the t a r g e t . We w i l l r e f e r to the f i r s t as "Target c o r r e c t i o n s " . The second.type, which g i v e s r i s e t o a n t i c o i n c i d e n c e counts with-out a t a r g e t w i l l be r e f e r r e d to as the " A n t i c o i n c i d e n c e background". 4.1. Target c o r r e c t i o n s . 4,1.1. E l a s t i c s c a t t e r i n g . As d e s c r i b e d i n S e c t i o n 4.1.2 of Chapter 2, knowledge of the d i f f e r e n t i a l e l a s t i c s c a t t e r i n g c r o s s s e c t i o n permits c a l c u l a t i o n of t h i s c o r r e c t i o n . I t s magnitude depends on the angle subtended by the f u l l energy d e t e c t o r . In the case of l a c k of experimental data f o r the energy or nucleus under c o n s i d e r a t i o n , i t i s p o s s i b l e In most cases to estimate the c o r r e c t i o n by doing an o p t i c a l model c a l c u l a t i o n , i n t e r p o l a t i n g - 76 -t h e p o t e n t i a l s o b t a i n e d f o r o t h e r e n e r g i e s p r n u c l e i , o r u s i n g s e m i e m p i r i c a l p o t e n t i a l s s u c h a s t h e " P e r e y p o t e n t i a l " . A c o m p o u n d e l a s t i c d e c a y w i l l e x p e r i m e n t a l l y a p p e a r a s a t r a n s m i t t e d p a r t i c l e w h e n i t r e a l l y a r i s e s f r o m a n a b s o r p t i o n e v e n t . T h e m e a s u r e d t o t a l r e a c t i o n c r o s s s e c t i o n w i l l t h e n b e s m a l l e r t h a n t h e r e a l o n e b y t h e a m o u n t o f c o m p o u n d e l a s t i c c r o s s s e c t i o n i n t o t h e t r a n s m i t t e d p a r t i c l e s d e t e c t o r . T h e p r o b l e m o f e x p e r i m e n t a l l y d i s t i n g u i s h i n g t h e c o m p o u n d e l a s t i c s c a t t e r i n g f r o m t h e d i r e c t e l a s t i c s c a t t e r i n g h a s b e e n d i s c u s s e d i n s e c t i o n 2 . 1 , t o g e t h e r w i t h i t s e n e r g y d e p e n d e n c e . T h e m e a s u r e m e n t f o r 1 0 M e v p r o t o n s i n ^ ^ P e , u s i n g f l u c t u a t i o n a n a l y s i s ( E r 6 5 ) , y i e l d i n g t h e v a l u e o f l e s s t h a n 2.5 m b s r - 1 , i s i n s u p p o r t o f c o n s i d e r i n g t h e c o m p o u n d e l a s t i c c o n t r i b u t i o n n e g l i g i b l e f o r t h e r a n g e o f e n e r g i e s c o n c e r n e d " w i t h i n t h e p r e s e n t w o r k o f I 5 . 8 M e v . 4 . 1 . 2 . I n e l a s t i c s c a t t e r i n g . , T h e p r e s e n c e i n t h e t r a n s m i s s i o n d e t e c t o r o f p a r t i c l e s t h a t s u f f e r e d i n e l a s t i c s c a t t e r i n g i n t h e t a r g e t b u t c a n n o t b e r e s o l v e d , i n e n e r g y , f r o m t h e e l a s t i c c o n t r i b u t i o n w i l l g i v e r i s e t o a c o r r e c t i o n t e r m i n t h e e x p e r i m e n t a l v a l u e o f t h e r e a c t i o n c r o s s s e c t i o n . T h e c o r r e c t i o n w i l l b e g i v e n b y t h e i n t e g r a l o f t h e c r o s s s e c t i o n f o r i n e l a s t i c s c a t t e r i n g o v e r t h e a n g l e s u b -t e n d e d b y t h e d e t e c t o r , a n d f o r e n e r g i e s o f t h e . s c a t t e r e d p a r t i c l e a b o v e a c e r t a i n v a l u e e,3J _ s c a b o v e w h i c h t h e y w i l l b e i n t e r p r e t e d b y t h e s y s t e m a s e l a s t i c s c a t t e r e d o n e s . . T h u s cr = I E : D I S C ° y ^ . C E s . e W - n ' c l - E : ( 3 . 1 6 ) - 7 7 -where E i s the energy of the s c a t t e r e d p a r t i c l e , s When the d e t e c t i o n system i s not p a r t i c l e s e n s i t i v e , i d e n t i c a l c o n s i d e r a t i o n s apply f o r r e a c t i o n s y i e l d i n g charged p a r t i c l e s as f i n a l products, d i f f e r e n t than the i n c i d e n t one. The importance of t h i s c o r r e c t i o n term depends l a r g e l y on the energy r e s o l u t i o n of the f u l l energy d e t e c t o r . 4.1.3. L a t t i c e e f f e c t s . Prom equation^2.9)once the a t t e n u a t i o n , & , of the beam i s measured the value of the r e a c t i o n c ross s e c t i o n , 0 " ^ , i s obtained from: where N L i s the number of n u c l e i per square centimeter In the sample. The i m p l i c i t assumption i n v o l v e d here, Is t h a t the n u c l e i are randomly d i s t r i b u t e d i n the, sample. The p o s s i b i l i t y of s i g n i f i c a n t o r d e r i n g of the d i s t r i b u t i o n of t a r g e t , n u c l e i w i t h i n a sample may r e q u i r e modi-f i c a t i o n of t h i s e x p r e s s i o n f o r p a r t i c u l a r experimental s i t u a t i o n s . R e c e n t l y , d u r i n g the l a s t t h r e e y e a r s , d e t a i l e d a n a l y s i s of l a t t i c e e f f e c t s from both an experimental and t h e o r e t i c a l p o i n t of view have been performed. I t i s found t h a t f o r some s i t u a t i o n s they can y i e l d s i g n i f i c a n t e f f e c t s , although they were p r e v i o u s l y c o nsidered n e g l i g i b l e . "Channeling" i s used to i n d i c a t e when an i n c i d e n t charged p a r t i c l e i s focused, i n a c r y s t a l , by Coulomb i n t e r a c t i o n s i n t o some l a t t i c e i n t e r s p a c i n g . The p a t t e r n of i n t e r a c t i o n w i l l then be changed, s i n c e the p a r t i c l e w i l l t r a v e l through r e g i o n s - 78 -of the c r y s t a l removed from the n u c l e i of the c r y s t a l atoms and thus w i l l s u f f e r c o l l i s i o n s only w i t h the e l e c t r o n s f i l l i n g the i n t e r s p a c i n g . "Shadowing" i n d i c a t e s the e f f e c t t h a t once a p a r t i c l e s u f f e r s s c a t t e r i n g from a r e p u l s i v e p o t e n t i a l , there i s an area d e f i n e d behind the ..scattering c e n t e r where the p r o b a b i l i t y of f i n d i n g t h e i n c i d e n t p a r t i c l e i s very low. In other words, the i n c i d e n t p a r t i c l e can no longer i n t e r a c t e f f e c t i v e l y with n u c l e i , or atoms, w i t h i n the shadowed a r e a . The experimental r e s u l t s are very remarkable and, as expected, l a t t i c e e f f e c t s manifest themselves more s t r o n g l y when s i n g l e c r y s t a l s are used, e i t h e r as samples or p a r t i c l e d e t e c t o r s . For a wide review of experimental r e s u l t s and t h e i r consequences f o r measurements i n n u c l e a r p h y s i c s r e f e r e n c e should be made to the r e c e n t a r t i c l e by Bergstrom and Domeij (Be 66). In g e n e r a l , the importance of l a t t i c e e f f e c t s i s governed not only by the presence of o r d e r i n g In the m a t e r i a l but a l s o by the angular divergency of the i n c i d e n t beam and i t s d i r e c t i o n w i t h r e s p e c t to some l a t t i c e i n t e r n a l a x i s . For the t h e o r e t i c a l treatment of the s u b j e c t r e f e r e n c e should be made to the a r t i c l e by J . Lindhard. ( L i 65). Since n u c l e a r processes take p l a c e only when the p a r t i c l e s are w i t h i n a d i s t a n c e of the order of n u c l e a r r a d i i of each other, they are expected to be very s e n s i t i v e to the presence of l a t t i c e e f f e c t s . T h e i r consequence i s to keep the p a r t i c l e s from the incoming beam away from p o s s i b l e i n t e r a c t i o n with a c e r t a i n f r a c t i o n of the sample n u c l e i . These e f f e c t s have been e x p e r i m e n t a l l y observed. - 79 -"Channeling" e f f e c t s are found i n the measurements of stopping power and r e a c t i o n y i e l d s f o r s i n g l e c r y s t a l s . "Shadowing" e f f e c t s are present i n the angular d i s t r i b u t i o n of decay products emitted from r a d i o a c t i v e n u c l e i l o c a t e d i n c r y s t a l l a t t i c e . Such l a t t i c e e f f e c t s , a s s o c i a t e d w i t h ordered matter, are not present i n gaseous or l i q u i d samples. Thus, experiments i n v o l v i n g s i n g l e c r y s t a l s should be c a r e f u l l y analysed t o determine the importance of these e f f e c t s . The use of p o l y c r y s t a l l i n e samples w i l l decrease the Importance of such c o r r e c t i o n s when the range of the p a r t i c l e s of i n t e r e s t i s much l a r g e r than the m i c r o c r y s t a l s dimensions. Furthermore one can not j u s t assume th a t the m i c r o c r y s t a l s are randomly o r i e n t e d . A c e r t a i n degree of alignment can be present a f t e r such processes as r o l l i n g , e v a p o r a t i o n e t c . Even f o r a p o l y c r y s t a l l i n e sample these e f f e c t s can not be, then, assumed t o be s m a l l u n t i l the o r d e r i n g i s checked by, f o r example, X-ray a n a l y s i s or by r o t a t i n g the sample wit h r e s p e c t t o the i n c i d e n t beam and counter i n the experimental set up (Be 66). 4.2. The a t t e n u a t i o n background. Applying (3.1) we can measure the a t t e n u a t i o n s w i t h and without the sample i n the proton beam, as before we w i l l r e f e r t o these a t t e n u a t i o n s as & •• and <^  ^TTrT,. The mechanical system IN OUT f o r i n s e r t i n g the sample i s d e s c r i b e d i n d e t a i l In S e c t i o n 2.4 of Chapter 4. As indicated, b e f o r e the a t t e n u a t i o n due to the sample i s : ^ = " ^OUT (3.17) To t h i s value the t a r g e t c o r r e c t i o n s d i s c u s s e d i n - 80 -S e c t i o n 4.1 should be a p p l i e d . & 0 U T a r i s e s from the presence of an a n t i c o i n c i d e n c e background. In the next s u b s e c t i o n s we w i l l d i s c u s s the c o n t r i b u t i o n s to i t and t h e i r I n f l u e n c e i n the d e s i g n of the present experiment. 4 . 2 . 1 . Background due to the backing f o i l . Due t o the geometry chosen f o r the source t a r g e t the protons are emitted through the backing f o i l of the heavy i c e t a r g e t . A c e r t a i n amount of a t t e n u a t i o n w i l l be i n t r o d u c e d both from those p a r t i c l e s r e a c t i n g i n the f o i l , and so absorbed, and those e l a s t i c a l l y s c a t t e r e d i n t o an angle l a r g e r than that subtended by the d e t e c t o r f o r t r a n s m i t t e d p a r t i c l e s . T h i s c o n t r i b u t i o n , c a n be minimized by u s i n g very t h i n backing f o i l s and by subtending a l a r g e r s o l i d angle w i t h the proton d e t e c t o r . In choosing the t h i c k n e s s of the f o i l s a com-promise has to be made wit h the t h i c k n e s s r e q u i r e d to conduct away the beam power d i s s i p a t e d by the primary beam. When.choosing the angle subtended by the proton d e t e c t o r a compromise must be made.between the l a r g e angle d e s i r e d , as i n d i c a t e d above, and the maximum a c c e p t a b l e c o u n t i n g r a t e t o the proton d e t e c t o r . The p r o t o n d e t e c t o r i s then exposed not only to the a s s o c i a t e d proton beam, but a l s o t o those protons c o i n c i d e n t w i t h ^He of d i f f e r e n t angles and e n e r g i e s . I f we assume a maximum s -1 / \ a l l o w a b l e proton r a t e of about 1 x 1CK s , then from (3.10) we — can e v a l u a t e the maximum s o l i d a n g l e , per ^A, A of primary beam c u r r e n t , t h a t the proton d e t e c t o r can subtend, = 9 - 4 * \ 0 " 2 ST ( 3 . 1 8 ) And f o r the a c t u a l maximum angle j O ( - £ f / 2 of eq. (3.12)1 , - 81 -cosoe = 1 . -Q^ =. ± - (. o i 5 A (3.19) m 2.T\ I o = I CO M T h e c o n t r i b u t i o n t o t h e . a n t i c o i n c i d e n c e b a c k g r o u n d f r o m f o r " t h e s p e c i a l c a s e o f 1 jucA, cv ^   10 , t h e b a c k i n g f o i l i s g i v e n b y : * ~ 12 E (3.20) ft ^ E w h e r e o R r e p r e s e n t s t h e a t t e n u a t i o n d u e t o a b s o r p t i o n i n t h e b a c k i n g f o i l a n d ^ t h e a t t e n u a t i o n d u e t o e l a s t i c s c a t t e r i n g f r o m t h e b a c k i n g f o i l i n t o a n g l e s g r e a t e r t h a n t h a t s u b t e n d e d b y t h e d e t e c t o r , R B F B F J> = N L cr R B S E S P = N L em ( ^ ( e ) d n ( 3 - 2 1 ) w h e r e ' L ' i s t h e t h i c k n e s s o f t h e b a c k i n g f o i l , ^ t h e t o t a l n o n - e l a s t i c c r o s s s e c t i o n a n d 0^ C 9 ) t h e d i f f e r e n t i a l e l a s t i c s c a t t e r i n g c r o s s s e c t i o n f o r i t s n u c l e i . I f w e e x p e c t t o m e a s u r e -h a t t e n u a t i o n s o f t h e o r d e r o f 5 x 10 t h e n w e w o u l d l i k e < 5x\o~ (3.22) O n t h e o t h e r h a n d i f t h e t e m p e r a t u r e o f t h e i c e J a y e r r i s e s a b o v e 173°K t h e t a r g e t w i l l v a p o r i z e r e l a t i v e l y f a s t ( M a 63 p . 685). ..- I f t h e f o i l i s a t t a c h e d t o a r e s e r v o i r a t l i q u i d n i t r o g e n t e m p e r a t u r e s ( 7 8 °K) t h i s r e q u i r e m e n t r e s t r i c t s t h e t e m p e r a t u r e r i s e i n t h e p r i m a r y t a r g e t t o a p p r o x i m a t e l y 1 0 0 °K. T h e t e m p e r a t u r e r i s e a t t h e t a r g e t c e n t e r w a s c a l c u l a t e d i n o r d e r t o d e t e r m i n e t h e n e c e s s a r y t h i c k n e s s o f t h e b a c k i n g f o i l f o r a g i v e n i n c i d e n t c u r r e n t . T h e d e t a i l s o f t h e c a l c u l a t i o n s - 82 -are g i v e n In Appendix I, and are p l o t t e d i n f i g u r e ftl.3as the temperature r i s e i n °K per LvA of i n c i d e n t beam as a f u n c t i o n of the t h i c k n e s s of the copper backing f o i l . The cases f o r two d i f f e r e n t beam diameters were c o n s i d e r e d . CASE I corresponds to a diameter of .318 cm (1/8 i n c h e s ) and CASE I I to .16 cm (1/6 i n c h e s ) . The a t t e n u a t i o n g i v e n by (3 .20) can be c a l c u l a t e d as a f u n c t i o n of the t h i c k n e s s "L" us i n g the angle as a parameter, .\e>o° S e F = N L ( c r ^ 4 - 2 T i J o; 6 FCQ)cla) (3.23) The i n t e g r a l was performed by g e n e r a t i n g the d i f f e r e n -t i a l e l a s t i c s c a t t e r i n g cross s e c t i o n s w i t h the SCAT 4 o p t i c a l model program. The f o l l o w i n g p o t e n t i a l s were used:, (p on Cu a t 15 Mev): . V = 50 .0 (as g i v e n by the Perey p o t e n t i a l ) , W = 7.5 Mev,•. V ' = 7.5 Mev, a = .5 f , r Q = 1 0 25 f . (See chapter I ) . The r e s u l t s are i n d i c a t e d In Tab l e 3 .1 and p l o t t e d i n F i g u r e 3.12 as a f u n c t i o n of the t h i c k n e s s 'L'. TABLE 3.1 Values f o r b a c k i n g ' f o i l background c a l c u l a t i o n s . C T R (jab) f\eo° , CT^-f / .cmb) C' S>BF(crr7') 10 ° © 9 1 7023 79/4 69 1 /3Q3 2274 .132 5 0 ° 89/ 6 O 6 /497 .127 F i n a l l y i n F i g u r e 3.13 we have i n d i c a t e d the counting r a t e i n the proton d e t e c t o r , per JX, A of i n c i d e n t beam, as a f u n c t i o n of the detector, angle Oi . i o " 5 i o " 4 io's 1 0 " B A C K I N G F O I L T H I C K N E S S ( c m ) Attenuation background due to the backing f o i l t h i c k n e s s , as a f u n c t i o n of the thickness and the angle subtended by the proton d e t e c t o r . ANGLE SUBTENDED BY PROTON DETECTOR Figure 3. 13 Counting rate at the proton detector as a function of subtended angle. - 85 -The F i g u r e s 3.12, 13, and AI . 3 enable us t o o b t a i n a good compromise f o r the t h i c k n e s s of the backing f o i l . I f the a t t e n u a t i o n of the backing f o i l was the main source of the a n t i c o i n c i d e n c e background then the choice should a l l o w S<£S"x (O ^ ( f o r t a r g e t a t t e n u a t i o n measurements of 5 x 10 I t would seem to be reasonable then to use a f o i l around 10 cm t h i c k . S e l f - s u p p o r t i n g Copper f o i l can be obtained down to - 6 _ 4 50 x 10 inches or 1.27 x 10 cm. T h i s would r e p r e s e n t a of approximately 2.5 x 10"^ f o r <X = 20°, From F i g u r e AI . 3 we o b t a i n a maximum prima r y beam c u r r e n t of around 1 / 4 j**A f o r A T l e s s than 100°K and 1/8 inches c o l l i m a t o r s . The counting r a t e from F i g u r e 3.19 w i l l be of the order of 10^ s " 1 . 4 . 2 . 2 . Background due to the proton d e t e c t o r . An important c o n t r i b u t i o n to t h e . a n t i c o i n c i d e n c e back-ground a r i s e s from n u c l e a r i n t e r a c t i o n s t a k i n g p l a c e i n the f u l l energy d e t e c t o r i t s e l f . Using s t o p p i n g cross s e c t i o n s to determine the amount of d e t e c t o r m a t e r i a l per f r a c t i o n of energy l o s s , d,E, and t o t a l r e a c t i o n c r o s s s e c t i o n data, the t o t a l expected a t t e n u a t i o n of the i n c i d e n t beam, i n the d e t e c t o r , can be c a l c u l a t e d : d < 5 = N c i d . t t = N c r 0 ( E ) d"= " B ( 3 . 2 4 ) i = f H cr f e (E ) 6 ' 1 J E where E i s the, i n c i d e n t energy and G the s t o p p i n g power of the d e t e c t o r m a t e r i a l . The best c h o i c e of d e t e c t o r should be the one t h a t p r o v i d e s the.lowest a t t e n u a t i o n , or a n t i c o i n c i d e n c e background. A second c o n s i d e r a t i o n i s the extent to which the - 86 -i n e l a s t i c channels of the r e a c t i o n s t h a t take p l a c e i n the d e t e c t o r n u c l e i w i l l g i v e r i s e t o counts of the lower energy r e g i o n of the proton spectrum, s i n c e a l a r g e background of t h i s type :would hamper,the i n e l a s t i c t a r g e t c o r r e c t i o n s . The t h i r d c o n s i d e r a t i o n r e l a t e d t o the f u l l energy d e t e c t o r i s g i v e n by i t s t i m i n g c h a r a c t e r i s t i c s or speed of response. A f a s t r i s e time i s convenient f o r good time r e s o l u t i o n when performing c o i n c i d e n c e s and a n t i c o i n c i d e n c e s . At h i g h counting r a t e s f o r good energy r e s o l u t i o n i t i s important t h a t the proton p u l s e i s not d i s t o r t e d by an immediately preceeding one. T h i s can be achieved w i t h a short f a l l time of the d e t e c t o r p u l s e ; s h o r t such t h a t the p r o b a b i l i t y of another proton being detected d u r i n g the f a l l time of the f i r s t one i s very low a t the g i v e n c o u n t i n g - r a t e . T h i s r e s t r i c t i o n can be made l e s s s t r i c t by e l e c t r o n i c a l l y a s s u r i n g t h a t a n a l y s i s of pu l s e s i s done onl y when a proton Is detected without being preceeded by a pre v i o u s one d u r i n g a c e r t a i n p e r i o d of time. T h i s method was employed i n the experiment here concerned u s i n g the "Dead time g e n e r a t o r " d e s c r i b e d i n Section 3.4 of Chapter 4. These c o n s i d e r a t i o n s must be taken i n t o account when s e l e c t i n g the p a r t i c u l a r type of f u l l energy d e t e c t o r . The case of a p l a s t i c s c i n t i l l a t o r can be used t o I l l u s t r a t e the p o i n t . Even though advantageous f o r timing,purposes the 4.4 Mev and 7.6 Mev e x c i t e d l e v e l s of i t s carbon n u c l e i produces a s i g n i f i c a n t low energy t a i l t o the f u l l energy peak t h a t can mask completely the i n e l a s t i c c o n t r i b u t i o n s a r i s i n g from the t a r g e t . When a n u c l e a r r e a c t i o n takes p l a c e i n the d e t e c t o r the energy recorded can be d i v i d e d i n t o two d i f f e r e n t c o n t r i b u t i o n s : - 87 --a) the energy deposited i n the d e t e c t o r u n t i l the r e a c t i o n takes p l a c e , b) the energy d e p o s i t e d i n the d e t e c t o r by the products of the r e a c t i o n . When a (p,n) r e a c t i o n takes p l a c e i n the d e t e c t o r the c o n t r i b u t i o n g i v e n by b) i s n e g l i g i b l e . F or I n e l a s t i c s c a t t e r i n g and events c h a r a c t e r i z e d by emi s s i o n of charged p a r t i c l e s , c o n t r i -butions, a) and b) w i l l t o t a l an amount equal to the f u l l energy of the p a r t i c l e i n c i d e n t on the d e t e c t o r minus the Q-value a s s o c i a t e d with the channel being c o n s i d e r e d , I t i s c l e a r then t h a t the recorded number of a n t i -c o i n c i d e n c e s w i l l depend on the s e n s i t i v i t y or t h r e s h o l d of the proton system. I t w i l l i n c r e a s e as the t h r e s h o l d i s moved towards the e l a s t i c peak. With the t h r e s h o l d s et above the i n -e l a s t i c c o n t r i b u t i o n s , so t h a t o n l y f u l l energy events are rec o r d e d , a t t e n u a t i o n a r i s i n g from the a n t i c o i n c i d e n c e s so recorded can be compared with the expected values c a l c u l a t e d from equation (3.24). In g e n e r a l , however, due to the f i n i t e energy r e s o l u t i o n of the d e t e c t o r some n o n - e l a s t i c events are always l o s t i n t o the f u l l energy peak. Except f o r the case of p l a s t i c s c i n t i l l a t o r s other d e t e c t o r m a t e r i a l s t o be chosen w i l l be used i n s i n g l e c r y s t a l form. This i s the case f o r C s l and N a l s c i n t i l l a t o r s or the case of e i t h e r Ge or S i s o l i d s t a t e d e t e c t o r s . The p o s s i b i l i t y of l a t t i c e e f f e c t s , which has been d i s c u s s e d i n S e c t i o n 4.1.3* should be taken i n t o account. T h e i r importance can a r i s e from the f a c t t h a t , i n g e n e r a l , the angular d i s t r i b u t i o n of the p a r t i c l e s i n c i d e n t on the d e t e c t o r w i l l change f o r t a r g e t - o u t to - 88 -t a r g e t - I n p o s i t i o n . T h i s c o n t r i b u t i o n to the change i n the a n t i c o i n c i d e n c e background could be checked by e i t h e r r o t a t i n g the d e t e c t o r with r e s p e c t t o the i n c i d e n t beam d i r e c t i o n , or by knowing that the angular divergency of the beam i s much g r e a t e r than the c r i t i c a l angle f o r these e f f e c t s . For a c c u r a t e e x p e r i -ments a r o t a t i o n of the d e t e c t o r p r o v i d e s the best check f o r the Importance of the l a t t i c e e f f e c t s . The i n t e g r a t i o n d e s c r i b e d by equation (3.24) was performed f o r S i , P l a s t i c NE102, N a l ( T l ) , and C s I ( T l ) i n order to choose the d e t e c t o r w i t h the lowest background c o n t r i b u t i o n . The r e s u l t s f o r 1 5 . 