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Proposed study of the reaction, 7Li(3He,da)4He, with a time-of-flight scattering chamber. Mint, Edward Theodore 1970

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PROPOSED STUDY OF THE REACTION, 7Li( 3He,da)^He, WITH A TIME-OF-FLIGHT SCATTERING CHAMBER b y EDWARD T. MINT B.Sc, The U n i v e r s i t y of B r i t i s h Columbia, 1967 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department of PHYSICS We accept t h i s t hesis as conforming to the required standard r THE, UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1970. In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Physics  The University of British Columbia Vancouver 8, Canada i Date June 9. 1970. i i ABSTRACT The re a c t i o n , 7Li( 3He,da)^He, i s proposed to search f o r an asymmetry about the d i r e c t i o n of motion of 6 L i i n the breakup of the 4.57 MeV excited state of t h i s nucleus as an intermediate state. This follows a f t e r the discovery i n 1967 by Reimann et. a l . of such an asymmetry about the d i r e c t i o n of motion of 5 L i i n the breakup of the ground state of t h i s nucleus, as an intermediate state i n the r e a c t i o n , 6Li( 3He,pa) t +He. The purpose of these experiments i s to attempt some understanding of the three-body r e a c t i o n mechanisms i n -volved, and the manner i n which the various p a r t i c l e s are c o r r e l a t e d i n the intermediate s t a t e . The three-body kinematics of the re a c t i o n , ^Li( 3He,da) 4He were thoroughly investigated, and because of p a r t i c l e i d e n t i f i c a t i o n problems, a charged p a r t i c l e t i m e - o f - f l i g h t technique was proposed to d i s t i n g u i s h the emitted deuterons from alpha p a r t i c l e s . A 23 inch s c a t t e r i n g chamber was designed and constructed f o r t h i s and other work, and subsequently tested using the r e a c t i o n 7Li(p,a) l tHe. i i i TABLE OF CONTENTS ABSTRACT . i i TABLE OF CONTENTS i i i LIST OF TABLES v LIST OF FIGURES v i ACKNOWLEDGEMENTS v i i i Chapter I Introduction 1. Three-Body Sequential Processes 1 2. Review of Experimental Techniques 3 Chapter II The Proposed Experiment 7Li( 3He,da)^He 1. Symmetry Aspects i n Sequential Processes ... 6 2. Kinematics of the Reaction 7Li( 3He,da)^He .. 14 3. The Experiment 19 Chapter I I I Design of the 23 Inch Scattering Chamber 1. Introduction 28 2. Beam Collimat i o n System 29 3. Detector Holder Assembly 31 4. Target Holder Assembly 33 Chapter IV The Reaction 7Li(p,a) t +He To Indicate Chamber Symmetry 1. Introduction 36 2. Detector P o s i t i o n s 37 3. Targets 40 4. Detectors 43 5. Scattering Chamber Alignment 45 6. E l e c t r o n i c s 47 iv 7. E l e c t r o n i c s C a l i b r a t i o n 50 8. Experimental Results 52 9. Conclusions 58 Chapter V Other Work 1. Other Experiments 60 2". Future Work With The 23 Inch Scattering Chamber 60 APPENDIX 62 BIBLIOGRAPHY 82 V LIST OF TABLES Table 1. Commercial E l e c t r o n i c Units 48 2. Coincidence and Monitor Counts for the Four Detector Configurations 57 3. D e f i n i t i o n of Output Symbols From "Kinem" 65 v i LIST OF FIGURES Figure 1 . Diagram of the two possible d i r e c t i o n s for the emis-sion of p a r t i c l e e and f . 7 2. Diagram of the primary r e a c t i o n i n the center-of-mass frame f o r 5 L i 10 3. Diagram of the primary re a c t i o n i n the center-of-mass frame f o r 6 L i . 12 4. Diagram of the primary r e a c t i o n i n the center-of-mass frame for e L i and t r i t o n t r a n s f e r 13 5. Kinematic phase diagram f o r 7 L i ( 3 H e , d a ) 4 H e 16 6. Energy l e v e l s of 6 L i ' 17 7. The two a l t e r n a t i v e p o s i t i o n s for the emission of the deuteron and the second alpha p a r t i c l e 18 8. Energy l e v e l s of 8Be 21 9. Ti m e - o f - f l i g h t of the second alpha as a function of laboratory angle 24 10. Differences i n t i m e - o f - f l i g h t of second alpha and the deuteron 25 11. E^t? as a function of E i 27 12. Layout of c o l l i m a t o r system 30 13. Photograph of outside of s c a t t e r i n g chamber 34 14. Photograph of i n s i d e of s c a t t e r i n g chamber 35 15. Detector p o s i t i o n s and target o r i e n t a t i o n s f o r two of the experimental runs 38 16. Kinematics of 7Li(p,a) 1 +He. 39 17. Block diagram of the e l e c t r o n i c arrangement 49 v i i 18. Single p a r t i c l e energy spectrum for a_=45° 53 19. Single p a r t i c l e energy spectrum for a 2=-126.1° 54 20. Schematic diagram of symbols used i n "Kinem"' ....... 