8 and 14 . 8 Mev protons and the r e f e r e n c e s f o r the data used are l i s t e d below. SILICON : & (15.8 MeV): 5010 x TO - 4;: & (14.8 MeV): 44.0 x 10~ 4 dE/dx (Wi 62a) (St 59) 22 . -3 Atomic d e n s i t y 5.0 x 10 cm Re a c t i o n Cross S e c t i o n Data f o r aluminum was used. At 5 . 5 Mev agrees w i t h 2 8 S i ( p , p 1 ) 2 8 S i * (Ya 58) C o m p i l a t i o n by P o l l o c k and Schrank (Po 65a) and (Fo 61) (Bu 65) (Be 6 5 a ) " (Me 60) ( P i 6 5 ) . PLASTIC NE 102: S ( l 5 . 8 Mev): 39.0 x 10" 4; <S (14.8 MeV): 34.0 x 10~ 4 dE/dx (Wh 58) Atomic d e n s i t y H = 5.4 x 1 0 2 2 cm" 3 ; C = 4 . 8 x 1 0 2 2 cm" 3 R e a c t i o n Cross S e c t i o n (Bu 59) (No 62) (Ma 65) (Wi 62) (Po 6 5 a ) . Nal ( T l ) : <S (15.8 MeV): 32.0 x 10" 4; & (14.8 MeV): 27.0 x 10~ 4 dE/dx Assumed d E / d x ( l ) = dE/dx(Xe); dE/dx(Na) = dE/dx(Ne) (Wh 58) 89 -Atomic d e n s i t y Reaction Cross S e c t i o n C s l (TI) dE/dx 1.48 x 1 0 2 2 cm"3 2 3 N a Charged p a r t i c l e Cross Sections (La 61), and data f o r 2^A1 as l i s t e d f o r S i . 127 I , data was i n t e r p o l a t e d from a c o l l e c t i o n of data from other n u c l e i i n c l u d i n g the (p,n) f o r Cs and I by BLASER et a l ( B l 51). & (15.8 MeV): 19.2 x I O - 4 ; £> (14.8 MeV): 15.9 x I O - 4 Assumed dE/dx(Cs) = dE/dx(l) = dE/dx(Xe); (Wh 58). Atomic d e n s i t y Reaction Cross S e c t i o n 1.04 x 10 cm D As above, assuming same values f o r Cs as f o r I . The low energy f o l l o w i n g values f o r 1 0 3 R h (Ha 62). The data used i n these c a l c u l a t i o n s i s a l s o presented i n g r a p h i c a l form. Figure.3.14 Is a p l o t of the energy l o s s , In Mev cm - 1, versus the proton energy f o r each detector m a t e r i a l considered. Figure 3.15 d i s p l a y s the values f o r t o t a l r e a c t i o n cross s e c t i o n s f o r ..the d i f f e r e n t n u c l e i as a f u n c t i o n of the proton; energy. Figure 3.16 i s a p l o t of the c a l c u l a t e d a t t e n u a t i o n , per Mev of energy l o s s i n the dete c t o r m a t e r i a l , as a f u n c t i o n of the proton energy. The attenuations quoted f o r 15.8 and 14 .8 Mev when d e s c r i b i n g the data used^corresponds to the i n t e g r a l s of these curves from zero to the i n d i c a t e d energy. - 90 -10 I 0 T 4 I 6 " T 10 12 14 16 "1 18 P R O T O N E N E R G Y (MeV) Figure 3.14 : Energy loss curves f o r d i f f e r e n t detectors - 9 1 -F i g u r e 3 . 1 5 P r o t o n t o t a l r e a c t i o n c r o s s s e c t i o n s , c o u l o m b b a r r i e r s a n d ( p , n ) t h r e s h o l d s f o r n u c l e i o f d i f f e r e n t d e t e c t o r s . - 92 -P R O T O N E N E R G Y ( MeV ) Figure 3.16 : Calculated attenuation per MeV of energy loss i d i f f e r e n t detectors. - 93 -S i n c e i t p r e s e n t e d t he l o w e s t e xpec t ed a t t e n u a t i o n o f t h e d i f f e r e n t d e t e c t o r s c o n s i d e r e d , C s l (Tl.) was chosen as t h e p r o t o n d e t e c t o r . I n a d d i t i o n , a l s o Cs and I have t h e l o w e s t energy t h r e s h o l d f o r t h e p r o d u c t i o n o f n e u t r o n s and t h e h i g h e s t Coulomb b a r r i e r o f t h e d e t e c t o r n u c l e i c o n s i d e r e d . These v a l u e s a r e i n d i c a t e d i n t h e upper p a r t o f F i g u r e 3.15. Because n e u t r o n e m i s s i o n ' I s t h e n f a v o u r e d f o r Gs and I w i t h r e s p e c t t o t h e o t h e r d e t e c t o r ' s n u c l e i , t h e i n t e n s i t y o f t he compet i ng e l a s t i c c h a n n e l s c o u l d be e xpec ted t o be c o r r e s p o n d i n g l y l o w e r . T h i s w i l l p roduce a c l e a n e r energy s pec t r um be low t h e f u l l energy peak , an i m p o r t a n t c o n s i d e r a t i o n when e s t i m a t i n g t h e i n e l a s t i c t a r g e t c o r r e c t i o n s . As d i s c u s s e d b e f o r e i n t h i s S e c t i o n , when a (p .n ) r e a c t i o n t a k e s p l a c e i n t h e d e t e c t o r , o n l y t h e energy d e p o s i t e d u n t i l t h e n i s r e c o r d e d . Due t o Coulomb e f f e c t s t h e r e a c t i o n c r o s s s e c t i o n d e c r e a s e s f o r d e c r e a s i n g p r o t o n e n e r g y . Thus coun t s a r i s i n g f r om t h e (p .n ) r e a c t i o n s w i l l be m a i n l y l o c a t e d i n t h e low energy p a r t o f t h e p u l s e h e i g h t s p e c t r u m , w i t h t h e number o f c oun t s d e c r e a s i n g f o r i n c r e a s i n g p u l s e h e i g h t . On t h e o t h e r hand i n e l a s t i c e ven t s w h i c h t a k e p l a c e i n t h e d e t e c t o r g i v e r i s e t o coun t s c o r r e s p o n d i n g t o an energy Q Mev be low t h e f u l l energy peak , where Q i s t h e e x c i t a t i o n energy o f t h e l e v e l i n v o l v e d . I n f i g u r e 3-17 we have p l o t t e d t h e dependence o f t h e a t t e n u a t i o n backg round on p u l s e h e i g h t t h r e s h o l d l e v e l f o r 15.8 and 14 .8 Mev p r o t o n s i n c i d e n t i n a C s l s c i n t i l l a t o r when as suming t h a t a l l compound n u c l e i formed i n t h e d e t e c t o r decay v i a n e u t r o n e m i s s i o n . I f t he p u l s e h e i g h t t h r e s h o l d l e v e l i s a d j u s t e d f o r an energy o f .5 Mev an a t t e n u a t i o n backg round o f t h e o r d e r o f 15 x 1 0 " ^ i s t o be e x p e c t e d . T h i s v a l u e i s a l ow l i m i t o f b a c k g r o u n d , b e i n g - 94 -26 -24 -22 -rr 2 3 4 5 6 7 8 9 l o 11 12 13 D I S C R I M I N A T I O N L E V E L ( M e V ) Figure 3. 17 : Calculated attenuation i n C s l as a function of the di s c r i m i n a t i o n l e v e l . - 95 -I m p r a c t i c a l t o c o n s i d e r t h r e s h o l d l e v e l s be low t h e one i n d i c a t e d above because t h e sy s tem may become t o o s e n s i t i v e t o n o i s e . The amount o f a n t i c o i n c i d e n c e s d e t e c t e d f o r a t a r g e t -out measurement w i l l depend on t h e t h r e s h o l d s e t t i n g and t h e i n c i d e n t p r o t o n energy i n t h e manner I n d i c a t e d by F i g u r e 3 . 1 7 . On t h e o t h e r hand , when t h e t a r g e t - i n measurement i s pe r f o rmed t h e i n e l a s t i c c o r r e c t i o n t o t h e t a r g e t a t t e n u a t i o n v a r i e s w i t h t h e p u l s e h e i g h t t h r e s h o l d l e v e l I n t h e o p p o s i t e way. The l o w e r t h e s e t t i n g t h e l a r g e r t h e i n e l a s t i c c o r r e c t i o n ( see S e c t i o n 4.1.2.) I t i s c l e a r t h a t t h e c h o i c e o f t h i s l e v e l w i l l a r i s e f r om a compromise o f t h e s e two e f f e c t s , and t h a t t h i s compromise w i l l depend on t h e p a r t i c u l a r sample b e i n g c o n s i d e r e d . We w i l l d i s c u s s t h e two ext reme c a s e s : CASE I, t h e t h r e s h o l d l e v e l I s s e t j u s t be low t h e e l a s t i c f u l l energy peak ; CASE I I , t h e t h r e s h o l d l e v e l i s s e t a t t h e l o w e s t p u l s e h e i g h t c o m p a t i b l e w i t h t h e n o i s e o f t h e s y s t e m . CASE I: I n t h i s ca se a l l i n e l a s t i c e v e n t s , e i t h e r due t o t h e d e t e c t o r n u c l e i o r t h e sample n u c l e i , a r e r e c o r d e d as a n t i c o i n c i d e n c e s w i t h t h e o n l y e x c e p t i o n o f a s m a l l c o r -r e c t i o n a r i s i n g f r om t h e f i n i t e energy r e s o l u t i o n o f t h e d e t e c t o r . The t a r g e t - o u t a t t e n u a t i o n w i l l t h e n be l a r g e and dependent on t h e energy o f t h e i n c i d e n t beam. S i n c e S OUT ^ s l a r S e r t h a n t h e t a r g e t a t t e n u a t i o n s t o be measu red , a l a r g e number o f c oun t s a r e r e q u i r e d f o r good s t a t i s t i c s on t h e a n t i c o i n c i d e n c e b a c k g r o u n d . Knowledge o f t h e backg round dependence w i t h I n c i d e n t energy i s n e c e s s a r y t o a c coun t f o r t h e energy l o s s i n t h e s amp le . T h i s ca se can be i l l u s t r a t e d w i t h t h e C s l s c i n t i l l a t o r , - 96 -F i g u r e 3.17. For a l e v e l s e t t i n g e q u i v a l e n t t o 12 Mev and f o r 15.8 Mev i n c i d e n t protons the expected a t t e n u a --4 t i o n i s 19.2 x 10 , and a change i n the proton energy of 1 Mev, down to 14.8 Mev, produces a change of 20$ i n e> • OUT CASE II:Most of the i n e l a s t i c events are recorded as coincidences.. Thus S ^ T T„ decreases to i t s lowest l i m i t . When S> OUT IN i s measured, a l l the i n e l a s t i c c o n t r i b u t i o n s from the sample are recorded as t r a n s m i t t e d p a r t i c l e s , and a much l a r g e r i n e l a s t i c c o r r e c t i o n than i n Case I i s necessary. On the other hand s i n c e S i s lower, the number of counts to be recorded i s g r e a t l y d i m i n i s h e d , and the dependence of the a n t i c o i n c i d e n c e background on the i n c i d e n t energy i s g r e a t l y decreased. With what accuracy the i n e l a s t i c c o r r e c t i o n can be made, depends on the previous knowledge of the i n e l a s t i c s c a t t e r i n g d i f f e r e n t i a l c r o ss s e c t i o n . f o r the sample c o n s i d e r e d . The case i s a l s o i l l u s t r a t e d i n f i g u r e 3.17 f o r the C s l s c i n t i l l a t o r ; the a n t i c o i n c i d e n c e background f o r a t h r e s h o l d l e v e l of -4 .5 Mev i s 1.5 x 10 and p r a c t i c a l l y independent of the i n c i d e n t energy. 4 . 2 . 3 . Background due to energy degraded protons The h i g h energy protons emitted from the primary t a r g e t i n d i r e c t i o n s other than t h a t of the proton d e t e c t o r , w i l l i n g e n e r a l , be s c a t t e r e d w i t h i n the chamber. These s c a t t e r e d protons w i l l g i v e r i s e t o the presence of backgrounds i n both d e t e c t o r s . To decrease i t s i n t e n s i t y the i n s i d e of the chamber was l i n e d - 97 -with . 042 inches t h i c k p o l y e t h y l e n e . The p o l y e t h y l e n e t h i c k n e s s being g r e a t e r than the expected range of 16 Mev protons. Although reduced i n i n t e n s i t y , a low energy proton background was s t i l l observed. Of p a r t i c u l a r concern was the f a c t t h a t many of these protons had energies of the order of the s e l e c t e d He e n e r g i e s . S i n c e these events are not a s s o c i a t e d w i t h any f u l l energy protons, they t h e r e f o r e generate background a n t i c o i n c i d e n c e events. A s i m i l a r e f f e c t could be produced from s l i t edge s c a t t e r i n g i n the c o l l i m a t o r d e f i n i n g the a l p h a a n g l e . Thus, the h i g h energy protons would be degraded ,in energy d u r i n g g r a z i n g c o l l i s i o n s w i t h the c o l l i m a t o r w h i l e on r o u t e t o the 4 • ' ( He d e t e c t o r . To e l i m i n a t e these e f f e c t s from c o n t r i b u t i n g t o the a n t i c o i n c i d e n c e background, p a r t i c l e i d e n t i f i c a t i o n was employed by choosing an a p p r o p r i a t e d e p l e t i o n t h i c k n e s s f o r the s u r f a c e b a r r i e r alpha d e t e c t o r . Values lower than 70 microns w i l l p r o v i d e a c l e a r d i s t i n c t i o n between ^He p a r t i c l e s of the order of 3.5 Mev, t y p i c a l of those i n the experiment, and a background of protons of a l l e n e r g i e s . In t h i s case, the proton spectrum i s a c t u a l l y a d i s t r i b u t i o n which f o l d s over at the energy corresponding t o a proton w i t h a range equal to the d e p l e t i o n depth. For the case of 70 microns of s i l i c o n t h i s occurs at 2.5 Mev. T h i s i s c l e a r l y seen i n F i g u r e 4 . 4 , a t y p i c a l s o l i d s t a t e d e t e c t o r spectrum obtained d u r i n g one of the runs. In f a c t , f o r good p a r t i c l e i d e n t i f i c a t i o n d e p l e t i o n l a y e r s of approximately 40 microns were used. S i n c e such s m a l l d e p l e t i o n depths r e q u i r e very low b i a s i n g v o l t a g e s , (e.g. 1 0 V, f o r 700 - 98 -ohm-cm), and s i n c e these low v o l t a g e s r e s u l t i n poor charge c o l l e c t i o n , s p e c i a l l y manufactured d e t e c t o r s of s i l i c o n with r e s i s t i v i t i e s of 200 ohm-cm and 35 ohm-cm were used i n the experiment. 4 . 2 . 4 . Background due to source t a r g e t t h i c k n e s s . Another source of a n t i c o i n c i d e n c e background may a r i s e 4 from He p a r t i c l e s o r i g i n a l l y emitted i n d i r e c t i o n s other than t h a t of the secondary beam d e t e c t o r . In l e a v i n g the primary t a r g e t they could be s c a t t e r e d i n t o the angle subtended by the 4 d e t e c t o r , and w i t h energies i n the range of the s e l e c t e d He energy. For not being a s s o c i a t e d w i t h protons emitted n e c e s s a r i l y i n t o the proton d e t e c t o r angle, they t h e r e f o r e generate back-ground a n t i c o i n c i d e n c e counts. As the primary t a r g e t i s a t h i n 4 l a y e r of heavy i c e , the main source of He s c a t t e r i n g w i l l be i fi the 0 n u c l e i from the D^O molecules. The d e t a i l s of the c a l c u l a t i o n performed t o , e s t i m a t e t h i s background are presented i n Appendix I . The c o n t r i b u t i o n obtained f o r a source t a r g e t t h i c k n e s s of 100 kev ( f o r 650 kev % e ) , a source t a r g e t angle of 30°, a s e l e c t e d energy range of 100 kev and an angle subtended by the proton d e t e c t o r g r e a t e r than. 1 0 ° can be n e g l e c t e d . There a re two other e f f e c t s whose importance depends on the source target, t h i c k n e s s . These are m u l t i p l e s c a t t e r i n g e f f e c t s and energy s t r a g g l i n g i n the secondary beam when l e a v i n g the source t a r g e t . T h e i r e f f e c t i s t o d i s t o r t the s p a c i a l d e f i n i t i o n of the a s s o c i a t e d beam by changing the d i r e c t i o n and energy of the secondary beam. These c a l c u l a t i o n s are a l s o presented i n Appendix I . The r e s u l t s f o r the t a r g e t t h i c k n e s s - .99 -assumed of 100 kev f o r 650 kev 3He a r e : a) Prom m u l t i p l e s c a t t e r i n g a mean square angle with r e s p e c t t o the i n i t i a l d i r e c t i o n of emission of |<A? 8 >|* = 0 .5° (3 .25) b) From energy s t r a g g l i n g a standard d e v i a t i o n f o r the energy l o s s i n l e a v i n g the t a r g e t of | < AEV| , / 2 = 3.<b Wev (3.26) We w i l l t h e r e f o r e n e g l e c t the c o n t r i b u t i o n s t o the a n t i c o i n c i d e n c e background a r i s i n g from the source t a r g e t t h i c k n e s s . 5. E l e c t r o n i c requirements. In t h i s s e c t i o n the "design requirements" f o r the e l e c t r o n i c system t o apply the a s s o c i a t e d p a r t i c l e technique to the measurements of t o t a l r e a c t i o n c r o s s s e c t i o n s w i l l be d i s c u s s e d . The e s s e n t i a l f e a t u r e of these requirements i s the pr e v e n t i o n of " a c c i d e n t a l " a n t i c o i n c i d e n c e counts, a r i s i n g from e l e c t r o n i c e f f e c t s and thus not c o r r e l a t e d with r e a l a n t i -c o i n c i d e n c e events. The occurence of such " a c c i d e n t a l " a n t i -c o i n c i d e n c e counts would r e s u l t i n an a r t i f i c i a l i n c r e a s e of the a n t i c o i n c i d e n c e a t t e n u a t i o n count. The d e t a i l e d d e s c r i p t i o n of the d i f f e r e n t e l e c t r o n i c u n i t s used i n the experiment i s presented i n S e c t i o n 3 of Chapter 4. In t h i s s e c t i o n we w i l l d e r i v e the c r i t e r i a a p p l i e d e i t h e r t o t h e i r d e s i g n or t o t h e i r s e l e c t i o n from commercially a v a i l a b l e ones. h In the r e s t of t h i s s e c t i o n we w i l l r e f e r t o the He d e t e c t o r as D l , t o the proton d e t e c t o r as D2, to t h e i r r e s p e c t i v e counting r a t e s as M(D1) and M(D2) and to the c o i n c i d e n c e and a n t i c o i n c i d e n c e r a t e s as M(D1D2) and M(D1D2) r e s p e c t i v e l y . - 100 -An a n t i c o i n c i d e n c e gate w i l l be r e f e r r e d to as AC and a c o i n c i -dence gate as C. Random a n t i c o i n c i d e n c e and c o i n c i d e n c e r a t e s are i n d i c a t e d as M(RAC) and M(RC) r e s p e c t i v e l y . We w i l l c o n s i d e r the s i t u a t i o n f o r 1 jx, A of i n c i d e n t 3He beam c u r r e n t , as d i s c u s s e d i n s e c t i o n 3.4 and 4.1. In a d d i t i o n we w i l l assume (as a l s o d i s c u s s e d i n 3.^) a h a l f angle o( subtended by d e t e c t o r D2 of 1 0 ° and a h a l f angle subtended by the D l d e t e c t o r of A f /2 = 2 . 5 ° . , S i n c e the p r i m a r y • r e a c t i o n i s e s s e n t i a l l y i s o t r o p i c the t o t a l r a t e s observed i n d e t e c t o r s D l and D2 are p r o p o r t i o n a l to t h e i r r e s p e c t i v e s o l i d angles subtended at the c e n t e r of the primary t a r g e t . As w i l l be seen i n S e c t i o n 2 of Chapter 4, 4 d e t e c t o r D l i s s e n s i t i v e to both He and protons, whereas 4 d e t e c t o r D2 i s s h i e l d e d from the He p a r t i c l e s . We can,then w r i t e down: (3.27) M(D1)/M(D2) = 2 / n 2 = 2 . ( l - c o s 2 . 5 ° ) / ( l - cos 10°) = .12 I f the maximum a c c e p t a b l e c o u n t i n g rate, f o r the D2 d e t e c t o r i s taken to be: M(D2) = 1 0 5 s " 1 we o b t a i n : M(D1) = 1.2 x 10^ a " 1 , (3.28) Of a l l these counts, the number of c o i n c i d e n c e counts between d e t e c t o r s D l and D2 i s g i v e n by 3.14 as: M(D1D2) = 2. 1 0 3 s " 1 (3.29) The b a s i c components of the e l e c t r o n i c equipment are an AC gate and a C gate. These are used to s e l e c t , out of the - lOtl -n o n - c o i n c i d e n t background, the M(D1D2) and the M(D1D2~) rat.es and thus determine the a t t e n u a t i o n f a c t o r a c c o r d i n g to equation^.l)» Prom equation ( 3.l) a r e l a t i v e e r r o r present i n the num-ber of c o i n c i d e n c e s M(D1D2) w i l l mean the same r e l a t i v e e r r o r i n the experimental value obtained f o r the a t t e n u a t i o n . I f a t t e n u a t i o n values are wanted t o an accuracy of a few per cent we w i l l r e s t r i c t the number of p o s s i b l e random c o i n c i d e n c e counts M(RC) to l e s s t h a t .5$ of the t r u e c o i n c i d e n t r a t e (3.29). The r e s o l u t i o n time necessary In the C gate would be g i v e n by: T = M(RC) / M(D1) M(D2) (3.30) A f a c t o r should be a p p l i e d . t o the value of M(D1), t o be used i n (3.30), due p r i m a r i l y t o the f a c t t h a t an a d d i t i o n a l energy r e s t r i c t i o n i s imposed on those pulses from D l which can c o n t r i -bute t o r e a l c o i n c i d e n c e s or a n t i c o i n c i d e n c e s ^ T h i s energy r e s t r i c t i o n i s r e q u i r e d i n order to o b t a i n the d e s i r e d angular c o l l i m a t i o n of the a s s o c i a t e d proton beam. Prom the r a t i o of (3.29) to (3.28), t h i s r e d u c t i o n amounts t o a f a c t o r of 1/6 f o r the case c o n s i d e r e d . Then from (3.30) we o b t a i n : t = 50 ns (3.31) t h i s w i l l r e q u i r e Dl;and D2 pu l s e s approximately 25 ns wide, and puls e t i m i n g to b e t t e r than 5 ns. T h i s value (50 ns) of the ' r e s o l v i n g time was then obtained on the b a s i s that the D l pulses are f i r s t energy s e l e c t e d with the r e q u i r e d r e s o l u t i o n of 40 kev ( S e c t i o n 3.2) .before' going i n t o the C gate. I f an RC a m p l i f i e r i s used i n connect ion,, w i t h the ,D1 p u l s e s , d i f f e r e n t i a t i o n and i n t e g r a t i o n time constants of the order of 1 yks are r e q u i r e d i f the above mentioned r e s o l u t i o n i s t o be a t t a i n e d . . Pulse t i m i n g - 102 -to w i t h i n 10 ns i s not a simple matter with p u l s e s of t h i s type. For t h i s reason, a "Fast-Slow" c o i n c i d e n c e system was employed. In t h i s method, f a s t c o i n c i d e n c e s are f i r s t obtained f o r a l l p u l s e s without energy s e l e c t i o n . Then the output of the "Fast C" gate i s checked i n c o i n c i d e n c e with the output of a s i n g l e channel a n a l y s e r that s e l e c t s those D l pu l s e s i n the s e l e c t e d energy range. In t h i s second C gate the p u l s e r a t e s are much lower due to the f i r s t f a s t s e l e c t i o n , thus l o n g e r r e s o l v i n g times and l e s s p r e c i s e t i m i n g , a r e p e r m i s s i b l e . R e s o l v i n g times i n the order of 50 ns can be r e a d i l y achieved with the t r a n s i s t o r techniques standard i n t h i s l a b o r a t o r y . Adopting t h i s as. the r e s o l v i n g time f o r the f a s t C gate, = 50 ns, from (3.30) we o b t a i n f o r the random c o i n c i d e n c e r a t e at the output of the f a s t C gate: M ( R C ) p a s t = 50 s " 1 (3.32) The random c o i n c i d e n c e r a t e at the f i n a l output of the "Fast-Slow" system i s g i v e n by random c o i n c i d e n c e s between (3.32) and the r a t e of p a r t i c l e s s e l e c t e d i n energy, assumed equal t o M(D1D2). I f , as b e f o r e , a f i n a l random c o i n c i d e n c e r a t e of .5$ of (3-29) i s wanted, from equation (3.30) the r e s o l v i n g time at the second c o i n c i d e n c e gate must be l e s s than: ^ 2 = 1 0 0 f 3 (3.33) T h i s allowed r e s o l v i n g time i s s u f f i c i e n t l y l a r g e , i t allows a m p l i f i c a t i o n and s e l e c t i o n of the pu l s e s from d e t e c t o r D l , u s i n g a s i n g l e channel a n a l y s e r , i n a slow system with h i g h energy r e s o l u t i o n . I t i s convenient t o adopt pulses i n the order of 1 a s l o n g f o r the second, slow c o i n c i d e n c e , gate. T h i s w i l l - 103 -r e s u l t i n a f i n a l random c o i n c i d e n c e r a t e much l e s s than 5 $ of the t r u e c o i n c i d e n c e r a t e . A l s o , the same form of "Fast-Slow" s e l e c t i o n i s convenient f o r the counting of the a n t i c o i n c i d e n c e events. The c o n s i d e r a t i o n s r e q u i r e d f o r determining the e f f e c t s of random pulse coincidences-and system dead times on the a n t i c o i n c i d e n c e r a t e are of an e n t i r e l y d i f f e r e n t nature, s i n c e the t r u e r a t e s i n v o l v e d M(D1D2~) are about 10^ times s m a l l e r than M(D1D2), and they w i l l be co n s i d e r e d l a t e r on. The problem of how to o b t a i n the necessary t i m i n g pulses to s a t i s f y the, c o n d i t i o n s r e q u i r e d f o r the f a s t s e l e c t i o n , i n the "Fast-slow" c o i n c i d e n c e system, i s d i r e c t l y r e l a t e d to the d i s c u s s i o n of the o r i g i n of " a c c i d e n t a l " a n t i c o i n c i d e n c e s and i s d i s c u s s e d next. , The occurence of wrong t i m i n g on e i t h e r of D l or D2 p u l s e s , t h a t i s the occurence of the e l e c t r o n i c p u l s e w i t h i n a d i f f e r e n t time of the p a r t i c l e d e t e c t i o n than normally, could r e s u l t i n f a l s e i n f o r m a t i o n recorded at the output of the f a s t C or AC gates. (For example, a r e a l c o i n c i d e n c e being recorded as an a n t i c o i n c i d e n c e ) . As the a n t i c o i n c i d e n c e r a t e i s a f a c t o r of 10 ^ lower than the c o i n c i d e n c e r a t e , even i f only few c o i n c i d e n c e s are m i s s i n g due to wrong t i m i n g the appearance of " a c c i d e n t a l " a n t i c o i n c i d e n c e s could r e s u l t i n a much l a r g e r apparent a t t e n u a t i o n than the c o r r e c t one. Two d i f f e r e n t ways of o b t a i n i n g t i m i n g s i g n a l s from a d e t e c t o r were co n s i d e r e d , "Leading Edge T h r e s h o l d " and "Zero Crossover Methods". A complete d i s c u s s i o n of these methods i s a v a i l a b l e i n an a r t i c l e by C.W. W i l l i a m s (Wi 67). Due to the l a r g e range of amplitudes recorded at the - 104 -d e t e c t o r D l (from 470 kev f o r the h i g h ..energy protons t o 3.5 Mev f o r the He p a r t i c l e s of i n t e r e s t ) i t seemed convenient to adopt a zero c r o s s o v e r t i m i n g system, s i n c e such methods present a b e t t e r a n t i - w a l k behaviour (change of t i m i n g as f u n c t i o n of pulse amplitude) compared t o l e a d i n g edge t r i g g e r i n g . Two c o n s i d e r a t i o n s l e d to the s e l e c t i o n of l e a d i n g edge t r i g g e r i n g i n a s s o c i a t i o n with d e t e c t o r D2. One i s the presence of the l a r g e n o n - c o i n c i d e n t background 100 times l a r g e r than the c o i n c i d e n t r a t e i t s e l f . The second i s the. l a r g e dead time e f f e c t s r e s u l t i n g from the same no n - c o i n c i d e n t background. A convenient zero c r o s s o v e r time f o r a C s l ( T l ) p u l s e i s of the order of .5 to 1 p.s. I f another p u l s e occurs b e f o r e the zero c r o s s o v e r has taken p l a c e , the c r o s s o v e r p o i n t and thus the t i m i n g p u l s e i t s e l f i s delayed by the time d i f f e r e n c e between the two p u l s e s . The p r o b a b i l i t y of a t l e a s t one pu l s e a r r i v i n g b e f o r e the c r o s s o v e r time " t 1 f o r a counting r a t e M(D2) i s : p = 1 - exp C~M(D2)* 0 (3-34) and f o r .5 jxs, p = 5 x 10" 2 (3.35) T h i s r e s u l t i s the' p r o b a b i l i t y t h a t a c o i n c i d e n t proton pulse g i v e s r i s e to a delayed t i m i n g p u l s e . T h i s value i s much l a r g e r than the expected a t t e n u a t i o n i n the proton beam of 5 x 1 0 ~ \ and thus would l e a d t o an e x c e s s i v e r a t e of f a l s e a n t i c o i n c i d e n c e counts. S i m i l a r c o n s i d e r a t i o n s apply t o the case of d e t e c t o r D l but due to the lower counting r a t e s the p r o b a b i l i t y of de l a y t i m i n g i s c o r r e s p o n d i n g l y s m a l l e r . I t i s convenient then to - 105 -operate the f a s t C and AC gates i n a d i f f e r e n t way. For the f a s t C gate s h o r t , f a s t p u l s e s 25 ns wide are used to prevent a l a r g e c o n t r i b u t i o n from random c o i n c i d e n c e s . At the AC gate, on the other hand, a f a s t p roton pulse l o n g e r than the zero c r o s s o v e r time i n the He channel i s d e s i r a b l e i n order to prevent the appearance of " a c c i d e n t a l " a n t i c o i n c i d e n c e s a r i s i n g from delayed t r i g g e r i n g of D l p u l s e s . The f i n a l e f f e c t t o be taken Into account i s . the presence of dead time i n the d e t e c t o r s . I f a p a r t i c l e a r r i v e s at one of the d e t e c t o r s w i t h i n the p a r a l y s i s time f o l l o w i n g a preceding p u l s e , e i t h e r the event f a i l s t o produce a pu l s e at a l l , or the pulse amplitude i s s e v e r e l y degraded. Loss of a s m a l l f r a c t i o n of D l p u l s e s due to dead .time e f f e c t s does not l e a d to any major e f f e c t s s i n c e I t reduces both the c o i n c i d e n c e and a n t i c o i n c i d e n c e counts by the same f a c t o r . I f the D l p u l s e i s produced w i t h degraded amplitude, the event w i l l be d i s r e g a r d e d when the energy s e l e c t i o n i s performed. On the other hand the disappearance of a pu l s e from the proton d e t e c t o r , D2, w i l l r e s u l t i n the r e c o r d i n g of an " a c c i d e n t a l " a n t i c o i n c i d e n c e count. I f the event corresponds to a degraded D2 p u l s e I t would be i n t e r p r e t e d as an i n e l a s t i c p r oton. Since these dead time e f f e c t s are enhanced i n the proton d e t e c t o r due to the l a r g e background of n o n - c o i n c i d e n t protons, i t i s d e s i r a b l e t o i n c o r p o r a t e i n the system a d d i t i o n a l c i r c u i t r y to prevent the r e c o r d i n g of pulses when they f o l l o w p r e v i o u s p u l s e s too c l o s e l y . That I s , the dead time e f f e c t s d e s c r i b e d can be e f f i c i e n t l y prevented i f pu l s e a n a l y s i s i s performed only when the time i n t e r v a l between proton p u l s e s i s g r e a t e r than a - 106 -p r e s e t time, ~£ D , the e f f e c t s of p u l s e degrading can be d r a s t i -c a l l y reduced. A p r a c t i c a l way of p a r a l y s i n g the system d u r i n g the a r t i f i c i a l dead timeT.p. i s to generate a "Dead Time P u l s e " , of le n g t h each time a proton i s d e t e c t e d , and use i t to b l o c k the D l pulses p r i o r t o the f a s t C and AC p o r t i o n of the system. Thus, n e i t h e r c o i n c i d e n c e nor a n t i c o i n c i d e n c e counts are recorded d u r i n g the p e r i o d of the "Dead Time P u l s e " . I t i s convenient t o choose the l e n g t h of the dead time p u l s e , lo n g e r than the puls e r e c o v e r y time of the slowest p a r t of the system. The f a c t t h a t a dead time p u l s e must be generated a f t e r each detected proton means t h a t I f a dead time p u l s e i s a l r e a d y present, i t must be extended i n l e n g t h by "2^. The b l o c k i n g of the D l channel with the dead time p u l s e must, however, f o l l o w t r a n s m i s s i o n to the f a s t gates of any a s s o c i a t e d D l p u l s e . T h i s means t h a t the "dead time a n t i c o i n c i d e n c e gate" must c l o s e approximately 2 5 ns a f t e r the f a s t AC c l o s e s . A resume of these d e s i g n requirements i s i l l u s t r a t e d i n F i g u r e 3.18. The d i f f e r e n t e l e c t r o n i c u n i t s have been separated i n t o b l o c k s a c c o r d i n g t o t h e i r f u n c t i o n . - 107 -DETECTOR # 1 DETECTOR # 2 DETECTION ZERO CROSS OVER TRIGGER LEADING EDGE TRIGGER TIMING PARALVSABLE DEAD TIME GENERATOR FAST AC GATE RC AMPLIFIER SINGLE CHANNEL ANALVISER PULSE STRETCHER . FAST C GATE ARTIFICIAL DEAD TIME FAST SELECTION ENERGY SELECTION C GATE C GATE SLOW SELECTION I ABSORPTION SCALER TRANSMISSION SCALER OUTPUT Figure 3.18 : Block diagram of e l e c t r o n i c requirements. - 108 -4. EXPERIMENTAL SET-UP. 1. General i n t r o d u c t i o n . In Chapter 3 the a p p l i c a b i l i t y of the r e a c t i o n 3ne(d,p) ^He t o t o t a l r e a c t i o n c r o s s s e c t i o n measurements was d i s c u s s e d . Parameters a f f e c t i n g the f l u x and kinematics of the a s s o c i a t e d beam and the a n t i c o i n c i d e n c e background were a l s o a n a l y s e d . In t h i s Chapter a d e s c r i p t i o n of the a c t u a l experimental set-up used i s p r o v i d e d . The d e s c r i p t i o n i s s u b d i v i d e d i n t o two p a r t s , t h a t concerning the chamber and mechanical p a r t s on-one hand and t h a t concerning the e l e c t r o n i c s on the o t h e r . 2. The chamber. F i g u r e 4.1 i s a schematic drawing of the chamber. I t i s attached to one of the beam l i n e s on the U n i v e r s i t y of B r i t i s h Columbia Van de G r a a f f g e n e r a t o r . A s i n g l y i o n i z e d He beam i s f e d t o the chamber v i a two s e t s of f o c u s i n g e l e c t r o s t a t i c quadrupoles and s t e e r i n g magnets. The beam enters the chamber through the c o l l i m a t o r s assembly A. The chamber has i t s own pumping system to permit good vacuum on both s i d e s of the c o l l i m a t o r s . I t a l s o prevents vapour from going i n t o the a c c e l e r a t o r vacuum system when b u i l d i n g the heavy i c e t a r g e t . The i n s i d e w a l l s of the chamber c o n t a i n a .042 inches p o l y e t h y l e n e l i n i n g as d e s c r i b e d i n S e c t i o n 4.2 .3. of Chapter 3. The heavy water vapour enters the chamber through the i n l e t B. The s o l i d s t a t e d e t e c t o r assembly C i s an i n t e g r a l p a r t of the chamber's bottom c o v e r . A = Incident B e a m B = 0^0 Inlet C = SI Counte r D = 0 2 0 Ice B a c k i n g (L .N . ) E = T a r g e t s a n d C o l l i m a t o r s F = C s l C o u n t e r G = L i g h t P i p e Figure 4.1: Schematic diagram of the Chamber - 110 -The backing f o i l on which the heavy i c e t a r g e t i s formed, i s l o c a t e d a t D at the cente r of the chamber. The p r o t o n d e t e c t o r assembly i s f i x e d a t 63° 50' with r e s p e c t to the i n c i d e n t beam d i r e c t i o n . The system i n d i c a t e d by E allows the i n s e r t i o n of c o l l i m a t o r s and/or d i f f e r e n t t a r g e t s on the a s s o c i a t e d proton beam. The C s l s c i n t i l l a t o r P i s connected t o the p h o t o m u l t i p l i e r v i a the l i g h t pipe G. 2.1. The c o l l i m a t o r assembly. The c o l l i m a t o r assembly i s .comprised of two d e f i n i n g a p e r t u r e s and a skimmer. Two s e t s of ap e r t u r e s and the corresponding skimmers were a v a i l a b l e . One set corresponding to a beam diameter of . l 6 0 cm (1/16 i n c h e s ) and the other set to a beam diameter of .318 cm (1/8 I n c h e s ) . The diameters of the ap e r t u r e s and skimmers were machined to .001 i n c h e s . A p i e c e of gun b a r r e l was used as a h o l d e r f o r the c o l l i m a t o r s i n order t o a l i g n them c o n c e n t r i c a l l y to b e t t e r than .001 Inches. The maximum angular divergency i n the i n c i d e n t 3 He beam, as d e f i n e d by the c o l l i m a t o r assembly was: .16 cm a p e r t u r e s 75"° — .02° .318 cm a p e r t u r e s 1.50° 1 .02° The c o l l i m a t o r assembly was a l i g n e d w i t h the i n c i d e n t beam d i r e c t i o n , d e f i n e d by the two s e t s of e l e c t r o s t a t i c quad-r u p o l e s , by means of a l a s e r beam. No s t r o n g f o c u s i n g was u s e d . i n order t o keep the i n c i d e n t 3 He -b earn on the c o l l i m a t o r s assembly as p a r a l l e l as p o s s i b l e , and w i t h a c r o s s s e c t i o n l a r g e r than t h a t of the ape r t u r e s i n use. The. u n i f o r m i t y of the c u r r e n t d e n s i t y on the beam r e g i o n f a c i n g the c o l l i m a t o r s was checked by obs e r v i n g the beam i n a quartz chopper. 2.2. The s o l i d s t a t e d e t e c t o r assembly. As mentioned above t h i s assembly forms p a r t of the chamber's bottom cover. The angular p o s i t i o n w i t h r e s p e c t t o the i n c i d e n t beam d i r e c t i o n , and t h e . v e r t i c a l p o s i t i o n r e l a t i v e t o the plane d e f i n e d by the primary beam d i r e c t i o n and the cente r of the p r o t o n d e t e c t o r , can be ad j u s t e d without b r e a k i n g the. vacuum. To cen t e r the s o l i d s t a t e d e t e c t o r , w i t h r e s p e c t t o the corresponding secondary beam, a s m a l l c o l l i m a t o r of .2 inches 0 i n diameter subtending approximately 1.75 h a l f angle from the center of the source t a r g e t , was. i n s t a l l e d a t the ce n t e r of the proton d e t e c t o r . Then the a n t i c o i n c i d e n c e background was measured as a f u n c t i o n of the angular and v e r t i c a l p o s i t i o n of the s o l i d s t a t e d e t e c t o r assembly. A minimum i n the measured r a t i o of a n t i c o i n c i d e n c e to c o i n c i d e n c e count r a t e s between the two d e t e c t o r s thus d e f i n e s t h e r e q u i r e d k i n e m a t i c a l r e l a t i o n s h i p . When,, t h i s is. done the s o l i d s t a t e d e t e c t o r i s f i x e d a t the angle and v e r t i c a l p o s i t i o n corresponding to the minima and the s m a l l c o l l i m a t o r i n f r o n t of the proton d e t e c t o r removed. T y p i c a l curves are reproduced i n F i g u r e s 4.2 and 4.3. The o r i g i n of the low energy proton background was d e s c r i b e d i n Chapter 3* S e c t i o n 4.2.3. The c o n t r i b u t i o n from the w a l l l i n i n g was reduced by e n c l o s i n g the r e g i o n between the s o l i d s t a t e d e t e c t o r and the c o l l i m a t o r w i t h p o l y e t h y l e n e t u b i n g . To reduce the c o n t r i b u t i o n from the c o l l i m a t o r edge s c a t t e r i n g , the d e t e c t o r - c o l l l m a t o r s p a c i n g was made as l a r g e as p o s s i b l e . HORIZONTAL , VERTICAL R E L A T I V E P R O T O N A N G L E Figure 4.2: Attenuation as a function of the Figure 4.3 : Attenuation as a function of the horiz o n t a l p o s i t i o n a detector. v e r t i c a l p o s i t i o n a detector. - 113 -A t y p i c a l p u l s e h e i g h t spectrum from the s u r f a c e b a r r i e r d e t e c t o r i s shown i n f i g u r e 4.4 f o r a d e t e c t o r d e p l e t i o n depth of approximately 70 microns. The continuous proton spectrum f o l d e d about the "proton edge" i s observed i n the c e n t e r p a r t of the spectrum with the edge w e l l r e s o l v e d from the a l p h a peak. The peak a t lower e n e r g i e s corresponds t o the h i g h energy protons going through the d e p l e t i o n l a y e r , l e a v i n g only a f r a c t i o n of t h e i r energy i n I t (470 k e v ) . The areas under the alpha peak and the low energy peak c o n t a i n r o u g h l y the same number of counts as expected I f these count r a t e s are determined simply by the d e t e c t o r s o l i d a n g l e . To prevent the 650 kev primary 3He beam s c a t t e r e d from the heavy i c e t a r g e t assembly from r e a c h i n g the s o l i d s t a t e d e t e c t o r a N i c k e l f o i l 20 x 10"^ inches t h i c k was I n s t a l l e d a g a i n s t the d e t e c t o r f a c e . T h i s f o i l Introduces an energy l o s s of 240 kev f o r 3.3 Mev ^He and 50 Kev f o r 15 Mev p r o t o n s . S i n c e i t i s mounted a g a i n s t the d e t e c t o r the f r a c t i o n of secondary beam l o s t due to s c a t t e r i n g from i t Is n e g l i g i b l e . 2 . 3 . The deuterium t a r g e t . The copper backing f o i l i s In thermal contact w i t h a l i q u i d n i t r o g e n r e s e r v o i r which i s an i n t e g r a l p a r t of the top chamber cover. The c o n t a i n e r i s e l e c t r i c a l l y i n s u l a t e d from the r e s t of the chamber so that the primary beam c u r r e n t can be measured. I t can a l s o be r o t a t e d so t h a t the angle between the source t a r g e t and the i n c i d e n t beam can be v a r i e d . A f t e r the backing f o i l has c o o l e d , the heavy i c e t a r g e t i s formed by l e t t i n g i n t o the chamber a measured amount of heavy water vapour. The vapour i n l e t has a d i f f u s o r , made wit h g l a s s l O K CL > 2 . - 114 C Qi O C P Q. (0 ro fl i K 4 LU Z z < X o CO z o o 1004 io • •• 2 x u. z g D _J O CO hi 40 80 120 160 200 C H A N N E L N U M B E R 240 Figure 4.4 : T y p i c a l s o l i d state detector spectrum - 115 -wool, to prevent n o z z l e e f f e c t s i n the incoming vapour j e t . The primary t a r g e t t h i c k n e s s was c a l i b r a t e d a g a i n s t the amount of vapour allowed i n t o the chamber. T h i s amount was measured by the vapour pressure measured wi t h r e s p e c t t o the chamber p r e s s u r e , i n a g l a s s c o n t a i n e r of a f i x e d volume,and so w i l l be quoted i n centimeters of S i l i c o n o i l of d i f f e r e n t i a l p r e s s u r e . The a c t u a l DgO t a r g e t t h i c k n e s s was measured u s i n g the 873 kev resonance i n the r e a c t i o n 1 9 F ( p , ^ H e ) l 6 0 * ( <** = 540 mb, P = 5 kev, Eg- = 6 Mev). A f l u o r i n e t a r g e t , approximately 10 kev t h i c k , was d e p o s i t e d onto one s i d e of the backing f o i l and the 0^  -ray y i e l d measured as a f u n c t i o n of the energy of the bombarding protons. S u c c e s s i v e amounts of D2O were then l e t i n t o the chamber and the energy s h i f t of the y i e l d curve measured i n each case. The energy s h i f t s are due to the proton energy l o s s i n the i c e l a y e r s formed on top of the f l o u r i n e t a r g e t . The r e s u l t s are p l o t t e d i n F i g u r e 4 . 5 . The energy l o s s f o r % e ions was determined from the measured energy l o s s f o r protons (Nu 60, p. l8)(We 52) (Wh 58), and i l l u s t r a t e d i n F i g u r e 4 , 6 . The t h i n backing f o i l s were attached to the h o l d e r by a simple, convenient technique. The backing f o i l h o l d e r frame was covered with a l a y e r of indium, and the f o i l s a t tached to i t by a simple' c o l d s o l d e r under p r e s s u r e . T h i s method permitted copper f o i l s of a few mlcroinches t h i c k n e s s t o be attached w i t h good thermal and e l e c t r i c a l c o n t a c t , q u i c k l y and e a s i l y . When the t a r g e t was exposed to beam c u r r e n t s of .2 jj^k through a 1/8 Inches c o l l i m a t o r , t h e 3He(d,p)^He r e a c t i o n y i e l d d e t e r i o r a t e d a t the r a t e of approximately 5 x 10 per hour ( r e l a t i v e 116 -> o 55 *2 as S i a. 60 50 40 3D 20 10 0 - — r ~ 4 DIFFERENTIAL PRESSURE T— r 8 10 C cm ) U 400 m 300 | h 2 0 0 $ 100 «. fl> < Figure 4. S : Calibration o£ heavy ice target thickness. 100 u 1-4 o B £3 u I 1—4 I o 1 0 — I al O a. »-( CL a. .01 protons - . - 3He 4 He T r - i | i i n ] 1 1 i | i i » i j .1 i. P A R T I C L E E N E R G Y —1 1—K | I I I 11 10 ( MeV ) Figure 4.6 : Stopping power of D2Q f o r d i f f e r e n t p a r t i c l e s , - 117 -change of y i e l d per hour) f o r a 120 x 1 0 " ^ inches t h i c k copper backing f o i l . The presence of X D 0 i n the i c e t a r g e t would g i v e r i s e t o competing r e a c t i o n s a r i s i n g from decays of the compound system ( 3He = " ^ 0 ) . The c r o s s s e c t i o n s f o r such r e a c t i o n s a r e , however, very s m a l l due t o the Coulomb b a r r i e r (of the order of 3 Mev f o r 3He on l 6 0 ) . Secondary r e a c t i o n s between the h i g h energy protons and the i c e t a r g e t do not c o n t r i b u t e s i g n i f i c a n t l y t o the a n t i c o i n -cidence background due to the very s m a l l t h i c k n e s s and hence low r e a c t i o n r a t e i n the heavy i c e l a y e r . 