64 v i i i ACKNOWLEDGEMENTS I am most g r a t e f u l f o r the patient supervision of Dr. P. Stephas during my course of study, and to Dr. P. W. Martin f o r h i s valuable comments and suggestions on the w r i t i n g of t h i s t h e s i s . Dr. G. M. G r i f f i t h s i s also thanked f o r h i s comments during the w r i t i n g of t h i s t h e s i s . The assistance of the students, f a c u l t y and te c h n i c a l s t a f f of the Van de Graaff group i s most app-r e c i a t e d , e s p e c i a l l y during the design and construction of the experimental apparatus. 1 CHAPTER 1 INTRODUCTION 1. Three-Body Sequential Processes Nuclear reactions which lead to f i n a l states c o n s i s t i n g of several heavy p a r t i c l e s have been of i n t e r e s t f o r some time. With the increasing a v a i l a b i l i t y of 3He p a r t i c l e s and t r i t o n s as p r o j e c t i l e s i n the study of nuclear reactions, a new means of achiev-ing these many-body f i n a l states has been found, p a r t i c u l a r l y be-cause of the large Q-values involved. These studies are e s p e c i a l l y i n t e r e s t i n g when the target p a r t i c l e i s a l i g h t nucleus, where gen-e r a l l y only the f i r s t few l e v e l s are bound for heavy p a r t i c l e emission, and the l e v e l spacing i s such that many sharp, d i s c r e t e l e v e l s often e x i s t w e l l above the threshold f o r heavy p a r t i c l e emission. One problem of nuclear physics i s to understand the r e -a c t i o n mechanism, or the means by which the m u l t i p a r t i c l e f i n a l state i s formed, i n the hope that t h i s can provide information regarding the nuclear forces involved. With the r e a c t i o n mechanism, we must attempt to determine whether the r e a c t i o n proceeds v i a a s i n g l e stage, by instantaneous breakup, by a s e r i e s of two-body decays, or by some' combination of these. However, when three or more p a r t i c l e s are i n -volved, the i n t r a c t a b l e many-body problem i s encountered. Fortunately, there i s a tendency for nucleons to group together into c l u s t e r s of p a r t i c l e s , such as alpha p a r t i c l e s , or into closed s h e l l s , which often reduces the problem to a two-body system. 2 P h i l l i p s , (1964), introduces the c l u s t e r model which sugg-ests that some three-body f i n a l state processes can be treated as a time sequence of two-body i n t e r a c t i o n s . Moreover, these processes were termed "sequential", (Gatlinberg, 1965), implying that the d i s t r i b u t i o n of events within the a v a i l a b l e phase space i s not ran-dom, but i s modulated by the i n t e r a c t i o n s among the f i n a l state components. This i s a u s e f u l d e f i n i t i o n i n the cases of many of the states of l i g h t n u c l e i which have extremely short l i f e t i m e s , and may be more meaningfully described as resonances i n the i n t e r a c t i o n between two of the f i n a l state componenets (e.g. the ^ f i r s t excited state of 5 L i ) . Consider the reaction, a + b - » - C * - > d + e + f which may be thought of as a time sequence of the following two reactions: C* -> D* + d D* •* e + f For t h i s treatment by P h i l l i p s , we require that the system D* stays together i n such a manner that i t s constituents, e + f, remain to-gether as an excited l o c a l i z e d system at l e a s t long enough for the emission of p a r t i c l e d beyond the short range nuclear force f i e l d of p a r t i c l e d. An e a r l i e r treatment of f i n a l state i n t e r a c t i o n s was given by Watson, (1952), where he separated the r e a c t i o n into two mechanisms, a primary mechanism and then a f i n a l state mechanism. The primary r e a c t i o n occurs within a c e r t a i n i n t e r a c t i o n volume and the f i n a l 3 state i n t e r a c t i o n over a s l i g h t l y l a r g e r volume of c o n f i g u r a t i o n space. By considering the time