4 The d i s t o r t i o n of the He secondary beam i n l e a v i n g the i c e t a r g e t i s considered i n d e t a i l i n Appendix I and the r e s u l t s d i s c u s s e d i n S e c t i o n 4 . 2 . 4 of Chapter 3 . 2 . 4 . The f i n a l t a r g e t assembly. The..mechanical d e s i g n of the f i n a l t a r g e t system was chosen to f a c i l i t a t e the i n s e r t i o n of one of s e v e r a l t a r g e t f o i l s i n f r o n t of the d e t e c t o r w h i l e a t the same time e n a b l i n g s e l e c t i o n of one of s e v e r a l d i f f e r e n t c o l l i m a t o r s s i t u a t e d immediately p r i o r to the t a r g e t . These items could be changed without b r e a k i n g vacuum or a l t e r i n g the mechanical c o n f i g u r a t i o n of any other p a r t of the chamber. F i g u r e 4 . 7 i s a schematics of the cross s e c t i o n of the f i n a l t a r g e t assembly. I t i s mounted at the end of the proton d e t e c t o r assembly and c o n s i s t s of two f i x e d c o l l i m a t o r s and two s l i d i n g h o l d e r s . The f i x e d c o l l i m a t o r s can not be changed from o u t s i d e the chamber, c o l l i m a t o r #1 d e f i n e s the angle c* r e f e r r e d - 118 -Figure 4.8 : Schematic diagram o f the r o t a r y assembly. - 119 -to i n S e c t i o n 4 . 2 . 1 . of Chapter 3 . When the sample i s i n s e r t e d , shown i n h o l d e r number 2, the angle "9 subtended by the proton d e t e c t o r at the center of the sample i s determined by c o l l i m a t o r #2 and remains f i x e d at 83 ° . The two s l i d i n g h o l d e r s , #1 and #2, move i n a d i r e c t i o n p e r p e n d i c u l a r t o the plane of the drawing. Each of them has two t a r g e t , or c o l l i m a t o r p o s i t i o n s a v a i l a b l e . In one p o s i t i o n of h o l d e r #1 the .2 inches diameter c o l l i m a t o r i s u s u a l l y kept, i n order t o a l i g n the secondary beam d e t e c t o r as d e s c r i b e d i n s e c t i o n 2 . 2 . 2 . 5 . The r o t a r y assembly. In S e c t i o n s 4 . 2 . 2 of Chapter 3 r e f e r e n c e was made to the p o s s i b i l i t y of l a t t i c e e f f e c t s i n the a t t e n u a t i o n background when the d e t e c t o r s i n use are s i n g l e . c r y s t a l s . T h i s i s the case f o r a C s l ( T l ) s c i n t i l l a t o r . The angular divergency of the proton beam i s l a r g e r than the c r i t i c a l angle f o r cha n n e l i n g (Li 65) of 15.8 Mev protons i n C s l of onl y . 3 ° . I t Is d e s i r a b l e , n e v e r t h e l e s s , t o know i f the change i n the angular divergency of the proton beam due to the i n s e r t i o n of the sample a l t e r s the a n t i c o i n c i d e n c e background. In order t o perform such measurements t h e " f i n a l ' t a r g e t assembly could be r e p l a c e d by the r o t a r y assembly, a schematic drawing of which i s presented i n F i g u r e 4 . 8 . The r o t a r y h o l d e r i n d i c a t e d by A i s designed t o h o l d the C s l c r y s t a l and can be r o t a t e d on i t s plane around the d i r e c -t i o n k, with r e s p e c t t o the r e s t of the proton d e t e c t o r assembly B attached to the chamber. T h i s r o t a t i o n can be performed from - 120 - . o u t s i d e the chamber v i a a 100:1 r e d u c t i o n . The angle between the h o l d e r A and the proton beam d i r e c t i o n can be v a r i e d o n l y by dis a s s e m b l i n g the proton d e t e c t o r . Using a c r y s t a l l o g r a p h i c method, l i k e Laue's back r e f l e c t i o n method,, the angle t h a t a p r i n c i p a l a x i s \jLt*)tc2 of the c r y s t a l forms w i t h i t s f a c e can be found. I f the angle "K of f i g u r e 4 .8 i s made equal t o the a x i s angle, when the c r y s t a l i s r o t a t e d around k, one i s e f f e c t i v e l y changing the angle between the proton beam and the ^ a , b , c j a x i s from 0° to ( l 8 0 ° - 27c°) The assembly i s , therijused t o measure the dependence of the a t t e n u a t i o n i n the c r y s t a l on.the l a t t i c e o r i e n t a t i o n w i t h r e s p e c t t o the I n c i d e n t beam. The same assembly can be used t o check the t a r g e t samples f o r l a t t i c e e f f e c t s ; s i n c e r e l a t i v e measurements are i n v o l v e d no problem a r i s e s from the l a c k of f a c i l i t i e s f o r i n s e r t i n g or removing the samples. 2 . 6 . The proton d e t e c t o r assembly. A 2 m i l i m e t e r t h i c k and 2 inches i n diameter C s l ( T l ) c r y s t a l s c i n t i l l a t o r i s coupled with o p t i c a l s i l i c o n grease t o a 2 inches diameter l i g h t p i p e made out of s o l i d " L u c i t e " r o d . The vacuum s e a l i s made to the l i g h t p i p e so t h a t the photo--m u l t i p l i e r tube, i t s s h i e l d i n g and e l e c t r o n i c s , are s i t u a t e d o u t s i d e the chamber, at atmospheric p r e s s u r e . The f i r s t runs were done u s i n g an RCA 6342 phototube. I t was l a t e r r e p l a c e d by a CBS 7817 because of i t s s u p e r i o r e l e c t r o n t r a n s i t time spread c h a r a c t e r i s t i c s , which enabled b e t t e r time r e s o l u t i o n t o be ob t a i n e d . The assembly i s connected t o the chamber at the port - 121 -i n d i c a t e d i n F i g u r e 4.1, l o c a t e d at 63° 50' from the d i r e c t i o n d e f i n e d by the primary beam c o l l i m a t o r s , corresponds to the angle p r o v i d i n g k i n e m a t i c a l c o l l i m a t i o n as d e s c r i b e d i n s e c t i o n 3.2 of Chapter 3. ' In order t o reduce the low energy n o n - c o i n c i d e n t back-ground count r a t e i n the proton d e t e c t o r due to d e t e c t i o n of the 4 He p a r t i c l e s produced by the source r e a c t i o n i n t o the angle subtended by the detector,^ the window f o r l i g h t r e f l e c t i o n on the open f a c e of the s c i n t i l l a t o r was made of aluminum f o i l 18. x 10"^ cm t h i c k . T h i s t h i c k n e s s a l l o w s i t to stop up to 4.5 MeV ^He, the energy of the alpha p a r t i c l e s emitted a t 6 3 ° . T h i s t h i c k n e s s of aluminum i s o n l y expected to c o n t r i b u t e an a n t i c o i n c i d e n c e background of about 6.6 x 10"^, a value t h a t i s much l e s s than the background from the d e t e c t o r i t s e l f . 3. E l e c t r o n i c s . The o v e r a l l e l e c t r o n i c requirements were d i s c u s s e d i n S e c t i o n 5 of Chapter 3. Most of the e l e c t r o n i c s was designed and b u i l t i n the l a b o r a t o r y at a time when such In s t r u m e n t a t i o n was not r e a d i l y a v a i l a b l e commercially. As the experiment progressed, many of these l o c a l l y manufactured u n i t s were r e p l a c e d w i t h more f l e x i b l e commercial u n i t s when they became a v a i l a b l e . The d e t a i l s of the l o c a l l y manufactured u n i t s s t i l l i n use i s presented i n Appendix 3. S p e c i a l a t t e n t i o n w i l l be g i v e n i n t h i s s e c t i o n , however, to the " p a r a l y s a b l e dead time ge n e r a t o r " s i n c e I t i s the main compo-nent to e l i m i n a t e the appearance of " a c c i d e n t a l " a n t i c o i n c i d e n c e s due to random e f f e c t s . - 122 -The b l o c k diagram of the e l e c t r o n i c s i s presented i n F i g u r e 4 . 9 . T h i s i s an "expanded" v e r s i o n of F i g u r e 3.18 used t o i l l u s t r a t e the b a s i c system. The f a s t and ,slow c i r c u i t s a re c l e a r l y d i s t i n g u i s h e d . In agreement with the de s i g n requirements p r e v i o u s l y d i s c u s s e d , the f a s t c i r c u i t r y i s composed of u n i t s having r i s e times of l e s s than 10 ns. The slow u n i t s have r i s e . times of over 100 ns. D e s c r i p t i o n of the system w i l l be presented i n t h r e e s u b s e c t i o n s , one being the s o l i d s t a t e d e t e c t o r channel and a s s o c i a t e d u n i t s , one d e s c r i b i n g the C s l s c i n t i l l a t o r channel and r e l a t e d equipment and the t h i r d b e i n g the " P a r a l y s a b l e dead time generator". 3.1. The s o l i d s t a t e d e t e c t o r channel. The s o l i d s t a t e d e t e c t o r s i g n a l i s f e d i n t o a charge s e n s i t i v e a m p l i f i e r . The output of the p r e a m p l i f i e r i s f e d Into both a "slow" channel f o r energy s e l e c t i o n of the ^ He p a r t i c l e s , and a l s o a "pulse shaper" c i r c u i t to o b t a i n the b i p o l a r p u l s e necessary f o r the zero c r o s s over t r i g g e r i n g . A zero cross over u n i t d e t e c t s the zero c r o s s over time of the "pulse shaper" out-put and t r i g g e r s a p u l s e 25 ns wide. The energy s e l e c t i o n i s performed with the "slow" u n i t c o n s i s t i n g of an ORTEC 410 Multimbde A m p l i f i e r , with d i f f e r e n t i a -t i o n and i n t e g r a t i o n time constants of 1 ^us, an ORTEC 408 B i a s e d A m p l i f i e r and a COSMIC .901 SCA S i n g l e Channel A n a l y s e r . The bi a s e d a m p l i f i e r and the s i n g l e channel a n a l y s e r were set to 4 s e l e c t H e - p a r t i c l e s i n the energy range 3.17 to 3.27 MeV f o r a p p r o p r i a t e " K i n e m a t i c a l c o l l i m a t i o n " of the a s s o c i a t e d protons - 123 -PRE-AMPLIFIER S.S.D. Csl LEADING EDGE TRIGGER ZERO CROSS OVER TRIGGER B i a s H.V. VARIABLE DELAY DEAD TIME GATE R C AMPLIFIER BIAS AMPLIFIER 50 ns DELAY PARALSSABLEj^j, DEAD TIMEPW"? GENERATOR 200 ns DELAY FAST AC GATE SINGLE CHANNEL ANALYSER SCALER lHe MONITOR He KICKSORTER ABSORPTION C GATE cg2 FAST C GATE TRANSMISSION C GATE SCALER TRANSMISSION COUNTER PROTON RATE PRE -AMPLIFIER VARIABLE DELAY LINEAR GATE PROTONS KICKSORTER R C AMPLIFIER SCALER ABSORPTION FAST SLOW Figure 4.9 ; Block diagram of the e l e c t r o n i c s . - 124 -as d e s c r i b e d i n S e c t i o n 3.2 of Chapter 3. The s o l i d s t a t e d e t e c t o r used possessed an o v e r a l l r e s o l u t i o n of 40 KeV as ? 4 l measured wi t h a Am alpha source. A 512 channel p u l s e amplitude a n a l y s e r NUCLEAR DATA ND120 at the output of e i t h e r the multimode a m p l i f i e r , or the bi a s e d a m p l i f i e r , was used i n c o i n c i d e n c e mode wit h the s i n g l e channel a n a l y s e r output to h e l p i n s e t t i n g the d e s i r e d energy. The output of the s i n g l e channel a n a l y s e r a l s o f e d a s c a l e r to monitor the number of /*He p a r t i c l e s of the d e s i r e d energy s e l e c t e d . 3.2. The p h o t o m u l t i p l l e r channel. The p h o t o m u l t i p l l e r was s u p p l i e d with n e g a t i v e h i g h v o l t a g e , and the anode s i g n a l f e d through an ORTEC 260 Time P i c k o f f u n i t i n t o the base of the f i r s t t r a n s i s t o r of the p r e -a m p l i f i e r . The time p i c k o f f u n i t p rovided the "Leading edge t r i g g e r " f o r t h i s channel. The t h r e s h o l d l e v e l , mentioned i n S e c t i o n 4.2 of Chapter 3, was c o n t r o l l e d with an ORTEC 403 Time P i c k o f f C o n t r o l u n i t t h a t p e r m i t t e d continuous adjustment of the t r i g g e r i n g l e v e l of the time p i c k o f f u n i t . The p r e a m p l i f i e r d e l i v e r s b i p o l a r p u l s e s , used t o e l i m i n a t e problems a s s o c i a t e d w i t h DC s h i f t s due to the h i g h c o u n t i n g r a t e s c h a r a c t e r i z i n g t h i s channel. The time from t h r e s -h o l d t o the zero c r o s s o v e r p o i n t can be v a r i e d by changing the l e n g t h of a delay l i n e . When u s i n g a C s l c r y s t a l i t was adjus t e d to approximately 500 ns. When a p l a s t i c s c i n t i l l a t o r was employed ( f o r the t e s t runs d e s c r i b e d i n Chapter 5) i t was ad j u s t e d to about 100 ns. - 125 -The output of the f a s t l e a d i n g edge t r i g g e r u n i t was fed i n t o a p a s s i v e v a r i a b l e delay u n i t used t o balance the delays i n the two channels p r i o r t o the f a s t c o i n c i d e n c e gate. T h i s time d e l a y u n i t was a l s o u s e f u l i n determining the time r e s o l u t i o n of the f a s t c o i n c i d e n c e gate. The f a s t pulse, i s a l s o used t o t r i g g e r the " P a r a l y s a b l e Dead Time Generator" whose d e s i g n w i l l be d i s c u s s e d i n s e c t i o n 3.^-. T h i s generator produces a pu l s e 16 JAS l o n g , w i t h r i s e and f a l l times of l e s s than 10 ns, each time a f a s t p roton p u l s e a r r i v e s , (as r e q u i r e d by S e c t i o n 5 of Chapter 4 f o r the Dead Time P u l s e ) . The Dead time p u l s e i s delayed by an a d d i t i o n a l 50 ns b e f o r e being f e d i n t o the "Dead time Gate" used t o p a r a l y s e the a l p h a channel. I t was found convenient t o use as a proton g a t i n g p u l s e i n the f a s t AC gate the non-delayed output of the dead time generator, i n s t e a d of employing an e x t r a p u l s e s t r e t c h e r u n i t , as i l l u s t r a t e d i n F i g u r e 3.18. The output of the p r e a m p l i f i e r was f e d v i a a p a s s i v e v a r i a b l e delay u n i t i n t o a LeCROY 1086 F a s t L i n e a r Gate operated i n c o i n c i d e n c e mode. The g a t i n g p u l s e was obtained from the out-put of the " t r a n s m i s s i o n " slow c o i n c i d e n c e u n i t . Thus, t h i s gate s e l e c t s only those proton p u l s e s corresponding to the alpha p a r t i c l e s s e l e c t e d In the a l p h a channel b e f o r e a m p l i f i c a t i o n by a "slow" system, f o r hig h energy r e s o l u t i o n . The gate p u l s e width i s a d j u s t e d to be approximately equal t o the zero c r o s s o v e r time In use i n the channel, so t h a t the output pulses of the gate are e s s e n t i a l l y u n i p o l a r . The slow u n i t f o l l o w i n g the f a s t l i n e a r gate was composed of a CAMBERRA 1410 Multimode A m p l i f i e r operated w i t h i n t e g r a t i o n - 126 -and d i f f e r e n t i a t i o n time constants of 1 jxs and a NUCLEAR DATA 160 m u l t i c h a n n e l p u l s e h e i g h t a n a l y s e r operated i n s i n g l e parameter mode and i n subgroups of 256 channels. Due to the h i g h counting r a t e i n t h i s channel, an e l e c t r o n i c counter was p r e f e r r e d over a s c a l e r f o r m o n i t o r i n g the t r a n s m i t t e d proton r a t e . The "instantaneous" r a t e i n s t e a d of the t o t a l number of counts accumulated over the long counting time i n t e r v a l , as obtained from such a u n i t , was found very use-f u l f o r d e t e c t i n g d e t e r i o r a t i o n of the heavy i c e t a r g e t . 3 . 3 . Coincidences and a n t i c o i n c i d e n c e s . The system of c o i n c i d e n c e s and a n t i c o i n c i d e n c e s as r e q u i r e d by the d e s i g n c o n s i d e r a t i o n s of S e c t i o n 5 of Chapter 3 , i s e s s e n t i a l l y a standard "Fast-Slow" system, a p p l i e d t o both the c o i n c i d e n c e and a n t i c o i n c i d e n c e channels. The f a s t c o i n c i d e n c e gate was f e d w i t h f a s t pulses from both the He and p r o t o n channels. As mentioned i n S e c t i o n 3 . 2 , the non-delayed output of the P a r a l y s a b l e Dead Time Generator was used as g a t i n g p u l s e f o r the Fast A n t i c o i n c i d e n c e u n i t . The f a s t alpha p u l s e s were delayed by 200 ns to ensure t h a t the gate was completely c l o s e d i n those cases where the alpha p u l s e was accompanied by a c o i n c i d e n t proton p u l s e . The f a s t a n t i c o i n c i d e n c e gate used as the "Dead time gate" d i f f e r s from the F a s t A n t i c o i n c i d e n c e u n i t only i n t h a t a 50 ns" delay f o r the dead time g a t i n g p u l s e i s i n c o r p o r a t e d . T h i s r e s u l t s i n d i f f e r e n t DC l e v e l s a t the g a t i n g i n p u t s . Both a n t i c o i n c i d e n c e gates were, however, DC connected to the g a t i n g p u l s e s (the reasons f o r t h i s requirement are presented i n s e c t i o n 3.4,where r e f e r e n c e Is a l s o made to the d i f f e r e n t DC l e v e l s mentioned above). The outputs of the f a s t gates were" f e d i n t o two sepa-r a t e d "slow" c o i n c i d e n c e u n i t s named the "Transmission Coincidence Gate" and the "Absorption Coincidence Gate". Here the slow s e l e c t i o n of the de s i g n requirements was s a t i s f i e d . The second input, t o each slow c o i n c i d e n c e u n i t was connected to the output of the alpha channel S i n g l e Channel A n a l y s e r d e s c r i b e d i n s e c t i o n 3.1. The slow c o i n c i d e n c e gate outputs were f e d i n t o two d i f f e r e n t s c a l e r s , a "Transmission S c a l e r " which p r o v i d e s a measurement of M(D1D2), and an "Absorption S c a l e r " used t o r e c o r d the number of absorbed protons or M(D1D2~). 3 . 4 . The p a r a l y s a b l e dead time gen e r a t o r . F i g u r e 4.10 i s a s i m p l i f i e d schematic drawing i n d i c a t i n g the e s s e n t i a l components of the p a r a l y s a b l e dead time generator. The d e t a i l e d u n i t a c t u a l l y used i s i l l u s t r a t e d i n F i g u r e 4.11. The s h o r t input p u l s e , (the t i m i n g p r o t o n p u l s e ) , i s f e d v i a C l i n t o a "pulse s t r e t c h e r " formed by T I , R2, R3 and C2. TI i s an e m i t t e r f o l l o w e r used t o charge C2 t o the value V i + V l , where V i i s the amplitude of the in p u t p u l s e and VI i s the DC l e v e l at the e m i t t e r of T I . T h i s o p e r a t i o n , of course, r e q u i r e s the d u r a t i o n o f the input p u l s e , t ^ , to be: t± » R3 . C2 (4.1) F o l l o w i n g the p u l s e , TI i s c u t - o f f , and the s t r e t c h c a p a c i t o r , C2, d i s c h a r g e s towards ground v i a R2 and R 3 . When the +B RI (A) A v — T l R3 R5 \ R6 14+: INPUT V. 1 4 l C l (A) (B) (C) A h — W VI (B) V2 T2 R2 C2 V3 A • 1 V4 R4 (D) L V J T.D. OUTPUT (E) T4 C3 Is) OO (E) "I Figure 4.10 : The paralysable dead time generator ( e s s e n t i a l components). 5.6K C 5.6K 560 6.8K INPUT 0 " (13.5V) l l 500 V+ AV 1N747A Z A 1 \ - * > --Hi' ft (12 V) 5.6K .1 yF BYZ57 Z S 1 BYZ57 2N2904 1N2032 .lyF 68pF 1 yF 2N706AX 2N2218 56 10K-lOOOpI .180K +20V 2N2712 2N2712 IK 1N747A 1N100 ASZ21 T7 J BZ100 2N797 TD 5mA ,1.8K - 9 V • 50V 15K DC.: 16V 470 ' OUTPUTS £ 4 yF 1N764 . j , Cd 9V 10K Figure 4.11 : C i r c u i t diagram-of the pararysable .dead time generator. - 130 -v o l t a g e at the e m i t t e r of TI r e t u r n s t o VI, TI comes i n t o conduc-t i o n a g a i n , and the di s c h a r g e ceases. For V i << VI the di s c h a r g e i s approximately l i n e a r , and the d i s c h a r g e time (or s t r e t c h i n t e r v a l ) i s g i v e n by: t = C2 . V i / I I (4.2) s ' where I I i s the DC c u r r e n t i n t r a n s i s t o r T I . For long t g , of the order of yus, and I I equal f o r example to 1 mA and V i of a few v o l t s , C2 i s of the order of I O 3 pF. Since the in p u t p u l s e s are onl y 25 ns wide, an i n t e r m e d i a t e s t r e t c h e r p r i o r t o the T1-C2 s t r e t c h e r d i s c u s s e d here was employed i n the complete c i r c u i t shown i n F i g u r e 4.11. T2 i s an e m i t t e r f o l l o w e r used to b u f f e r the d i s c h a r g e waveform (B) from the r e s t of the c i r c u i t . The DC c o n d i t i o n s f o l l o w i n g the s t r e t c h e r c a p a c i t o r C2 are s e t as f o l l o w s . T3 i s h e l d i n s a t u r a t i o n with the t u n n e l diode TD i n i t s low s t a b l e s t a t e , so t h a t V3—V. Due to the V B E v o l t a g e drop i n T I , V2< V3 and T2 i s o f f . F o l l o w i n g an inp u t p u l s e V2 r i s e s , and when V2 > V3^T2 goes i n t o conduction causing T3 to be turned o f f . T h i s f o r c e s the c u r r e n t 24 through the t u n n e l diode TD, which switches i n t o the upper s t a b l e c o n d i -t i o n . T h i s s i t u a t i o n p e r s i s t s u n t i l the value of V2, now c o n t r o l l e d by the d i s c h a r g e of C2, f a l l s below V. T3 then goes back i n t o the s a t u r a t i o n mode and the TD switches back t o i t s DC c o n d i t i o n . A.V i s a v a r i a b l e v o l t a g e supply t h a t allows V2 t o be a d j u s t e d w i t h r e s p e c t t o V3 thus p e r m i t t i n g the width of the square p u l s e a t (D) to be v a r i e d . The s i t u a t i o n i s i l l u s t r a t e d by the waveform diagrams (A) to (E) of F i g u r e 4.10. The dashed - 131 -l i n e i n waveform (B) i n d i c a t e s the s w i t c h i n g l e v e l s et by V+AV, The t u n n e l diode i s used t o produce a pulse with short r i s e and f a l l times. T h i s p u l s e i s used t o d r i v e T4 i n t o s a t u r a t i o n , thus d e f i n i n g the output p u l s e . I f a second pulse occurs before V2 has recovered t o i t s DC c o n d i t i o n , C2 i s recharged and the output p u l s e width i s extended f o r an a d d i t i o n a l d i s c h a r g e p e r i o d . Since the c i r c u i t i s completely DC coupled, the o p e r a t i o n as d e s c r i b e d was found to apply even f o r pu l s e r a t e s so l a r g e t h a t 100^ p a r a l y s i s r e s u l t e d . The matching of DC l e v e l s w i t h the a n t i c o i n c i d e n c e gates i s provided by TJ i n the complete diagram of F i g u r e 4.11. 4. E l e c t r o n i c s performance. The performance of the e l e c t r o n i c system was checked w i t h a r t i f i c i a l l y generated p a i r s of c o i n c i d e n t a l p h a and proton p u l s e s . High r a t e s of "proton" p u l s e s , produced by a pul s e generator randomly t r i g g e r e d w i t h a X -source, were super-imposed on the c o i n c i d e n t p a i r s . The system could then be t e s t e d f o r the appearance of " a c c i d e n t a l " a n t i c o i n c i d e n c e events due to hi g h background r a t e s . 3 -1 For a c o i n c i d e n t count r a t e of 2 x 1 0 J s and random r a t e s up t o 120 x 10-^ s " 1 , much above experimental v a l u e s , not a s i n g l e a n t i c o i n c i d e n c e was observed. 4 .1 . The p a r a l y s a b l e dead time g e n e r a t o r . The same set-up of a r t i f i c i a l l y generated p u l s e s a l s o p e r m i t t e d a d e t a i l e d examination of the performance of the " P a r a l y s a b l e dead time g e n e r a t o r " . When the random proton r a t e - 132 -Is superimposed on the c o i n c i d e n t r a t e , a c e r t a i n f r a c t i o n of the c o i n c i d e n t p u l s e s are e l i m i n a t e d at the dead time gate. T h i s gate, as d i s c u s s e d b e f o r e , remains c l o s e d f o r a le n g t h of time a f t e r each detected proton. 'cT D was chosen t o be 16 jU. s. The p r o b a b i l i t y of having no counts appearing i n a time i n t e r v a l ^-Q> *" o r Pulses with a Poi s s o n d i s t r i b u t i o n correspond-i n g to r a t e 'n' i s gi v e n by: P Q = e x p [ - n Z D - J (4.3) I f a c o i n c i d e n t p a i r of alpha and proton pulses appears a f t e r a p e r i o d ^-Q l n w t i :*- c l 1 n o Photons were de t e c t e d , a c o i n c i d e n t count i s re c o r d e d . Then, the recorded c o i n c i d e n c e r a t e M(C) i s give n by the t r u e c o i n c i d e n t r a t e M(D1D2) m u l t i p l i e d by the p r o b a b i l i t y of no random protons \of r a t e M(D2)"j o c c u r r i n g d u r i n g the pre c e d i n g ~?~ i n t e r v a l , o r : M(C) = M(D1D2) e x p H -M(D2) *>Td3 (4-4) The f r a c t i o n of c o i n c i d e n c e s l o s t at the dead time gate, ^ M ( C ) , i s then g i v e n by: A M ( C ) = M(D1D2) Q 1 - exp |-M(D2) t \~] (4.5) From (4.4) we o b t a i n : * In [ M ( C ) / M(D1D2)] = -M(D2) Z * D (4.6) The number of c o i n c i d e n c e counts, corresponding to M(C) are obtained d i r e c t l y at the "Transmission S c a l e r " (See F i g u r e 4.9). The t r u e number of c o i n c i d e n c e counts M(D1D2) i s recorded at the ,,2|He Monitor S c a l e r " . The proton r a t e M(D2) i s g i v e n by the e l e c t r o n i c counter i n the proton channel. - 133 -In F i g u r e 4.12 the r e s u l t of the " P a r a l y s a b l e dead time generator" check i s presented. The r a t i o between the t r u e and detected c o i n c i d e n c e counts i s p l o t t e d a g a i n s t the proton r a t e . The f u l l l i n e i s the expected behaviour as obtained from equation ( 4 . 6 ) , assuming a "Z~D of 16 LA.s. 4.2. Proton channel t h r e s h o l d t r i g g e r i n g and c a l i b r a t i o n . With the experimental c o n f i g u r a t i o n used, two d i f f i -c u l t i e s were experienced with the s e t t i n g of the proton channel d i s c r i m i n a t i o n l e v e l . One i n v o l v i n g the o p e r a t i o n of the Time P i c k o f f U n i t at low d i s c r i m i n a t i o n l e v e l s , and the other a r i s i n g from the use of h i g h count r a t e s ; 1) the u n i t (ORTEC model 260) tended t o m u l t i t r i g g e r when the d i s c r i m i n a t i o n was set below a l e v e l corresponding to about 3 Mev f o r our experimental c o n f i g u r a t i o n . In t h i s case, f o r each incoming p u l s e or p a r t i c l e d e t e c t e d , a t r a i n of p u l s e s of d e c r e a s i n g amplitude was produced. 2) a number of spurious counts were produced below the " c u t - o f f " s e t t i n g of the d i s c r i m i n a t i o n l e v e l when hig h proton r a t e s were used, t h e i r t o t a l number being l e s s than 10 J of the counts i n the f u l l energy peak. For the measurements presented i n S e c t i o n 4- of Chapter 5 the t o t a l number of counts i n t h i s r e g i o n f o r the d i f f e r e n t t a r g e t s used (Au, Cu, Fe) agreed w i t h i n s t a t i s t i c s . S i n c e the o p e r a t i o n of the "time p i c k o f f " u n i t s i s dependent on the r i s e time of the c u r r e n t p u l s e at the anode of the phototube, i t was d i f f i c u l t t o c a l i b r a t e the d i s c r i m i n a t o r s e t t i n g s as a f u n c t i o n of energy w i t h a f a s t p u l s e r . The c a l i b r a -. - 135 -t i o n was t h e r e f o r e obtained by producing a continuous proton energy d i s t r i b u t i o n . A number of aluminum f o i l s , 12 x 10~ 3 cm t h i c k , stacked i n a "wedge" arrangement were placed i n f r o n t of the proton d e t e c t o r . Enough c l e a r area was l e f t so the 15.8 Mev peak could be seen, i n order t o d e f i n e the energy s c a l e . The f o i l s produced a reasonable counting r a t e of protons with e n e r g i e s d i s t r i b u t e d between very low energies and the f u l l energy peak. A m u l t i c h a n n e l a n a l y s e r was gated i n c o i n c i d e n c e with the output of the "Time p i c k o f f " u n i t so t h a t the c u t - o f f at the d i s c r i m i n a t o r l e v e l could be seen i n the energy spectrum. The r e s u l t i s presented i n F i g u r e 4.13. The l a c k of l i n e a r i t y was c h a r a c t e r i s t i c of a l l the "Time p i c k - o f f " u n i t s used i n our l a b o r a t o r y . The e r r o r bars i n the energy values correspond to the u n c e r t a i n t y i n the experimental d e t e r m i n a t i o n of the channel at which the d i s c r i m i n a t o r c u t - o f f o c c u r r e d . - 136 -5 . PERFORMANCE & CONCLUSIONS. 1 . General: i n t r o d u c t i o n . The d e t a i l s of the method of a p p l y i n g the "A s s o c i a t e d p a r t i c l e t echnique" to the measurements of proton t o t a l r e a c -t i o n c r oss s e c t i o n s were d i s c u s s e d i n Chapter 3. In Chapter 4 the a c t u a l experimental set-up was d e s c r i b e d . In t h i s chapter the performance of the system i s presented, t o g e t h e r with t h e d i s c u s s i o n of measurements f o r p a r t i c u l a r t a r g e t s . Measurements were performed f o r r e a d i l y a v a i l a b l e t a r g e t s of n a t u r a l copper, n a t u r a l i r o n and g o l d , with the aim of t e s t i n g the u s e f u l n e s s of the technique. 2 . The a s s o c i a t e d beam p r o f i l e . Knowledge of the angular d i s t r i b u t i o n of the a s s o c i a t e d beam of protons, or beam p r o f i l e , i s necessary t o determine i f g e o m e t r i c a l c o r r e c t i o n s are r e q u i r e d i n the e l a s t i c c o r r e c t i o n of the type d e s c r i b e d i n s e c t i o n 4 . 1 . 1 of Chapter 3. Measurements of the a t t e n u a t i o n as a f u n c t i o n of the angular and v e r t i c a l p o s i t i o n s of the s o l i d s t a t e d e t e c t o r assembly were, as mentioned i n S e c t i o n 2 . 2 of Chapter 4, used to p o s i t i o n i t . These measurements were a l s o used to o b t a i n the angular p r o f i l e of the a s s o c i a t e d proton beam. 4 A change i n the angular p o s i t i o n of the He d e t e c t o r can be t r a n s l a t e d (using the data of F i g u r e 3.7) i n t o the corresponding s h i f t i n the angular p o s i t i o n of the proton beam. A s i m i l a r technique can be employed f o r the v e r t i c a l p o s i t i o n . The observed r a t i o : f = M (D1D2)/(number \[e) = M (D1D2 ) / J M ( D 1 D 2 ) + M ( D 1 D 2 ) | or f = ( l + S ) _ 1 ( 5 . 1 ) - 137 -0 VERTICAL HORIZONTAL —I 1 i 1 j r. 1 1 1 1 +S° +6° +4° +2° 0° -2° -4° -6° -8° A N G L E F R O M B E A M . C E N T E R J Figure 5.1 : Associated proton beam p r o f i l e . - 138 -obtained from the data of F i g u r e s 4.2 and 4.3 i s t h e r e f o r e a measure of the a s s o c i a t e d proton beam i n t e n s i t y over an angular i n t e r v a l of approximately 3 . 4 ° (as d e f i n e d by the proton c o l l i m a t o r s i z e ) . These r e s u l t s are presented i n F i g u r e 5.1, and show t h a t more than 90$ of the c o i n c i d e n t proton beam i s contained i n the r e g i o n between 0 ° and 4 ° from the ce n t e r o f the beam. (The assymetry observed i n the f i g u r e f o r the h o r i z o n t a l p r o f i l e was produced by a change of heavy i c e t a r g e t t h i c k n e s s d u r i n g t h a t p a r t i c u l a r r u n ) . T h i s angular spread was found to be s u f f i c i e n t l y s m a l l so t h a t no s i g n i f i c a n t c o r r e c t i o n was r e q u i r e d i n the t a r g e t e l a s t i c s c a t t e r i n g c o r r e c t i o n . For t h i s reason a d e t a i l e d q u a n t i t a t i v e measurement of the p r o f i l e shape was not performed. An example of the extent of such a c o r r e c t i o n f o r " the ease of protons i n copper where the e l a s t i c c o r r e c t i o n " i s of the order of 5 5 mb ( 8 3 ° to 180° ) would l e a d f o r a 4 ° change i n the d i r e c t i o n of i n c i d e n c e and assuming R u t h e r f o r d s c a t t e r i n g f o r s i m p l i c i t y , t o a m o d i f i c a t i o n i n t h i s v a l u e ' o f the order of 1 mb. T h i s value i s n e g l i g i b l e as compared t o the cross s e c t i o n s measured of the order of 900 mb. 3. The a n t i c o i n c i d e n c e background. , 3.1. The primary beam parameters. To check f o r p o s s i b l e e f f e c t s of very s h o r t p e r i o d 3 He beam i n s t a b i l i t i e s t h a t were not detected by o b s e r v i n g t h e beam p e r i o d i c a l l y , measurements were made under extreme f o c u s -i n g c o n d i t i o n s . By means of the quadrupole l e n s e s and s t e e r i n g magnets the beam was focused i n t o e i t h e r a sharp h o r i z o n t a l or - 139 -a sharp v e r t i c a l l i n e and moved ac r o s s the c o l l i m a t o r a p e r t u r e s . W i t h i n the 10$ s t a t i s t i c a l e r r o r s , the a n t i c o i n c i d e n c e back-ground was independent of the f o c u s i n g c o n d i t i o n s . Normally the beam was focused so as to have a cross s e c t i o n l a r g e r than the c o l l i m a t i n g a p e r t u r e s and a roughly uniform c u r r e n t d e n s i t y across i t . The a n t i c o i n c i d e n c e background was a l s o measured f o r two d i f f e r e n t c o l l i m a t o r a p e r t u r e diameters (1/8 and 1/16 I n c h e s ) . The l a r g e r a p e r t u r e , as d e s c r i b e d i n Appendix I, permitted l a r g e r beam c u r r e n t s , and so h i g h e r counting r a t e s . No depen-dence was found i n the a n t i c o i n c i d e n c e background, agai n w i t h i n the s t a t i s t i c a l e r r o r s of 10$. 3.2. The heavy i c e t h i c k n e s s . No dependence, to 10$, was found i n the a n t i c o i n c i -dence background as a f u n c t i o n of the heavy i c e t a r g e t t h i c k -ness f o r the range of t h i c k n e s s e s employed i n t h e measurements. Only when the t h i c k n e s s exceeded about 3 times t h a t used d u r i n g the measurements, d i d a r i s e i n the a n t i c o i n c i d e n c e background occur. 3 . 3 . The p l a s t i c s c i n t i l l a t o r . S i n c e p l a s t i c s c i n t i l l a t o r s have been used by other workers, a measurement of the t o t a l a t t e n u a t i o n background, u s i n g our system, was performed f o r t h i s s c i n t i l l a t o r as a f u r t h e r check of the o v e r a l l o p e r a t i o n . P o l l o c k and Schranlc (Po 65a) f o r example, obtained an a t t e n u a t i o n value o f : £> - 5.00 x 10~ 3 (5.2) - 140 -f o r 17 Mev protons when t h e i r d i s c r i m i n a t i o n l e v e l was set i n the v a l l e y at approximately 3 .3 Mev below the e l a s t i c peak. T h i s i s i n the r e g i o n between the low energy t a i l of the e l a s t i c peak and the c o n t r i b u t i o n s from I n e l a s t i c s c a t t e r i n g t o the 4 . 4 3 Mev l e v e l of 1 2 C . For our measurements a p l a s t i c s c i n t i l l a t o r was s u b s t i t u t e d f o r the C s l c r y s t a l and the a t t e n u a t i o n measured f o r the 15.8 Mev a s s o c i a t e d protons. The d i s c r i m i n a t i o n l e v e l was chosen t o be i n the same energy r e g i o n as that used by P o l l o c k and Schrank. The value obtained f o r the a t t e n u a t i o n was: § = ( 5 . 0 0 1 .13) x I O " 3 ( 5 . 3 ) The h i g h e r bombarding'energy used by P o l l o c k and Schrank would be expected to i n c r e a s e t h i s value by: A 8 = ( . 6 0 1 .05) x 1 0 " 3 ( 5 . 4 ) T h i s estimate i s based on the t o t a l r e a c t i o n c r o s s s e c t i o n f o r carbon obtained by P o l l o c k and Schrank. Adding the values g i v e n by ( 5 . 3 ) and ( 5 . 4 ) we o b t a i n : £ = ( 5 . 6 0 1 .18) x IO" 3 ( 5 . 5 ) S i n c e P o l l o c k and Schrank d i d not a s s i g n any experimental e r r o r to t h e i r value, the agreement of ( 5 . 2 ) and ( 5 . 5 ) w i t h i n 10% i s considered a s a t i s f a c t o r y check of the o v e r a l l o p e r a t i o n of our system. 3 . 4 . The C s l d e t e c t o r . As p r e v i o u s l y d i s c u s s e d i n S e c t i o n 4 . 2 of Chapter 3> of the r e a d i l y a v a i l a b l e s c i n t i l l a t o r s , C s l i s the most convenient due t o i t s low background c o n t r i b u t i o n . - 141 -The dependence of the a t t e n u a t i o n i n the C s l as a f u n c t i o n of the d i s c r i m i n a t o r l e v e l was estimated f o r I5.8 and 14 .8 Mev protons from t o t a l r e a c t i o n c r o s s s e c t i o n data f o r neighbouring n u c l e i , assuming t h a t the (p,n) r e a c t i o n s dominate. These r e s u l t s were presented In F i g u r e 3.17-For the experimental c o n f i g u r a t i o n used, the energy of the protons i n c i d e n t on the C s l s c i n t i l l a t o r i s 14 .8 Mev a f t e r t r a v e r s i n g the sample. S i n c e the a t t e n u a t i o n i n the C s l i s a f u n c t i o n of the proton energy an a c c u r a t e measurement of the sample a t t e n u a t i o n r e q u i r e s e i t h e r an a c c u r a t e knowledge of the dependence of the C s l a t t e n u a t i o n as a f u n c t i o n of energy, or the use of a comparison t a r g e t of the same energy t h i c k n e s s as the sample under i n v e s t i g a t i o n , whose cross s e c t i o n s are w e l l known. For the r e f e r e n c e sample a gold f o i l was chosen because i t c o n t r i b u t e s an a t t e n u a t i o n lower than most other f o i l s and was r e a d i l y a v a i l a b l e i n the d e s i r e d t h i c k n e s s . A t t e n u a t i o n measurements were performed f o r both the bare C s l s c i n t i l l a t o r (15.8 Mev protons) and with the gold f o i l (3.617 x l O - 3 cm t h i c k ) i n f r o n t of i t (14 .8 Mev p r o t o n s ) , y i e l d i n g the f o l l o w i n g v a l u e s : ^ C s l ^ 1 5 ' 8 M e v ) = ( 1 9 ' 7 - -5). x 1 0 " 4 ' ( 5- 6) £ C s I ( l 4 . 8 Mev) + = (18.97 1 .23) x l O " 4 (5.7) For both measurements the d i s c r i m i n a t o r l e v e l was set on the f l a t r e g i o n of the curves i n F i g u r e 3.17, at approximately 10 Mev. - 142 -(5.6) c a n b e c o m p a r e d w i t h t h e e s t i m a t e d v a l u e f r o m F i g u r e 3.17 o f : & ^ 0 (15.8 M e v ) = 19.2 x I O " 4 (5.8) OS x f o r 15.8 Mev p r o t o n s i n C s l . T h e a g r e e m e n t b e t w e e n (5.6) a n d (5.8) ( i n t h e 2.5$ o r d e r ) I s c e r t a i n l y b e t t e r t h a n i s w a r r a n t e d b y t h e a s s u m p t i o n s i n v o l v e d i n t h e e s t i m a t e d v a l u e . D i r e c t c o m p a r i s o n o f t h e e x p e r i m e n t a l v a l u e (5.7) w i t h t h e e s t i m a t e d , a t t e n u a t i o n f o r 14.8 Mev p r o t o n s I n C s l c a n n o t b e d i r e c t l y p e r f o r m e d . T h e e x p e r i m e n t a l v a l u e i n c l u d e s t h e c o n t r i b u t i o n a r i s i n g f r o m t h e e l a s t i c s c a t t e r i n g a n d r e a c t i o n s t h a t t a k e p l a c e I n t h e g o l d f o i l . T h e c l o s e a g r e e m e n t b e t w e e n (5.6) a n d (5.8) i s f e l t t o j u s t i f y t h e u s e o f t h e e s t i m a t e d v a l u e s f o r t h e d e p e n d e n c e o f t h e a t t e n u a t i o n i n C s l o n t h e p r o t o n e n e r g y t o a n a c c u r a c y o f 5$, o v e r t h e s m a l l e n e r g y r a n g e (15.8 t o 14.8 M e v ) I n v o l v e d . W i t h t h e g o l d f o i l i n p o s i t i o n t h e a t t e n u a t i o n was m e a s u r e d a s a f u n c t i o n o f t h e d i s c r i m i n a t i o n l e v e l a s I l l u s -t r a t e d I n F i g u r e 5 .2. A d e t e r m i n a t i o n o f t h e a t t e n u a t i o n i n C s l f o r 14.8 Mev p r o t o n s a s a f u n c t i o n o f t h e d i s c r i m i n a t i o n l e v e l c a n b e o b t a i n e d b y s u b t r a c t i n g f r o m t h i s c u r v e t h e c o n -t r i b u t i o n a r i s i n g f r o m t h e g o l d f o i l . A s i s i n d i c a t e d i n T a b l e 5.1 o f t h i s C h a p t e r t h e e s t i m a t e d c h a n g e i n t h e a t t e n u a t i o n f o r C s l b e t w e e n 15„8 Mev p r o t o n s a n d 14.85 Mev ( a s d e f i n e d b y t h e e n e r g y t h i c k n e s s o f t h e g o l d f o i l ) i s : A £ * h e o = (3.17 t .16) x i o " 4 (5.9) L> S I - 143 -Figure 5.2 : Attenuation background as a function o f the d i s c r i m i n a t i o n l e v e l . - 144 -w h e r e t h e u n c e r t a i n t y i s g i v e n b y t h e 5$ l e v e l d e t e r m i n e d a b o v e . T h e u s e o f ( 5 . 6 ) , (5-7) a n d (5-9) e n a b l e s u s t o e s t i -m a t e t h e a t t e n u a t i o n a r i s i n g f r o m t h e g o l d f o i l . T h a t I s , w h e r e : (5.10) (5.11) f r o m (5.6) a n d (5.7) w e o b t a i n : A&'= (.73 t .55) x 10" 4 (5.12) T h u s , £ A u = (2.44 t .58) x 10" 4 (5.13) I f o n e a s s u m e s t h a t t h e m a j o r c o n t r i b u t i o n t o t h e r e a c t i o n c r o s s s e c t i o n i n G o l d a r i s e s f r o m ( p , n ) r e a c t i o n s , t h e n t h e m e a s u r e d a t t e n u a t i o n f o r g o l d w o u l d b e I n d e p e n d e n t o f t h e d i s c r i m i n a t i o n l e v e l . T h u s t h e a t t e n u a t i o n c o n t r i b u t e d b y t h e C s l ( a t 14 . 8 5 M e v ) a s a f u n c t i o n o f t h e d i s c r i m i n a t o r l e v e l w o u l d , o n t h i s b a s i s , b e o b t a i n e d b y s u b t r a c t i n g t h e c o n s t a n t v a l u e (2.44 1 .58). x 1 0 " 4 g i v e n b y (5.13). I n t h i s w a y t h e p o i n t s s h o w n a s t r i a n g l e s i n . F i g u r e 5.2 w e r e o b t a i n e d . T h e e x p e r i m e n t a l e r r o r b a r s h a v e b e e n a s s i g n e d t o t h e m e a s u r e d v a l u e s m i n u s t h e c o n t r i b u t i o n f r o m g o l d , i n o r d e r , t o c o m p a r e t h e m w i t h t h e e s t i m a t e d c u r v e s h o w n b y t h e f u l l l i n e . T h i s c u r v e i s t h e s a m e a s t h a t p r e s e n t e d i n F i g u r e 3.17. I n g e n e r a l t h e a g r e e m e n t i s g o o d , w i t h t h e e x p e r i m e n t a l p o i n t s s l i g h t l y a b o v e ( a p p r o x i m a t e l y 8 $ ) . t h e e s t i m a t e d v a l u e s . T w o r e g i o n s o f l a r g e d i s c r e p a n c i e s w i t h t h e m e a s u r e d v a l u e s a r e o b s e r v e d , o n e f o r d i s c r i m i n a t i o n l e v e l s b e l o w 3 M e v - 145 -and t h e o t h e r f o r s e t t i n g s above 1 1 Mev. The sha rp i n c r e a s e i n t h e e x p e r i m e n t a l v a l u e s above 1 1 Mev c o r r e s p o n d s t o t h e low energy t a l l o f t h e e l a s t i c peak s t a r t i n g t o be i n c l u d e d be low t h e s e t t i n g o f t he d i s c r i m i n a t o r . The p o s s i b i l i t y o f an i n c r e a s e i n t h e a t t e n u a t i o n a t l ow e n e r g i e s a r i s i n g f r om b a c k s c a t t e r i n g i n t h e C s l d e t e c t o r was c o n s i d e r e d . A f r a c t i o n o f t h e p r o t o n s i n c i d e n t on t h e d e t e c t o r w i l l be b a c k s c a t t e r e d out o f t h e d e t e c t o r l e a v i n g i n i t o n l y a p o r t i o n o f t h e i r t o t a l e n e r g y . A computer program was w r i t t e n t o p e r f o r m t h i s c a l c u l a t i o n by as suming R u t h e r f o r d s c a t t e r i n g f r om t h e Cs and I n u c l e i . The energy spec t rum a r i s i n g f r om b a c k s c a t t e r i n g was t h e n c a l c u l a t e d and f ound t o y i e l d a peak a t about 3 Mev, but w i t h an a t t e n u a t i o n . _A. o f a t l e a s t an o r d e r o f magn i tude t o o low ( . 1 x , 1 0 ) t o e x p l a i n t h e d i v e r g e n c y between t h e measured and e s t i m a t e d a t t e n u a t i o n s "at 3 Mev. T h i s d i s c r e p a n c y , a t 3 Mev, appea r s i n t h e same energy r e g i o n o f d i s c r i m i n a t i o n s e t t i n g s as t h a t o f m u l t i -t r i g g e r i n g o f t h e "T ime P i c k o f f " u n i t f o r a s i n g l e i n p u t p u l s e (See S e c t i o n 4 . 2 o f Chap te r 4 ) . I t i s assumed t h a t i n t h i s r e g i o n t h e u n i t f a i l s t o t r i g g e r p r o p e r l y f o r t h e low energy p r o t o n s and so g i v e s r i s e t o a c o n s t a n t d e t e c t e d a t t e n u a t i o n f o r d e c r e a s i n g d i s c r i m i n a t i o n l e v e l . The t endency o f t h e e x p e r i m e n t a l p o i n t s t o l i e above t h e e s t i m a t e d v a l u e s , i n t h e r e g i o n f r om 4 t o 9 Mev, c o u l d r e f l e c t t h e p r e s e n c e o f a s i g n i f i c a n t c o n t r i b u t i o n t o t h e t o t a l r e a c t i o n c r o s s s e c t i o n f o r g o l d f r om o t h e r t h a n (p ,n ) p r o c e s s e s . F o r a l l subsequent measurements , t he d i s c r i m i n a t i o n - 146 -l e v e l was set at around 10 Mev, i n the f l a t p o r t i o n of the curve of F i g u r e 5 .4. The reasons f o r t h i s s e t t i n g are d i s c u s s e d i n S e c t i o n 4. 3 .4.1 . L a t t i c e e f f e c t s . The "Rotary Assembly" d e s c r i b e d i n S e c t i o n 2.5 of Chapter 4 was employed t o measure the a n t i c o i n c i d e n c e background as a f u n c t i o n of the C s l c r y s t a l o r i e n t a t i o n with ..respect to the a s s o c i a t e d proton beam. Using Laue's back r e f l e c t i o n method (Cu 60) the o r i e n -t a t i o n of the £ 1,1,l3 a x i s of the C s l c r y s t a l l a t t i c e was found to be at an angle of 14° with the c r y s t a l s u r f a c e . X-Ray r a d i a t i o n from molybdenum was used. R e f e r r i n g back t o F i g u r e 4 . 8 , the angle was made equal t o 14° and the c r y s t a l r o t a t e d 3 6 0 & , i n 36° s t e p s , around the a x i s k. The a n t i c o i n c i d e n c e background was independent of the o r i e n t a t i o n of the C s l l a t t i c e w i t h i n a 10$ s t a t i s t i c a l e r r o r . Thus, f o r the experimental arrangement used d u r i n g a t t e n u a t i o n measurements, the a t t e n u a t i o n background due to the proton d e t e c t o r i s assumed to be independent of changes i n the angular d i s t r i b u t i o n of protons i n c i d e n t on the C s l c r y s t a l s c i n t i l l a t o r . No q u a n t i t a t i v e measurements of the m i c r o c r y s t a l s i z e s , or l a t t i c e e f f e c t s were performed f o r the samples used. 4. T o t a l proton r e a c t i o n c r o s s s e c t i o n measurements. In S e c t i o n 4.2.2 of Chapter 3 two d i f f e r e n t p o s s i b i l i -t i e s f o r performing a t t e n u a t i o n measurements were d i s c u s s e d . The - 147 -f i r s t i nvolved s e t t i n g the d i s c r i m i n a t i o n l e v e l i n ' t h e proton channel as,low as i s compatible w i t h the noise of the system. This method e s s e n t i a l l y e l i m i n a t e s the problem of c o r r e c t i n g f o r the v a r i a t i o n i n a t t e n u a t i o n with energy i n the f u l l - e n e r g y d e t e c t o r . On the other hand i t r e q u i r e s d e t a i l e d knowledge of i n e l a s t i c s c a t t e r i n g and (p,q) cross s e c t i o n s f o r the sample to be measured. A m o d i f i c a t i o n of t h i s method employing an a d d i t i o n a l counter to y i e l d an improved geometry and b e t t e r energy r e s o l u -t i o n has r e c e n t l y been described by D i c e l l o et a l (Di 6 6 ) . They are capable by these means of ac h i e v i n g measurements of t o t a l proton r e a c t i o n cross s e c t i o n s to 2% - 3 $ . In the second case, using high s e t t i n g s of the d i s c r i -mination l e v e l (below the e l a s t i c peak) d e t a i l e d knowledge of (p,p') and (p,q) cross s e c t i o n s f o r the sample are l e s s important, but r e q u i r e a background c o r r e c t i o n due to the change i n i n c i d e n t energy of the protons i n t o the C s l d e t e c t o r . The geometry used i n the present experiment i s imposed by the nature of the proton beam inherent to the technique. I t s angular divergency r e q u i r e s a l a r g e angle to be subtended by the proton det e c t o r i n order to make an accurate e l a s t i c s c a t t e r i n g c o r r e c t i o n f o r the sample to be measured. The l a r g e angle i s a l s o r e q u i r e d In order to have a low c o n t r i b u t i o n to the atte n u -a t i o n background due to proton s c a t t e r i n g i n the heavy i c e backing f o i l . S i g n i f i c a n t i n e l a s t i c c o r r e c t i o n s i n the sample' a t t e n u a t i o n w i l l only occur f o r t h i s l a r g e angle when a low d i s c r i m i n a t i o n l e v e l i s used. Because of l a c k of d e t a i l e d experimental data on angular - 1 4 8 -d i s t r i b u t i o n s of n o n - e l a s t i c c r o s s s e c t i o n s the d i s c r i m i n a t i o n l e v e l was set j u s t below the e l a s t i c peak. As mentioned b e f o r e , t h i s Introduces the n e c e s s i t y of c o r r e c t i n g the a t t e n u a t i o n background f o r the change i n the proton energy o c c u r r i n g at the proton d e t e c t o r when a sample i s i n s e r t e d . By n o r m a l i z i n g the measurements t o a comparison t a r -get of the same energy t h i c k n e s s as the sample, i . e . " d i f f e r e n c e " measurements, the values so obtained are Independent of the energy dependence of the a t t e n u a t i o n i n the C s l d e t e c t o r . In a d d i t i o n , the comparison t a r g e t can be chosen t o be a m a t e r i a l of l a r g e dE/dx (e.g. gold) f o r which the a t t e n u a t i o n r e s u l t i n g f o r the same energy t h i c k n e s s i s approximately h a l f of t h a t f o r Copper, Iron, e t c . T h e r e f o r e i f a c c u r a t e " d i f f e r -ence" measurements are performed, the u n c e r t a i n t i e s i n the a b s o l u t e values c h a r a c t e r i z i n g the v a r i o u s samples would be approximately h a l f of the u n c e r t a i n t y In the a b s o l u t e determina-t i o n of the comparison t a r g e t . Measurements were performed f o r r e a d i l y a v a i l a b l e t a r -gets of n a t u r a l copper and n a t u r a l i r o n i n a d d i t i o n to those f o r gold t h a t were d i s c u s s e d i n S e c t i o n 3 .4. The c h a r a c t e r i s t i c s of the t a r g e t s used are presented i n Table 5.1. In row #1 the t h i c k n e s s i s g i v e n as determined by weighing the t a r g e t s , the quoted e r r o r a r i s e s from determining the s u r f a c e area f o r the t a r g e t s ( t a r g e t s dimension : 2 inches d i a m e t e r ) . Row #6 g i v e s the estimated change i n the C s l a t t e n u a t i o n due to the decrease, i n pro t o n energy (from 15.8 Mev) by the energy l o s s g i v e n i n row #5. The u n c e r t a i n t i e s assigned In row #6 correspond t o the 5$ value d i s c u s s e d i n S e c t i o n 3-4. - 149 TABLE 5.1 Ch a r a c t e r i s t i c s of the d i f f e r e n t targets # TARGET GOLD COPPER IRON 1 Thickness 10" 3 cm 3.617 1 .002 4.998 + .0025 5.674 ! .003 2 -2 Molecules . cm x 10 21.340 42.283 48.124 3 Stopping Power nn-15 2 x 10 ev-cm 4.45 (Wh 58) 2.1 (Wh 58) 1.95 (Wh 58) 4 Stopping Power MeV cm * 262.6 177.9 165.4 5 Energy loss by 15.8 MeV protons MeV .950 .889 .939 6 Estimated A6 i n Csl ( x 10" 4) -3.17 + .16 -2.97 t .15 -3.13 + .16 - 150 -4.1. Summary of r e s u l t s f o r g o l d . The value of the a t t e n u a t i o n obtained f o r gold (5.13) (2.44 i .58) x 10~ 4 i s an a b s o l u t e measurement of i t s a t t e n u a t i o n . The l a r g e u n c e r t a i n t y a r i s e s from the u n c e r t a i n t y i n the depend-ence of the C s l a t t e n u a t i o n w i t h energy. The h i g h s e t t i n g s of the d i s c r i m i n a t o r assure a value f o r g o l d p r a c t i c a l l y independent of n o n - e l a s t i c c o n t r i b u t i o n s . For the same geometry the i n e l a s t i c c o r r e c t i o n f o r copper and i r o n r e p r e s e n t s an a t t e n u a t i o n of the order of .15 x 1 0 " 4 . Since the l a r g e r Coulomb b a r r i e r f o r gold would be expected to f u r t h e r i n h i b i t charged p a r t i c l e emission i n f a v o r of neutron emission, g i v i n g r i s e t o a s m a l l e r c o n t r i b u t i o n than t h a t of copper Or i r o n , which i s a l r e a d y of such magnitude to be w i t h i n the experimental u n c e r t a i n t y , a more q u a n t i t a t i v e estimate f o r g o l d was not attempted. The c o r r e c t i o n a r i s i n g from e l a s t i c s c a t t e r i n g o u t s i d e the d e t e c t o r angle was c a l c u l a t e d by g e n e r a t i n g the angular d i s t r i b u t i o n u s i n g the O p t i c a l Model program SCAT 4 mentioned In Chapter 1. Experimental values f o r the s c a t t e r i n g of protons from gold i s a v a i l a b l e f o r 17 Mev protons (Da 56). T h i s data has been f i t t e d w i t h O p t i c a l Model p o t e n t i a l s by a number of a u t h o r s . The p o t e n t i a l s obtained by G l a s s g o l d and K e l l o g (GI 57) were chosen because they f i t the l a r g e angle e l a s t i c s c a t t e r i n g d a t a . These a n g l e s , between 83° and 180°, are the ones r e q u i r e d f o r the c o r r e c t i o n . In order t o account f o r the lower.proton energy the r e a l p o t e n t i a l was i n c r e a s e d by the energy dependence of the "Perey p o t e n t i a l " (See Chapter 1 eq. (1 .4) , .55 E ) . The imaginary p a r t was decreased a c c o r d i n g to the g e n e r a l t r e n d of - 151 -t h i s p o t e n t i a l w i t h i n c i d e n t proton energy f o r heavy n u c l e i . (Ho 63,p. 105). The values of the parameters used f o r the p o t e n t i a l were: V = 61.3 Mev a = .55 f (5.14) - - / W = 7.2 Mev r = 1.23 f o w i t h both the r e a l and imaginary p a r t s having the same Saxon-Woods r a d i a l dependence. The c r o s s s e c t i o n s obtained were: E l a s t i c s c a t t e r i n g ; Q.theo ^ _ l g Q ^ = ^ ^ * (5.15) Reactions ; CT^ h e° = 768 mb R For the t h i c k n e s s of gold used t h i s g i v e s r i s e t o t h e o r e t i c a l a t t e n u a t i o n s o f : %lheo = . 5 2 X 1 0 " 4 r theo . _A-4 (5.16) & R = 1.64 x 10 or a t o t a l value o f : = 2.16 x I O " 4 (5.17) The value so obtained i s 13$ s m a l l e r than the e x p e r i -mental value but w i t h i n the experimental e r r o r . The f i n a l r e s u l t f o r gold i s presented t o g e t h e r w i t h the r e s u l t s f o r copper and i r o n i n TABLE 5 . 2 . 4.2.. Measurements f o r copper and i r o n . A summary of r e s u l t s i s presented i n TABLE 5 . 2 . Measurements were obtained by a l t e r n a t i n g e i t h e r copper or i r o n w i t h the gold comparison t a r g e t . In t h i s way a l l values could be checked f o r c o n s i s t e n c y with each other d u r i n g the run and - 152 -TABLE 5.2 Experimental r e s u l t s # TARGET GOLD COPPER IRON 1 Measured 6 x 10" 4 18.97 i .23 21.05 1 .25 21.09 t .28 2 6 C £.lS.8MeV)-A6 x 10" 4 16.53 t . .53 16.73 + .53 16.57 1 .53 3 Sample attenuat. x 10" 4 2.44 .58 4.32 ! .58 4.52 i .58 4 Measured cross section mb 1143 t 272 1022 + 137 939 ± 121 5 E l a s t i c correc-t i o n mb , 242 ± 24 53 * 5 46 t 5 6 I n e l a s t i c correc-t i o n mb 34 ± 7 32 i 7 7 Total reaction cross section mb 901 t 274 1003 i 138 925 1 122 8 Uncertainty % 30 14 14 - 153 -systematic d e v i a t i o n s , i f present, d e t e c t e d . The a n t i c o i n c i d e n c e counting r a t e was 20 per minute f o r 3 He beam c u r r e n t s of the order of .15 J J . A . T h i s r e p r e s e n t s a counting time between 3 and 4 hours f o r the approximately 1$ s t a t i s t i c a l u n c e r t a i n t y i n the t o t a l a t t e n u a t i o n obtained (sample plu s background). The e l a s t i c c o r r e c t i o n s were c a l c u l a t e d by i n t e r p o l a t i n g , w i t h the h e l p of the o p t i c a l model, the experimental e l a s t i c s c a t t e r i n g data of Dayton and Schrank (Da 56) f o r copper and i r o n at 17 Mev; t h a t of Koike et a l (Ko 65), f o r 14 .6 Mev protons i n copper; and t h a t of K i k u c h i et a l ( K i 59) f o r 14 .6 Mev protons i n i r o n . An u n c e r t a i n t y of 10$ was assigned t o the r e s u l t i n g c o r r e c t i o n s . The i n e l a s t i c c o r r e c t i o n s were c a l c u l a t e d from the r e s u l t s of Cohen et a l (Co 59) f o r 14 .6 Mev protons i n copper and i r o n . Prom the measured c r o s s s e c t i o n at 90° the c o n t r i b u t i o n o o i n t o the angles between 83 and 180 was obtained by assuming i s o t r o p y i n the angular d i s t r i b u t i o n . From the same r e f e r e n c e , u s i n g the r e l a t i v e i n t e n s i t y of the i n e l a s t i c protons as a f u n c t i o n of t h e i r energy, the f r a c t i o n of the cr o s s s e c t i o n f o r i n e l a s t i c s c a t t e r i n g i n t o the d e t e c t o r angle with e n e r g i e s above the d i s c r i m i n a t i o n l e v e l of 9-5 Mev was ob t a i n e d . An u n c e r t a i n t y of 20$ was assigned t o these v a l u e s . No c o r r e c t i o n s a r i s e from such processes as (p,d), (p,t) or ( p , % e ) . T h e i r l a r g e n e g a t i v e Q-values r e s u l t i n the f i n a l p a r t i c l e of any of these r e a c t i o n s , i f present, being d e t e c t e d with e n e r g i e s below the d i s c r i m i n a t i o n l e v e l and, thus recorded as an a n t i c o i n c i d e n c e count. On the other hand (p, He) - 154 -r e a c t i o n s have a p o s i t i v e Q-value but t h e i r c ross s e c t i o n s are estimated to be only 20% of those f o r i n e l a s t i c s c a t t e r i n g on the b a s i s of measurements a t 10 Mev (Be 61) and were not con-s i d e r e d i n d e t a i l . Based on the d i s c u s s i o n of S e c t i o n 4 . 1 .1 of Chapter 3> c o r r e c t i o n s due to compound e l a s t i c s c a t t e r i n g were, considered n e g l i g i b l e . 4 . 3 . . " D i f f e r e n c e " measurements. The l a r g e errors^ a s s o c i a t e d w i t h the r e a c t i o n c r o s s s e c t i o n measurements l i s t e d i n TABLE V . 2 a r i s e mainly from the u n c e r t a i n t y i n the c o r r e c t i o n i n v o l v e d i n the C s l a t t e n u a t i o n . I t i s p o s s i b l e , : n e v e r t h e l e s s , t o o b t a i n from the experimental data, values f o r the " d i f f e r e n c e s " i n a t t e n u a t i o n s between samples. For samples of the, same energy t h i c k n e s s d i f f e r e n c e s between measured a t t e n u a t i o n s are independent of the C s l a t t e n u a t i o n . For the case of equal energy t h i c k n e s s , the measured a t t e n u a t i o n d i f f e r e n c e between t a r g e t s A and B i s g i v e n by: D- ^ - £ B « N f t c f t - N b c r B ( 5 # 1 8 ) 2 A where i s the number of atoms per cm of t a r g e t A, and CT i n d i c a t e s the c r o s s s e c t i o n f o r t a r g e t A as measured, without c o r r e c t i o n s . We w i l l c o n s i d e r t a r g e t B as being a comparison t a r g e t . By adding and s u b t r a c t i n g Q* from the f i r s t term of e q u a t i o n ( 5 . 1 8 ) : D - N ^ ( o - A _ c r ^ 4 - ^ ( H A - N O ( 5 . 1 9 ) - 155 -Prom here, an e x p r e s s i o n f o r the d i f f e r e n c e between the measured -cross s e c t i o n s of sample A and B i s ob t a i n e d . Thus, <\T*-cr a) - D Sift' + 0 " B ( N A N ^ - 1 ) (5.20) The e r r o r a s s o c i a t e d w i t h t h i s value has two d i f f e r e n t o r i g i n s . The f i r s t term c o n t r i b u t e s a c e r t a i n e r r o r a r i s i n g from the a t t e n u a t i o n measurements f o r the two samples A and B. The e r r o r c o n t r i b u t e d by the second term depends on the uncer-t a i n t y i n qr f o r the g i v e n experimental geometry m u l t i p l i e d by the value of the f a c t o r between b r a c k e t s . I f the comparison t a r g e t i s chosen so t h a t the f a c t o r i n the second term i s l e s s " than u n i t y the u n c e r t a i n t y t r a n s m i t t e d to the " d i f f e r e n c e " , value w i l l decrease a c c o r d i n g l y . B We must emphasize here t h a t the value of . 0 * used i n equation (5.18) Is the cr o s s s e c t i o n a p p r o p r i a t e t o the sample B f o r the geometry used i n the ^ A and measurements. The r e s u l t s of a p p l y i n g equation (5.18) to the measured a t t e n u a t i o n s f o r g o l d , copper and i r o n a re presented i n TABLE 5 .3. The e f f e c t of removing the u n c e r t a i n t y i n the change of the C s l a t t e n u a t i o n can be seen. Although l a r g e r e l a t i v e e r r o r s a re pre s e n t , they are s m a l l e r than f o r the d i f f e r e n c e s obtained d i r e c t l y from the a b s o l u t e values of TABLE 5.2. These d i f f e r e n c e s are presented f o r comparison purposes i n row #4 of TABLE 5.3. In the d i f f e r e n c e s (Cu -Au) and (Pe - Au) the major c o n t r i b u t i o n t o the e r r o r a r i s e s from the l a r g e e r r o r i n the measurement f o r g o l d . A d i r e c t comparison of the d i f f e r e n c e s w i t h the work of other authors i s l i m i t e d by the l a c k of an - 156 -TABLE 5.5 Measured differences # DIFFERENCE Copper - Gold Iron - Gold Iron - Copper 1 D x 10" 4 1.88 t .34 2.08 t .36 .20 ! .38 2 Measured differe n c e mb - 121 * 157 - 204 ± 169 - 83 t 81 3 Corrected difference mb 102 1 160 24 + 172 - 78 i 82 4 Differences from TABLE 5.2 mb 102 ± 307 24 * 300 - 78 + 185 5 g O* of compari-son target mb 901 i 274 901 i 274 1003 t 138 TABLE 5.4 Tota l reaction cross sections generated from differences # TARGET GOLD COPPER IRON 1 768 936 866 1 mb i 77 + . 126 i 125 2 Uncertainty 10 14 14 % - 157 -a c c u r a t e measurement f o r gold i n t h i s energy range. For the purpose of comparison, a b s o l u t e values f o r copper and i r o n were generated from the measured d i f f e r e n c e s by u s i n g as the c r o s s s e c t i o n f o r gold t h a t obtained from an o p t i c a l model f i t to the e l a s t i c s c a t t e r i n g data, as d e s c r i b e d i n S e c t i o n 4 . 1 . In g e n e r a l , when an o p t i c a l model p o t e n t i a l i s optimized f o r a p a r t i c u l a r t a r g e t , bombarding energy and p a r t i c l e , an o v e r a l l f i t to b e t t e r than 10$ i s o b t a i n e d . Thus, a 10$ u n c e r t a i n t y was assigned to the t h e o r e t i c a l c r o s s s e c t i o n s quoted i n ( 5 . 1 5 ) . The value f o r a i n equation ( 5 . 1 8 ) i s then taken as (1010 _t 101) mb. To the r e s u l t i n g c o r r e c t e d d i f f e r e n c e s the t h e o r e t i c a l v alue f o r the r e a c t i o n c ross s e c t i o n f o r gold was added, (768 i 77) mb. These r e s u l t s are presented i n T a b l e 5 . 4 . In t h i s case both c o n t r i b u t i o n s to the u n c e r t a i n t i e s , the e r r o r i n the experimental d e t e r m i n a t i o n of the a t t e n u a t i o n d i f f e r e n c e s and t h a t of the a b s o l u t e value i n O" are comparable In magnitude. 5 . C o n c l u s i o n s . The r e s u l t s l i s t e d In Table 5 . 2 have been p l o t t e d i n F i g u r e 5.3 t o g e t h e r with measurements by other authors i n the same energy range. The values f o r s i n g l e i s o t o p e s by D i c e l l o et a l (Dl 6 6 ) , are presented as a f u n c t i o n of t h e i r mass numbers. The r e s u l t s of P o l l o c k et a l (Po 65a) and of the present work are p l o t t e d at the mass values c o r r e s p o n d i n g to the n a t u r a l t a r g e t s . Although the agreement Is good, the l a r g e experimental e r r o r s i n our r e s u l t s make t h i s comparison l e s s s i g n i f i c a n t . 1100-o H 1000• C_) CO CO CO o CJ 900-o I—I E-< •J o H 800-l i A 54 55 I 56 I Fe 57 I 58 63 I 64 I Cu 65 Cn 00 • D i c e l l o et a l (Di 66) 14.6 MeV tg Pollock and Schrank (Po 65a) 16.4 MeV A Present work 15.8 MeV Figure 5.3 : Comparison of the r e s u l t s f o r i r o n and copper with other, measurements i n the same energy range. - 159 -The v a l u e s o b t a i n e d f r om t h e " d i f f e r e n c e " measurements ( T a b l e 5 . 4 ) a r e not more s i g n i f i c a n t t h a n t h e a b s o l u t e v a l u e s ( Tab l e 5 . 2 ) due t o t h e i r comparab le e r r o r s . I f an e x p e r i m e n t a l v a l u e f o r t he c r o s s s e c t i o n s f o r g o l d becomes a v a i l a b l e i n t h i s energy r ange w i t h a r e l a t i v e e r r o r o f 5 $ , t h e e r r o r s quoted i n T a b l e 5 . 4 w i l l d e c r e a s e t o t h e 1 0 $ l e v e l . The r e m a i n i n g u n c e r -t a i n t y i s due t o t h e s t a t i s t i c a l e r r o r s i n the ' e x p e r i m e n t a l d e t e r m i n a t i o n o f t h e a t t e n u a t i o n d i f f e r e n c e s , and c o u l d , o f c o u r s e , be r educed w i t h l o n g e r r u n n i n g t i m e s o r improvements i n c o u n t i n g r a t e . A u s e f u l a p p l i c a t i o n o f t h e " d i f f e r e n c e ' m e a s u r e m e n t s i s t o t h e s t u d y o f i s o t o p e s o f t h e same n u c l e u s . I n t h i s c a s e , and f o r t a r g e t s o f t h e same energy t h i c k n e s s , t h e second t e rm i n e q u a t i o n ( 5 . 2 0 ) becomes n e g l i g i b l e . Thus , t h e s o l e s o u r c e o f e r r o r i n t h e measured " d i f f e r e n c e " v a l u e i s t h e s t a t i s t i c a l u n c e r t a i n t y i n t h e d e t e r m i n a t i o n o f D. I n a d d i t i o n , t h e e l a s t i c c o r r e c t i o n t o t h e measured v a l u e , t o o b t a i n t h e r e a l " d i f f e r e n c e " , w i l l be v e r y s i m i l a r f o r a l l i s o t o p e s . T h e r e f o r e , a c c u r a t e mea-surements o f t h e d i f f e r e n c e s between t h e t o t a l p r o t o n r e a c t i o n c r o s s s e c t i o n o f d i f f e r e n t i s o t o p e s o f t h e same n u c l e u s w o u l d be r e a d i l y o b t a i n a b l e f r om t h e e x p e r i m e n t . These measurements a r e e x p e c t e d t o p r o v i d e u s e f u l i n f o r m a t i o n on t he dependence o f t h e o p t i c a l model p o t e n t i a l w i t h t h e number o f n e u t r o n s . The p rob l em o f d e c r e a s i n g t h e e x p e r i m e n t a l e r r o r s o f t h e a b s o l u t e v a l u e s by t h i s t e c h n i q u e i s d i f f e r e n t . A more com-p l e t e knowledge o f t h e dependence o f t h e C s l a t t e n u a t i o n w i t h ene rgy w i l l be r e q u i r e d . - 160 -With the present experimental arrangement the l i m i t t o the counting r a t e i s imposed by the l a r g e background of non-c o i n c i d e n t protons present i n the proton d e t e c t o r . As can be i n f e r r e d from F i g u r e 4.12 the maximum counting r a t e a f t e r the "dead time gate" = l6yms) occurs f o r an i n c i d e n t proton f l u x of about 70 x 1 0 3 a " 1 . The r a t i o of c o i n c i d e n t to non-coincident proton r a t e s i s determined by the angle subtended by the proton d e t e c t o r at the c e n t e r of the heavy i c e t a r g e t . T h i s angle i s chosen so t h a t the s c a t t e r i n g of the a s s o c i a t e d p r o t o n beam i n the heavy i c e backing f o i l does not c o n t r i b u t e s i g n i f i c a n t l y t o the a t t e n u a -t i o n background ( S e c t i o n 4.1 Chapter 3 ) . As mentioned In S e c t i o n 1 of Appendix Ljwe were u n s u c c e s s f u l i n u s i n g s e l f -s u p p o r t i n g f i l m s of deuterated p o l y e t h y l e n e i n s t e a d of the heavy i c e t a r g e t . T h i s would have r e s u l t e d i n e l i m i n a t i o n of the backing f o i l and thus i n a l a r g e r e d u c t i o n of the s c a t t e r i n g s u f f e r e d by the a s s o c i a t e d proton beam. Recent developments i n our l a b o r a t o r y i n c o n n e c t i o n with deuterated p o l y e t h y l e n e t a r g e t s p r o v i d e the p o s s i b i l i t y of primary t a r g e t s w i t h p r a c t i c a l l y no backing f o i l . ( O l i v o , p r i v . comm.) I f the s c a t t e r i n g of the a s s o c i a t e d proton beam can be reduced by removing th'e backing f o i l j t h e angle subtended by the proton d e t e c t o r can be reduced a c c o r d i n g l y . In a d d i t i o n s f o r an energy t h i c k n e s s of 100 keV f o r 650 keV ^He, approximately 2.5 times more deuterium atoms would be a v a i l a b l e a t the source t a r g e t than i n the case of heavy i c e . The angle subtended by the proton d e t e c t o r c o u l d , then, be reduced to an angle, compatible w i t h the Inherent angular - 161 -divergency of the a s s o c i a t e d proton beam of approximately 3 ° f o r 100 Kev range of s e l e c t e d He e n e r g i e s . ( F i g u r e 3 . 1 0 ) . The i n c r e a s e i n the r a t i o of c o i n c i d e n t t o non-coin-c i d e n t protons p l u s the l a r g e r :number of deuterium atoms a v a i l a b l e a t the primary t a r g e t could p r o v i d e an i n c r e a s e by at l e a s t a f a c t o r of 4 i n the. c o i n c i d e n t counting r a t e t r a n s -m i t t e d through the dead time gate. T h i s i n c r e a s e i n counting r a t e w i l l r e s u l t i n h a l f the experimental e r r o r s of the d i f -f e r e n c e measurements f o r the same running time. As mentioned b e f o r e , i f a b s o l u t e measurements t o 5$ become a v a i l a b l e f o r a comparison t a r g e t the i n c r e a s e i n accuracy would r e s u l t i n f i n a l e r r o r s f o r the a b s o l u t e values obtained from the d i f f e r e n c e measurements of about 5 $ . For the improvement of the accuracy i n the d i r e c t measurement of a b s o l u t e v a l u e s , a more d e t a i l e d a n a l y s i s would have t o be made of the experimental set-up. In order t o use low d i s c r i m i n a t i o n l e v e l s ^ f o r which measurements w i l l be i n -dependent of the v a r i a t i o n s of the C s l a t t e n u a t i o n w i t h energy, an improvement i n the geometry of the system w i l l be r e q u i r e d . Although a geometry as the one employed by D i c e l l o et a l (Di 66) would h e l p to decrease the otherwise l a r g e i n e l a s t i c c o r r e c t i o n s , the i n h e r e n t angular divergency Of the a s s o c i a t e d p r o t o n beam makes i t s u s e d i f f i c u l t . T h i s angular divergency could be reduced t o approximately 1 . 5 ° hy d e c r e a s i n g the range of 4 s e l e c t e d He energie s with the consequent l o s s i n counting r a t e . An a l t e r n a t i v e approach would Involve a more complete I n v e s t i g a t i o n of the C s l s c i n t i l l a t o r . A d i r e c t measurement of the proton r e a c t i o n c ross s e c t i o n s f o r C s l , u s i n g t h i n c r y s t a l s - 162 -commercially a v a i l a b l e , could be attempted. The l a c k of s c a t -t e r i n g data w i l l n e v e r t h e l e s s make d i f f i c u l t the e x t r a c t i o n of the c r o s s s e c t i o n from the raw experimental data. Complementary i n f o r m a t i o n could be obtained from the dependence of the a n t i c o i n c i d e n c e background i n C s l as a f u n c -t i o n of low d i s c r i m i n a t i o n l e v e l s . In t h i s r e g i o n the shape of the curve i s s e n s i t i v e to the (p,n) cross s e c t i o n s . The r e s u l t s presented i n t h i s t h e s i s i n d i c a t e the u s e f u l n e s s of the technique d e s c r i b e d . Although the e r r o r s c h a r a c t e r i z i n g the measurements performed i n t h i s work are l a r g e r than those quoted by other workers i n t h i s f i e l d , t h e ever present p o s s i b i l i t y of s y s t e m a t i c e r r o r s f o r any t e c h -nique means that measurements by a v a r i e t y of techniques i s p a r t i c u l a r l y important f o r a s s e s s i n g the o v e r a l l accuracy of such a measurement. In a d d i t i o n , a number of improvements are, suggested, by means of which i t should be p o s s i b l e t o decrease the experimental e r r o r a s s o c i a t e d w i t h t h i s technique to about 5 $ . - 163 -APPENDIX I CONSIDERATIONS IN THE DESIGN OF THE HEAVY ICE TARGET 1 . The t a r g e t . I n o r d e r t o o b t a i n i n t h e l a b o r a t o r y t h e r e a c t i o n 3 , .A ^ He(d ,p ) He i t i s c l e a r l y more c o n v e n i e n t t o employ an i n c i d e n t 3 He beam on a d e u t e r i u m t a r g e t . I t i s d i f f i c u l t t o make a % e t a r g e t o f t h e t h i c k n e s s r e q u i r e d i n t h i s e xpe r imen t and , i n a d d i t i o n , t h e n e u t r o n backg round a s s o c i a t e d w i t h d e u t e r o n beams makes w o r k i n g i n t h e e x p e r i m e n t a l a r e a s u n n e c e s s a r i l y d i f f i c u l t . A r e v i e w o f t h e d i f f e r e n t t y p e s o f d e u t e r i u m t a r g e t s used f o r n e u t r o n p r o d u c t i o n i s a v a i l a b l e i n t h e l i t e r a t u r e (See Ma 63, C hap te r 4 . D ) . They a r e : D g0 i c e , D 2 o c l u d e d i n m e t a l s (Zr o r T i ) and gas t a r g e t s . As f a r as t h i s e xpe r imen t i s conce rned t h e DgO i c e t a r g e t s seem t o be t h e more advan tageou s . The o c l u d e d t a r g e t s p r e s e n t t h e p rob l em o f t h e t h i c k m e t a l l a y e r , o f h i g h Z, t h a t wou ld p roduce l a r g e s c a t t e r i n g i n t h e seconda r y beam. A s i m i l a r s i t u a t i o n a r i s e s f r om t h e windows i n a gas t a r g e t , p l u s t h e f a c t t h a t t h e d e n s i t y o f d e u t e r i u m n u c l e i f o r T>2 gas (NTP) i s t h r e e o r d e r s of magn i tude s m a l l e r t h a n f o r i c e . Even more c o n v e n i e n t t h a n t h e heavy i c e t h i n l a y e r , t h a t r e q u i r e s a good t h e r m a l c o n d u c t o r b a c k i n g , a r e t h e s e l f -s u p p o r t i n g f i l m s o f " d e u t e r a t e d " p o l y e t h y l e n e . The ma in c o n t r i b u t i o n t o s c a t t e r i n g f r om t h e t a r g e t i t s e l f w i l l t h e n 12 a r i s e f r om t h e C n u c l e i i n t h e p o l y e t h y l e n e . The p r e p a r a t i o n t e c h n i q u e o f t h e s e t a r g e t s has undergone some deve lopment i n ou r l a b o r a t o r y (Tr 67). T r i a l r un s i n t h e sy s tem d e s c r i b e d i n C h a p t e r 4, have shown t h a t t a r g e t s o f t h e d e s i r e d t h i c k n e s s , ( i . e . 100 KeV f o r 65O KeV H e ) , c an not however , w i t h s t a n d t h e - 164 -beam c u r r e n t s necessary to o b t a i n cross s e c t i o n s measurements i n a reasonable running time. 2. Power d i s s i p a t i o n . As a r e s u l t of the c o n s i d e r a t i o n s of S e c t i o n 1 the t a r g e t was chosen to be a t h i n l a y e r of heavy i c e . I f the DgO i c e temperature r i s e s above 173°K, however, the t a r g e t v a p o r i z e s r e l a t i v e l y q u i c k l y (Ma 63 p. 6 8 5 ) . I t i s t h e r e f o r e convenient to b u i l d the i c e l a y e r on a good heat conductor h e l d a t l i q u i d n i t r o g e n temperatures. We w i l l r e f e r to the t a r g e t backing as to the "backing f o i l " . The a b i l i t y to conduct away the i n c i d e n t beam power and s t i l l m a i n t a i n the heavy i c e temperature below 1 7 3 °K i s not the only requirement f o r the backing f o i l , however. As d i s c u s s e d i n S e c t i o n 4 . 2 . 1 . of Chapter 3* the t h i c k n e s s of the backing f o i l must a l s o be chosen t a k i n g i n t o account the a n t i c o i n c i d e n c e background. The heat to be d i s s i p a t e d by the backing f o i l i s g i v e n by the 1 0 0 KeV energy l o s s i n the i c e l a y e r p l u s the energy l o s s i n the f o i l i t s e l f . In order t o estimate a maximum value f o r the temperature r i s e of the heavy i c e t a r g e t , the f o l l o w i n g approximate model was c o n s i d e r e d . I t i s assumed t h a t the f i r s t 1 0 0 Kev of energy l o s s are d e p o s i t e d at the f r o n t of the i c e l a y e r . T h i s energy i s then conducted away as heat, i n the d i r e c t i o n of the i n c i d e n t beam, acro s s the l a y e r of i c e and i n t o the backing f o i l . From t h e r e , t h i s heat p l u s t h a t deposited i n the f o i l i t s e l f i s r a d i a l l y d i s s i p a t e d towards the l i q u i d n i t r o g e n c o n t a i n e r . T h i s i s s c h e m a t i c a l l y i l l u s t r a t e d i n F i g u r e - 165 -A I . l , where a beam of diameter 'd' i s i n c i d e n t at the cente r of a backing f o i l of diameter *D1 and t h i c k n e s s 'L' h e l d i n contact with a l i q u i d n i t r o g e n r e s e r v o i r at i t s outer edge. The arrows i n d i c a t e the assumed d i r e c t i o n f o r the heat f l o w . Conduction through the t h i n i c e l a y e r p a r a l l e l t o the*, beam d i r e c t i o n o n l y , and not r a d i a l l y i n the i c e , i s j u s t i f i e d by the much l a r g e r thermal c o n d u c t i v i t y of the f o i l . The c a l c u l a t i o n w i l l be d i v i d e d i n t o t h r e e d i f f e r e n t p a r t s : the temperature r i s e a c r o s s the i c e l a y e r A T l , the r a d i a l dependence of the temperature f o r r a d i i s m a l l e r than the beam r a d i u s A T2, and the temperature r i s e between the beam diameter and the backing f o i l outer diameter ZSkT3. The equation f o r heat conduction i s : 9-.- A T ^ t LT' ( A l . l ) where AT i s the temperature r i s e a c r o s s a m a t e r i a l with thermal c o n d u c t i v i t y ^ , area 'a', t h i c k n e s s 'L', and 'Q' the heat i n c a l o r i e s conducted i n time ' t ' . The c o n v e r s i o n f a c t o r from Mev to c a l o r i e s and f o r 1 yuA i s : 1 MeV j x A ' 1 s " 1 = . 2 3 9 9 c a l s " 1 ^ A - 1 ( A I . 2 ) In the c a l c u l a t i o n s two i n c i d e n t beam diameters w i l l be c o n s i d e r e d : CASE I : d = . 3 1 8 cm ( 1 / 8 i n c h e s ) : CASE I I : d = . 1 6 cm ( 1 / 1 6 i nches) 7? d 2 / 4 = 8 x 1 0 " 2 cm 2 H d 2 / 4 = 2 x 1 0 " 2 cm 2 The value f o r the thermal c o n d u c t i v i t y , 3 , f o r normal i c e can be c a l c u l a t e d at 1 7 3 K t o be: 8 x 1 0 ~ 3 c a l d e g " 1 s - 1 cm" 1 - 166 -L Liquid N i i r o ^ e n Figure A I . l : Source target power d i s s i p a t i o n . - 167 -(Po 65). Prom ( A I . l ) and ( A I . 2 ) , we get the temperature r i s e a c ross the i c e l a y e r i n the d i r e c t i o n of the i n c i d e n t beam us i n g the value of 'L' g i v e n by 3.7: CASE I : T = 2 x 10" 2 deg ^ A _ 1 (AI.3) CASE I I : T = 8 x 10" 2 deg ^A" 1 In order to c a l c u l a t e A .T2, we d e f i n e a heat d e n s i t y : q = Q 4 / T I d 2 t (AI . 4 ) t h a t i s , the heat d e p o s i t e d by the beam per u n i t of area, and assumed constant a c r o s s the beam diameter. In c a l c u l a t i n g the values f o r A T2 and A T3 the amount of heat to be d i s s i p a t e d , Q / t , now i n c l u d e s the energy l o s s e s i n the f o i l . I t w i l l of course depend on the f o i l m a t e r i a l and i t s t h i c k n e s s . Copper was chosen as a backing m a t e r i a l because of i t s h i g h heat c o n d u c t i v i t y , ^ = 1.097 c a l deg" 1 s _ 1 cm - 1, at 113 K (Ha 60 p. 2433). Aluminum i s almost as good, having a c o n d u c t i v i t y of h a l f t h i s v a l u e , and i s b e t t e r from the p o i n t of view of s c a t t e r i n g of the proton beam. However the presence of an aluminum oxide l a y e r makes the conduction of heat i n t o the aluminum more d i f f i c u l t . For 'L' values s m a l l e r than the 3He range i n Cu a t 550 KeV, Q/t i s a f u n c t i o n of 'L'. The amount of energy, per i n c i d e n t 3He, d i s s i p a t e d i n the t a r g e t as a f u n c t i o n of 'L' i s p l o t t e d i n F i g u r e A I . 2 . For L = 0 the value of 100 KeV corresponds to the DgO i c e t h i c k n e s s . T h i s data i s obtained from the energy l o s s f o r protons i n Cu (Wh 58). Thus, i n the e x p r e s s i o n (AI . 4 ) f o r the heat d e n s i t y , Q/t i s a f u n c t i o n of - 168 -'L 1 and w i l l be i n d i c a t e d i n the f o l l o w i n g by the n o t a t i o n q(L) Equation ( A I . l ) may be r e w r i t t e n as: dT = - r dQ / ?l a t (AI . 5 ) where ' r ' i s the r a d i a l d i s t a n c e t o the c e n t e r of the t a r g e t , and a = 2 T) r L . In the r e g i o n f o r '2 r 1 l e s s than 'd', Q/t i s a l s o a f u n c t i o n of V . The amount of heat d i s s i p a t e d i n a r i n g 'dr' a t the r a d i u s ' r ' i s : dQ = 271 r q(L) dr ( A I . 6 ) R e p l a c i n g i n ( A I . 5 ) , dT = q ( l ) r dr / /\ Lt A T 2 * | cJT=(|(L) d 7 ^ t c 3 T d where Tc Is the temperature at the c e n t e r of the t a r g e t and Td the temperature a t r = d/2. I f we r e p l a c e the value g i v e n by (AI.4) f o r q(L) i n (AI.7): A T 2 = [ Q ( L ) / t ] /2-nL - T i ( A I > 8 ) For the r e g i o n D/2 ^ r ^ d/2 the amount of heat to be conducted i s j u s t Q(l_). R e w r i t i n g ( A I . l ) as: T (AI .9) ^ T 5 - f °AT , S ib) - 3 L XL L, -t >2T1 L d The maximum temperature r i s e w i l l be at the c e n t e r of the beam spot, on the f r o n t f a c e of the i c e l a y e r , and i s g i v e n by adding up (AI . 3 ) , . (AI .8) and (AI.9), A T ^ A T * + _ J : ( i + Gh 2.) ( A L I O ) - 169 -The second term of equation (AI .10) was s o l v e d f o r D = 1.27 cm (1/2 i n c h e s ) and f o r the two cases of 'd' mention-ed above. The values f o r Q ( L ) t - 1 are obtained from F i g u r e A I . 2 . The r e s u l t s of the c a l c u l a t i o n s are presented i n F i g u r e A I . 3 . The temperature r i s e at the c e n t e r of the heavy i c e t a r g e t per JJLA of i n c i d e n t beam c u r r e n t , i s g i v e n as a f u n c t i o n of the Cu backing f o i l t h i c k n e s s 'L 1 f o r the two i n c i d e n t beam diameters CASE I: d = .318 cm; CASE I I : d = .16 cm. 3. Energy s t r a g g l i n g and m u l t i p l e s c a t t e r i n g . The p a r t i c l e s corresponding to the a s s o c i a t e d and secondary beam, a r i s i n g from r e a c t i o n s t a k i n g p l a c e i n the primary t a r g e t , w i l l s u f f e r I n t e r a c t i o n s with t a r g e t m a t e r i a l i n t r a v e r s i n g i t . The importance of these e f f e c t s on the p r o t o n beam were d i s c u s s e d i n S e c t i o n 4 . 2 . 1 . of Chapter 3. T h e i r r e s u l t s on the secondary beam were presented i n s e c t i o n 4.2.4 of Chapter 3. Here the d e r i v a t i o n of the r e s u l t s i s d e s c r i b e d f o r an assumed t a r g e t t h i c k n e s s of 100 KeV f o r 650 Kev i n c i d e n t 3He. 3.1. Energy s t r a g g l i n g . . The v a r i a n c e Po of the energy t r a n s f e r per u n i t of path l e n g t h i s g i v e n by (B,o 15) ' ? 4 Po = 4 Tl z e N Z ( A l . l l ) where z and Z are the atomic numbers of the i n c i d e n t p a r t i c l e •a and t a r g e t n u c l e i and N i s the number of atoms per cm J i n the t a r g e t . In the case of D2O i c e the main c o n t r i b u t i o n to the - 170 -Figure AI.3 : Temperature r i s e at the center of the heavy i c e t a r g e t . - 171 -16 4 energy l o s s a r i s e s from the 0 atoms. For He p a r t i c l e s and 16 the value of N g i v e n i n (3.6) the value f o r 0 i s : Po = .28 MeV 2 cm" 1 (AI .12) For the D^O i c e t h i c k n e s s assumed, 4 , 6 6 x 10~^ cm, (see eq, 3.7) P = 1.30 x 1 0 " 5 MeV 2 (AI .13) 4 Thus the standard d e v i a t i o n i n the energy l o s s by the He beam i s : ( P o ) 1 / / 2 = 3.6 KeV ( A I . 1 4 ) a value much l e s s than the i n t r i n s i c r e s o l u t i o n of the 4He d e t e c t i o n system thus, s m a l l enough t o be n e g l e c t e d . 3.2. M u l t i p l e s c a t t e r i n g . The e f f e c t of m u l t i p l e s c a t t e r i n g i s c h a r a c t e r i z e d by the mean square s p a t i a l a n g l e , which i n the approximation of assuming a Gaussian d i s t r i b u t i o n i n angles i s g i v e n as (Di 53) (Ma 66): « > - e>z fcv (E t/E iV ( A I > 1 5 ) 4 K ) ^(2€)7(o2.- , / 2; where E i and Ef are the i n i t i a l and f i n a l e nergies of the s c a t t e r e d p a r t i c l e , (M/ m) i s the r a t i o of the mass of the s c a t t e r e d p a r t i c l e t o the mass of the e l e c t r o n , Z i s the atomic number of the s c a t t e r i n g n u c l e i , B i s d e f i n e d by the t r a n s c e n -d e n t a l equation: es g'_ fe7!o £ Z4'3 z ? ( A I . 1 6 ) A (!? ( 1 + 3 . 3 3 and y =  z z- / 1 ^ 7 p> - 172 -A i s the atomic weight.of the s c a t t e r i n g n u c l e i , e> the t h i c k -—2 ness of the s c a t t e r i n g media i n g cm" . C a l c u l a t i n g f o r 4He p a r t i c l e s i n l 6 0 , E i = 3.22 MeV, Ef = 3.12 Mev and c> = 5.17 x 1 0 " 5 g cm " 2 , we o b t a i n : And f o r the mean square angle: <<e^> - 21S x \ .cf B r a i 2 and f o r the standard d e v i a t i o n : <e^>' = 5.2 x io . 29° (A I . 1 7 ) S i n c e t h i s standard d e v i a t i o n from the o r i g i n a l d i r e c t i o n of emission i s much s m a l l e r than the angular range of 5 ° d e f i n e d by the energy window s e t t i n g s and the t a r g e t t h i c k n e s s , ( S e c t i o n 3.2 Chapter 3) t h i s m u l t i p l e s c a t t e r i n g e f f e c t can a l s o be n e g l e c t e d . h 4. A n t i c o i n c i d e n c e background due t o He s c a t t e r i n g . In S e c t i o n 4.2.4 of Chapter 3 was d i s c u s s e d the p o s s i b l e 4 c o n t r i b u t i o n t o the a n t i c o i n c i d e n c e background from those He p a r t i c l e s o r i g i n a l l y emitted i n d i r e c t i o n s other than the secondary beam d e t e c t o r , but s c a t t e r e d i n t o i t with ener g i e s i n the s e l e c t e d range. T h i s problem was analysed u s i n g the Van de Gr a a f f PDP-8 computer, as o u t l i n e d i n the f o l l o w i n g . I t was assumed t h a t a l l the s c a t t e r i n g a r i s e s from the " ^ 0 n u c l e i of the DgO molecules. Experimental data f o r the 4 16 e l a s t i c s c a t t e r i n g of He by 0 i s a v a i l a b l e f o r i n c i d e n t - 173 -energies between 2.4 and 3.9 Mev (Ca 53) and 3.7 t o 5.6 Mev (Mc 66). The secondary beam d e t e c t o r , the s o l i d s t a t e d e t e c t o r , was assumed to be at 9 6 . 2 ° w i t h r e s p e c t t o the i n c i d e n t 3He beam d i r e c t i o n , the c e n t e r angle f o r the secondary beam i n the case of " k i n e m a t i c a l c o l l i m a t i o n " of the a s s o c i a t e d proton beam. 4He p a r t i c l e s emitted with angles g r e a t e r than 96.2° w i l l a l r e a d y have energ i e s below the s e l e c t e d energy range of 3.17 to 3.27 Mev. Energy l o s s In l e a v i n g the t a r g e t or due t o r e c o i l i n g 0 n u c l e i w i l l f u r t h e r degrade them i n energy. 4 Thus, c a l c u l a t i o n s were performed f o r He emitted with angles s m a l l e r than 96.2 , angles f o r which the energy of emission i s above the s e l e c t e d range. Background events a r i s e from those p a r t i c l e s s c a t t e r e d i n t o the secondary beam d e t e c t o r which l o s e s u f f i c i e n t energy w h i l e t r a s v e r s i n g the t a r g e t t o be accepted by the energy window.-To o b t a i n an upper l i m i t f o r t h i s background c o n t r i b u -t i o n i t was assumed t h a t a l l 4He p a r t i c l e s were produced i n r e a c t i o n s t a k i n g p l a c e on the back f a c e of the i c e t a r g e t . T h i s i s j u s t i f i e d by the f a c t t h a t an energy l o s s by the 4He g r e a t e r than the one provided by the t h i c k n e s s of i c e i n the d i r e c t i o n of the secondary beam d e t e c t o r i s necessary f o r them to f a l l i n the s e l e c t e d energy range. •4 The angle of He emission was v a r i e d i n s t e p s , and f o r each angle the l a b o r a t o r y energy of i t was c a l c u l a t e d from the kinematics of the 3He(d,p) 4He r e a c t i o n . With the data of F i g u r e 4.6 the energy l o s s by the 4He In t r a s v e r s i n g the i c e - 174 -4 ta r g e t was c a l c u l a t e d . The energy of the He p a r t i c l e emerging i n the d i r e c t i o n of the secondary beam dete c t o r was checked to see i f i t f e l l i n t o the s e l e c t e d energy range. I f i t d i d , the f r a c t i o n of a l l the p a r t i c l e s o r i g i n a l l y emitted i n t o that angle of emission, i n c i d e n t i n the dete c t o r was obtained. In order to o b t a i n an upper l i m i t f o r the background c o n t r i b u t i o n , the n o r m a l i z a t i o n f a c t o r f o r each angle of emission was taken to be the s o l i d angle defined by the angular Increment ( i n the emission angle) i n t o the same hemisphere of the source t a r g e t plane where the detector was l o c a t e d . The r e s u l t s are presented i n Figure AI.4, f o r the se l e c t e d energy range from 3.13 to 3.31 Mev. This energy range i s that corresponding to the k i n e m a t i c a l c o l l l m a t i o n considered e a r l i e r plus 40 Kev i n each extreme i n order to take i n t o account p o s s i b l e indeterminations a r i s i n g from the energy r e s o l u t i o n i n the alpha d e t e c t i o n system. The p l o t shows the upper l i m i t of the a n t i c o i n c i d e n c e counts per jxA and per second a r i s i n g from k the s c a t t e r i n g i n t o the dete c t o r of He o r i g i n a l l y emitted i n other d i r e c t i o n s than that one of the secondary beam. The r e s u l t s i n d i c a t e c o n t r i b u t i o n to the background f o r ±\ 4 values of The angle of He emission i n the range: 9>l.2° A ^ 4= S><b.2° The proton d e t e c t o r subtends at l e a s t 10° t o each side of the, associated beam d i r e c t i o n to the nHe emitted i n t o 96.2 , i n order to prevent background due to the source t a r g e t backing f o i l . This causes the d e t e c t i o n of the protons associated w i t h the 4He p a r t i c l e s emitted i n t o 91 .2 °^ £ £ 93.7° > even though they do not belong to the wanted secondary beam. No c o n t r i b u t i o n - 175 -- 176 -to the a n t i c o i n c i d e n c e background w i l l then a r i s e from t h i s s c a t t e r i n g e f f e c t . - 177 -A P P E N D I X I I NATURAL F O C U S I N G . E v e n t h o u g h t h i s e f f e c t was n o t u s e d I n t h e p r e s e n t e x p e r i m e n t i t w i l l b e b r i e f l y d i s c u s s e d h e r e . I t c a n b e s e e n iT> F i g u r e 3 . 7 t h a t a c h a n g e A ^ i n t h e a n g l e o f e m i s s i o n o f t h e s e c o n d a r y beam c o r r e s p o n d s , d u e t o t h e 3 He i n c i d e n t e n e r g y b e i n g m u c h l e s s t h a n t h e Q - v a l u e o f t h e r e a c t i o n , t o a c h a n g e o f a n g l e f o r t h e a s s o c i a t e d b eam g i v e n b y : A Vp = — A | ( A I I . l ) T h i s i s t r u e f o r ^ = ^ = 80° T h e c o r r e l a t i o n b e t w e e n t h e a n g u l a r i n c r e m e n t s o f t h e r e a c t i o n p r o d u c t s d e s c r i b e d b y ( A I I . l ) c o u l d b e u s e d t o p r o d u c e f o c u s i n g o f t h e a s s o c i a t e d beam i n c a s e s w h e n a l a r g e p r i m a r y beam s p o t w i l l n o r m a l l y g i v e r i s e t o a d i s p e r s e d a s s o c i a t e d b e a m . A l a r g e s i z e o f t h e p r i m a r y b eam i s c o n v e n i e n t , t o a c h i e v e l o w d e n s i t y c u r r e n t s o n t h e p r i m a r y t a r g e t , f o r r e a s o n s m e n t i o n -e d w h e n d i s c u s s i n g t h e d e u t e r i u m t a r g e t ( S e e A p p e n d i x I ) . T h e e f f e c t o f a l a r g e s i z e o n t h e p r i m a r y beam i s i l l u s t r a t e d i n F i g u r e A I I . l , c a s e A - A ' „ T h e s o u r c e t a r g e t I s a s s u m e d t o b e p e r p e n d i c u l a r t o t h e i n c i d e n t b e a m d i r e c t i o n , a n d t h e beam s i z e i s p u r p o s e l y a u g m e n t e d t o I l l u s t r a t e t h e p o i n t . F o r a p o i n t s i z e s e c o n d a r y b eam d e t e c t o r , A, l o c a t e d a t ^ = 45 f r o m t h e i n c i d e n t b e am d i r e c t i o n , t h e c o r r e s p o n d i n g a s s o c i a t e d b e a m , A', i s w i d e l y d i s p e r s e d . B y o b s e r v i n g Figure A I I . l , t h e e f f e c t s o f t h e a n g u l a r c o r r e l a t i o n ( A I I . l ) c a n b e e a s i l y s e e n . T h e p a r t i c l e s o f t h e s e c o n d a r y beam e m i t t e d f r o m d i f f e r e n t s e c t o r s o f t h e p r i m a r y beam Figure A I I . l : Natural focusing e f f e c t . Figure A l l . 2 : Natural focusing i n conjunction with kinematical c o l l i m a t i o n - 179 -s p o t i n t o t h e s e c o n d a r y b e a m d e t e c t o r f o r m d i f f e r e n t a n g l e s ^ . F o r e a c h o n e o f t h e s e a n g l e s , a d i f f e r e n t a n g l e , V|> , o f e m i s s i o n f o r t h e a s s o c i a t e d p a r t i c l e w i l l b e s e l e c t e d . T h e c h a n g e i n a n g l e ^ g i v e n b y t h e c h a n g e i n ^ c a n e i t h e r c o n t r i -b u t e t o f u r t h e r d i s p e r s i o n o f t h e a s s o c i a t e d b e a m o r t o g i v e a t e n d e n c y . t o f o c u s i n g . W h i c h o n e o f t h e s e e f f e c t s i s p r e s e n t , i s g i v e n b y w h e t h e r b o t h r e a c t i o n p r o d u c t s a r e e m i t t e d i n t o t h e s a m e h e m i s p h e r e d e f i n e d b y t h e s o u r c e t a r g e t p l a n e , f o r f o c u s -i n g , o r i n t o d i f f e r e n t o n e s . F r o m F i g u r e 3.7 c a n b e s e e n t h a t a s o u r c e t a r g e t a n g l e | i t h a t s a t i s f i e s t h e f o c u s i n g c o n d i t i o n c a n b e f o u n d f o r a l l v a l u e s o f £ . W e w i l l r e f e r t o t h i s f o c u s i n g e f f e c t a s " n a t u r a l  f o c u s i n g " . B e s t " n a t u r a l f o c u s i n g " w i l l o c c u r f o r a s o u r c e t a r g e t a n g l e s u c h t h a t t h e a n g l e f o r m e d b y i t s p l a n e w i t h t h e d i r e c t i o n s d e f i n e d b y t h e a n g l e <^ a n d t h e c o r r e s p o n d i n g a n g l e *\y a r e t h e s a m e . I n F i g u r e , A I I . l , c a s e B - B ' i l l u s t r a t e s t h e f o c u s i n g e f f e c t s f o r ^ = | = 8 0 ° . F o r t h i s c a s e e q u a t i o n ( A I I . l ) I s e x a c t , a n d f o r a t a r g e t a n g l e o f |2> = 90° b e s t f o c u s i n g o c c u r s . T h u s , i n t h i s p a r t i c u l a r c a s e , t h e a s s o c i a t e d b e a m w i l l b e f o c u s e d a t a d i s t a n c e L ' f r o m t h e s o u r c e t a r g e t c e n t e r e q u a l t o t h e d i s t a n c e L f r o m t h a t c e n t e r t o t h e s e c o n d a r y b e a m d e t e c t o r . I f b e s t " n a t u r a l f o c u s i n g " i s t o b e u s e d i n c o n j u n c -t i o n w i t h " k i n e m a t i c a l c o l l i m a t i o n " o c c u r r i n g f o r ^ = 96.2 ° ( S e c t i o n 3.2 o f C h a p t e r 3)> t h e n t h e s o u r c e t a r g e t a n g l e m u s t b e (2> = 106.5° . T h i s c a s e i s i l l u s t r a t e d i n F i g u r e A l l . 2 . - 180 -N a t u r a l f o c u s i n g i s i n c o n s i s t e n t with s m a l l angular divergency. I t tends t o c a n c e l the e f f e c t s of the f i n i t e s i z e of the primary beam by a p p r o p r i a t e change i n the angle of emis-s i o n f o r the a s s o c i a t e d p a r t i c l e . Small angular divergency, on the other hand, means t h a t a l l a s s o c i a t e d p a r t i c l e s are emitted with approximately the same angle with r e s p e c t t o the i n c i d e n t beam d i r e c t i o n . A p a r a l l e l a s s o c i a t e d beam, with no angular divergency a r i s i n g from the f i n i t e s i z e of the primary beam, could be obtained f o r a d e t e c t o r angle equal t o the source; t a r g e t angle, as suggested by the diagrams. I t i s , of course, i m p o s s i b l e e x p e r i m e n t a l l y to d e t e c t the secondary beam under such c o n d i t i o n s . N e v e r t h e l e s s , the angular divergency of the a s s o c i a t e d beam due to the f i n i t e s i z e of the primary beam can a l s o be m i n i -mized by d e c r e a s i n g the angular spread on the secondary beam. T h i s can be achieved by l o c a t i n g the secondary beam d e t e c t o r , when p o s s i b l e , at a d i s t a n c e from the primary t a r g e t c e n t e r much l a r g e r compared with the primary beam s i z e . One of the d i f f i c u l t i e s i n making p r a c t i c a l use of " n a t u r a l f o c u s i n g " e f f e c t s i n the present experiment i s t h a t , i n order to be used i n c o n j u n c t i o n w i t h " k i n e m a t i c a l c o l l i m a t i o n " the i n c i d e n t beam must go through the backing f o i l of the primary t a r g e t . - 181 -APPENDIX I I I ELECTRONIC CIRCUITS. In t h i s appendix the d e t a i l e d c i r c u i t s of the l o c a l l y manufactured e l e c t r o n i c u n i t s , s t i l l i n use i n a s s o c i a t i o n with the experimental set-up d e s c r i b e d i n Chapter 4, are presented. The d i f f e r e n t u n i t s are mentioned i n the same order as t h a t of S e c t i o n 3 of Chapter 4. The S o l i d S t a t e D e t e c t o r P r e a m p l i f i e r i s a charge s e n s i t i v e one, an improved d e s i g n of one d e s c r i b e d by T.K. A l e x -ander ( A l 63). The c i r c u i t diagram i s presented i n F i g u r e (A3.1) The cascode input i s a combination of two 8056 n u v i s t o r s ( V i , V 2 ) connected i n p a r a l l e l , and a 2N70Q t r a n s i s t o r ( T l ) . The u n i t i s b i p o l a r and can d e l i v e r up to i 3 v o l t p u l s e s i n t o a 50 ohms l o a d . The e q u i v a l e n t n o i s e i s approximately g i v e n by: FWHM = (5.4 + 3.68 x I O - 2 C ± p F " 1 ) KeV (A3.1) where C i Is the c a p a c i t a n c e i n pF connected at the Input of the p r e a m p l i f i e r . E q u a t i o n (A3.1) does not take Into account n o i s e due to p o s s i b l e leakage c u r r e n t In the d e t e c t o r s . These r e s u l t s were measured as d e s c r i b e d by E. F a i r s t e i n (Fa 6 l ) u s i n g an RC a m p l i f i e r w i t h i n t e g r a t i o n and d i f f e r e n t i a t i o n time constants set at .8 j j j S . The r i s e time of the p r e a m p l i f i e r i s approximately g i v e n by: t r = (4.5 + .19 C± pF" 1) ns (A3.2) The Pulse Shaper c i r c u i t used to o b t a i n from the output of the p r e a m p l i f i e r the b i p o l a r p u l s e necessary f o r the zero c r o s s o v e r t r i g g e r i n g i s i l l u s t r a t e d i n F i g u r e A 3 .2 , with a zero c r o s s o v e r time of 500 ns. F i g u r e A3.1 : C i r c u i t diagram o f the low n o i s e change s e n s i t i v e p r e a m p l i f i e r . INPUT 2K V 5 0 1 5 0 0 p F I K . - T — O + 3 0 V 5.6K H H 2 0 0 0 8 0 0 n s 2.2K 2 N 7 0 3 1 5 K 3 . 3 K A V I K IK 57 . L N 7 6 7 .001 .001 O + 1 5 V 5.6K° 1 0 K + 1 5 V o 2 N 9 6 3 2 N 9 6 3 OUTPUT 7 K F i g u r e A 3 . 2 : C i r c u i t d i a g r a m o f p u l s e s h a p e r . -. 184 -T h e Z e r o C r o s s o v e r U n i t w h i c h i s b a s e d o n a d e s i g n b y T.K. A l e x a n d e r ( A l 63) i s i l l u s t r a t e d i n F i g u r e A3.3. T h e z e r o c r o s s o v e r p o i n t i s d e t e c t e d w i t h a S c h m i t t t r i g g e r (T1,T2) w i t h " h y s t e r e s i s " c o m p e n s a t i o n . P I i s a d j u s t e d s o t h a t m i n i m u m " w a l k " i s o b t a i n e d . O p t i m u m a d j u s t m e n t c o r r e s p o n d s t o a w a l k o f l e s s t h a n 10 ns. f o r a 10:1 r a n g e o f I n p u t s i g n a l s . T h e b a c k e d g e o f t h e o u t p u t ( w h i c h o c c u r s a t t h e c r o s s o v e r t i m e ) i s u s e d t o t r i g g e r a " F a s t t r i g g e r c i r c u i t " w h i c h p r o d u c e s a p u l s e 25 n s w i d e . T h e " F a s t t r i g g e r " i s b a s e d o n a d e s i g n b y G. J o n e s ( J o 63) a n d t h e c i r c u i t i s i l l u s t r a t e d i n F i g u r e A3.4. T h i s s h o r t " t i m i n g p u l s e " i s u s e d i n t h e f a s t g a t e s t o b e d e s c r i b e d b e l o w . T h e c i r c u i t d i a g r a m o f t h e P h o t o m u l t i p l i e r P r e a m p l i -f i e r i s I l l u s t r a t e d i n F i g u r e A 3 . 5 . I t d e l i v e r s a 10 n s r i s e t i m e a n d a b i p o l a r l i n e a r o u t p u t u p t o 1 6 v o l t i n t o a 50 ohm l o a d . T h e c i r c u i t d i a g r a m o f t h e F a s t C o i n c i d e n c e g a t e i s p r e s e n t e d i n F i g u r e A3.6. T h e t i m e r e s o l u t i o n f o r t h e 25 n s w i d e i n p u t p u l s e s was m e a s u r e d a s 5 0 n s . T h e o u t p u t o f t h e f a s t c o i n c i d e n c e g a t e c o n s i s t s o f a p u l s e 1 jxs l o n g g e n e r a t e d b y a t r i g g e r c i r c u i t o f t h e t y p e i n d i c a t e d i n F i g u r e A3.4 w i t h a v a l u e o f C = .005 p-F„ T h e c i r c u i t d i a g r a m o f t h e F a s t A n t i c o i n c i d e n c e g a t e i s i l l u s t r a t e d i n F i g u r e - A 3 . 7 . T h e o u t p u t a g a i n c o n s i s t s o f a I^ JLS w i d e p u l s e o b t a i n e d a s i n d i c a t e d f o r t h e f a s t c o i n c i d e n c e c i r c u i t . T h e c i r c u i t d i a g r a m o f t h e t w o s l o w c o i n c i d e n c e g a t e s i s i l l u s t r a t e d i n F i g u r e A 3 . 8 . + 3 0 V 5 6 0 + 2 0 V 1 5 0 5 0 I N P U T -11 1 O U T P U T » 2 . 2 K + 2 0 V + 1 0 V o 1 0 2 . 7 K 39 1 N 1 0 0 2 N 7 0 6 A 31 K I N P U T -»—IF 5 0 0 2 . 2 K 1 . 8 K < 2 N 9 6 3 C = 1 0 0 p F H I -+ 5 V o-W-1 N I 0 0 OA 1 0 -w-N 9 6 3 47K ^ 6 8 0 < O +30V 2 N 2 2 1 8 O U T P U T •o 270 4 7 K S . 2 7 0 F i g u r e A 3 . 3 : C i r c u i t d i a g r a m o f z e r o c r o s s o v e r t r i g g e r . F i g u r e A 3 . 4 : C i r c u i t d i a g r a m o f f a s t t r i g g e r . 5.6K TEST 2l > 10K ,05 INPUT (anode photomultipller) O +30V 2.2K _-. HH 2000 AA/ 6.8K IK 3K 0 + 15V 3.3K 2N705 >.1K < 00 Figure A3.5 : Circuit-Diagram of photomultiplier p r e a m p l i f i e r . O +30V INPUT GATING PULSE INPUT DC le v e l s 0 Q Fast AC gate 9.3V Dead time gate 16.0V 00 Figure A3.6 : C i r c u i t diagram of f a s t AC gates. O +30V 0A10 INPUT A © H h .01 50 2N963 H9V O-INPUT B ,01 50 00 00 BZY63 01 100 OUTPUT "7>> O +9V 3:5 Core: FX2237 Figure A3.7 : C i r c u i t diagram of fast C gate. 5.6K «<2.2K ^ 2.2* -O •sov 2N2218 2N221iN. OUTPUTS 270. INPUT A 0-ii4 50 > >150 2N1305 1N764 '10 50 .1 o) INPUT 2N1305 Single channel analyser •10 INPUT B -50 Figure A3.8 : C i r c u i t diagram of double slow C gates. - 190 -BIBLIOGRAPHY Alexander, private communication (1963). Arnolds and.Koertz, Congres. Intern, de Phys. Nucl., . Paris (1964) 136. Bargman, Phys. Rev. 75 (1949) 301; Rev. Mod. Phys. 21 (19,49) 488. . Barsch a l l , Phys. Rev, 86 (1952) 431. Bethe, Phys.. Rev. 47 (1935) 747. Bethe, Phys, Rev. 57 (1940) 1125, Benveniste, Booth and Mitchell., Phys. Rev. 123 (1961)" 18181 Bearpark,Graham, and Jones, Nuclear Instrum. Methods , 35 (1965) 235. ,. Bearpark., Graham and Jones, Nuclear Phys. 73 (1965) 206. Bergstrom and Domeij, Nuclear Instrum. Methods 43 (1966) 146 Blaser, Boehm, Marmier and Scherrer, Helv. Phys. Acta 24 (1951) 441. Bohr, P h i l . Mag. 30 (1915) 581.r Bohr, Nature (G.B.) 137 (1936) 344. Booth, H i l l , Price and Roaf, Proc. Phys. Soc. A70 (195,7) 863 Brown, Proc. Phys, Soc. A70 (1957) 351. B r e i t , Handbuch der Physik (Springer-Verlag, 1958). Brown and Haeberly, Phys.. Rev. 130 (1963) 1163, Burge, Nuclear Phys., 13 (1959) 511, Buck, Maddison and Hodgson, P h i l , Mag, 5 (1^ '6'0) 1181. Burge, p r i v a t e communication (1961). Bulman, Greenless and Sametband, Nuclear Phys. 69 (1965) 536. Cameron, Phys, Rev. 90 (1953) 839, Cassels and Lawson, Proc, Phys. Soc. A67 (1954) 125. Campbell, Fesbach, Porter and Weisskopf, Massachusetts I n s t i t u t e of Technology, Report 73 (I960).. - 191 -Co 59 Cohen and Rubin, Phys. Rev. 113 (1959) 579.-. Cu 60 C u l l i t y , Elements of X-ray D i f f r a c t i o n (Addison-Wesley Inc, 1960). Da 56 Dayton and Schrank,. Phys. Rev. 10 (1956) 1358-; Di 53 Dickson and Doddler, Rev. S c i . Instrum. 24 (1953) 428. Di 66 D i c e l l o , Igo and Roush, Proton T o t a l Reaction Cross Sections" •for 22 Isotopes of f i , Fe, Ni, Cu, Zn, 2r and Sri'.at 14*75 MeV Los Alamos Report LA-DC 8075 (1966). Di 66a Dickens, Phys.. Rev. 143 (1966) 758. E i 60 Eisberg, Yennie and Wilkinson, Nuclear .Phys. 18 (1960) 338. Er 65 Ernst, Von Brentano and Mayer-rKuckuk, Phys:. Letters 19 (1965) 41. Fa 61 F a i r s t e i n , IEEE Trans. Nuclear S c i . NS.-8: (1961) 129. . Fe 54 Fesbach, Porter and Weisskopf, Phys. Rev. 96 (1954) 448. Fe 54a Fermi, Nuovo Cimento 11 (1954) 407... Fe 55 Fermi, Nuovo Cimento Supplement 2 (1955) 17. Fe 55a Fernbach, Heckrotte and Lepore, Phys. Rev. 97 (1955) 1059. Fo 50 Ford and Bohm, Phys. Rev. 79 (1950) 745. Fo 61 Fox and A l b e r t , Phys. Rev. 121 (1961) 1779. Fr 62 Friedman and Weisskopf; N i e l s Bohr and the Development ef Physics (Pergamon Press, 1962). Fu 59 Fubmer, Phys. Rev; 116 (1959) 418. GI 57 Glassgold and Kellog, Phys. Rev..107 (1957). 1372. Gr 61 Greenless and J a r v i s , Proc. Phys. Soc.,.78-(1961) 1275. Gu 54 Gugelot, Phys. Rev ; 93 (1954) 425. Ha 52 Hansen and A l b e r t , Phys. Rev. 87 (1952) 366u Ha 60 Handbook of Chremislrry and Phywes 42 ed-; (Chemical Rubber i Publishing Co., 1960)v Ha 62- Hansen and A l b e r t , Phys. Rev. 128 (1962) 29-L. Ho 63 Hodgson, The O p t i c a l Model of E l a s t i c Scattering '<Cftcford Un i v e r s i t y Press, 1963). Ho 64 Hodgson, Congres Intern, de Phys. Nucl., Paris (1964) 258. - 192 -Holdeman and Thaler, Phys, Rev. Letters 14 (1965).81. Holdeman and Thaler, Phys. Rev. 139 (196S) JL186.. Hodgson, Canad. J . Phys. 45 (T967) 449.. Jones, Rev; S c i . Instrum. 34 (1963.) 938. . de Juren and Kunable, Phys. Rev. 77 (195B;) 606. Kikuchi, Kobayashi and Matsuda, J . Phys... Soc. Japan 14 (1959) 121 Koike, Maki, Matsuda, Mikumo,. Nagahara, Nanaka., Suzuki and Kikuchi, J . Phys, Soc. Japan 20 (1965) 679. Kunz, Phys. Rev. 88 (1952) 473. Lane, Rev, Mod.: Phys. 29 (1957) 191. Charged P a r t i c l e "Gross Sections, ed. :D. -' Smith-. Los Alamos ' Report LA-2424 (1961), Lane, Nuclear Phys, 35 (1962) 676. Lauritzen and Ajzenberg-Slove, Nuclear Phys~ 78 (1966) 13. Lindhard, Mat. ;Fys. Medd. Dan. Vid.. Selsk?. 34' (1965) 1. Lutz, Mason and Eccles, The Shape .of the Imaginary Nuclear O p t i c a l P o t e n t i a l . University; of C a l i f o r n i a Radiation Laboratory Report, UCRL'7501 (1963):. Marion and Fowler, Fast Neutron Phyglcs (interscience, 1963). Makino, Waddell and Eisberg, Nuclear. Phys. 68 (1965) .378. Marion and Zimmerman, M u l t i p l e Scattering ;of'Charged P a r t i c l e s ^ C a l i f o r n i a I n s t i t u t e of Technology Report,, October (1966). McDermott, Jones,. Smotrich and Benenson; Phys. Rev. 118 (1966) 175. Meyer and Hintz, Phys. Rev. Letters 5 (I960) 207. Melkanoff, Saxon, Sawada'and: Nodvik, Congres Intern, de Phys. Nucl. , Paris (1964) 4b'(I)/c 147, Nodvik, Intern. Conf. of Nucl. Phys. , F l o r i d a (1959) 16. Nodvik, Dyke and-Mel-kan-off, Phys. Rev. 125 (1962) 975. Nuclear Data Tables, Part 3 (1960), ed. J.B. Marion (National Academy of Sciences, National Research. Council 1960). - 193 -Oxley, Cartwright, Rouvina, Baskix., Kle i n , Ring and Skillman, Phys. Rev. 91 (1953) 419. Perey, Phys. Rev. 131 (1963) 745. Picard, Nuclear Phys-. 68 (1965) 153. Pounder, The Physics of Ice (Pergammon Press, 1965). , Pollock and Schrank, Phys. Rev. 140 (1965) 575. Pollock and Schutz, B u l l . Amer. Phys. Soc. 12 (1967) 112. Rosen, Beery, Goldhaber and Averbach, Ann. Phys. (U.S.A.) 34 (1965) 96. S c h i f f , Quantum Mechanics (McGraw H i l l Book Company,1955). Slaus and A l f o r d , Rochester University Report 8059 (1959). Sternheiner, Phys. Rev. 115 (1959) 137. Trippard and White, Rev. S c i . Instrum. 38 (1967) 435. Wenzel and Whaling, Phys. Rev. 87 (1952).499. Whaling, Handbuch der Physik (Springer-Verlag, 1958, rev. 1962). Wilkins and I go, 10 MeV Prtrton-'Regctloirffi Several Elements, University of C a l i f o r n i a Radiation Laboratory Report, UCRL-10281 (1962), and Phys. Letters 2 (1962) 342. Williamson and Boujot, CEA-2189 (1962). Williams, Phys. Today 17 (1964) 28. Williams, Timing with Photomultip t i e r s , Ortec-News, March (1967). Yamabe, Kondo, Yamazaki and T o i , J. Phys. Soc. Japan 13 (1958) 777. 

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