reversed r e a c t i o n , i n which the par-t i c l e s are sent backward into the compound nucleus i n t e r a c t i o n volume, the e f f e c t of the f i n a l state i n t e r a c t i o n can u s u a l l y be determined. The energy spectrum function, d 3a/dEdft, for one f i n a l par-t i c l e , and the t r i p l e - c o r r e l a t i o n d i s t r i b u t i o n , d3a/dEidfiid£22, for two f i n a l state p a r t i c l e s , are found to be proportional to the c o r r -esponding t r a n s i t i o n p r o b a b i l i t i e s . The t r a n s i t i o n p r o b a b i l i t i e s are proportional to the square of a compound matrix element i n -v o l v i n g the summation over intermediate st a t e s . For d i r e c t break-up into three p a r t i c l e s the matrix element i s assumed to be a con-stant, so that the decay p r o b a b i l i t y i s uniform over the a v a i l a b l e phase space. For sequential decay processes, however, t h i s compound matrix element i s no longer constant, and must be evaluated. These two d i s t i n c t approaches by Watson and by P h i l l i p s provide a t o o l for obtaining spectroscopic information about the states of r e l a t i v e l y l o n g - l i v e d intermediate systems and about the nuclear r e a c t i o n mechanism.... The d e t a i l e d study of the decay of s h o r t - l i v e d intermediate systems i s also of i n t e r e s t , since i t helps i n the understanding of the e f f e c t s of the t h i r d p a r t i c l e on the decay processes. 2. ..Review of Experimental Techniques Early experiments attempted to study m u l t i p a r t i c l e f i n a l state reactions by d e t a i l e d a n a l y s i s of the s i n g l e p a r t i c l e spectra for such re a c t i o n s . These studies often led to ambiguous r e s u l t s , because some peaks i n the s i n g l e p a r t i c l e spectra can be misinterpreted, p a r t i c u l a r l y i n the s i t u a t i o n where i d e n t i c a l p a r t i c l e s (say two alpha 4 p a r t i c l e s ) are emitted, and when there are several competing r e a c t i o n channels. The primary d i f f i c u l t y i n obtaining q u a n t i t a t i v e informat-ion from experimental r e s u l t s i s the unambiguous i d e n t i f i c a t i o n of the three f i n a l state p a r t i c l e s . In order to determine the f i n a l state exactly nine measurable v a r i a b l e s are involved, but conservation of energy and momentum considerations reduces these to f i v e q u a n t i t i e s . Usually the energies and the mementa of two of the three p a r t i c l e s are measured, which, with the t o t a l center-of-mass energy of the system, are s u f f i c i e n t to completely determine the kinematics. Con-sequently, i t i s usually necessary to measure simultaneously the energies of two or more of the p a r t i c l e s emitted at s p e c i f i e d angles i n order to obtain information concerning the nature of the i n t e r -a c t i o n . The advent of dual parameter multichannel a n a l y s i s has provided a powerful t o o l f or such coincidence studies. When the d i r e c t i o n s of motion of two of three f i n a l s t ate p a r t i c l e s are deter-mined, conservation of energy and momentum r e s t r i c t s a l l events to a kinematic contour on the two-dimensional energy plane, T^ vs. T^. The d i s t r i b u t i o n of events along the contour i s determined by the i n t e r a c t i o n s taking place between the p a r t i c l e s during the breakup, showing an increase i n the coincidence y i e l d at points along the con-tour at which the r e l a t i v e energy of one of the two-particle systems corresponds to a state of that system. For example, a sequential process, which uniquely determines the energy, appears as a dense point, while sequential processes going through s h o r t - l i v e d i n t e r -mediate, states appear as d i s t i n c t l i n e segments on the contour, i f these states have a natural width. If the three p a r t i c l e s i n the three-body breakup are of a d i f f e r e n t mass, there w i l l be s i x d i s t i n c t 5 curves of vs. T corresponding to the s i x permutations of three p a r t i c l e s with two detectors. Hence, the problem of a s s o c i a t i n g each event with the appropriate contour i s s i m p l i f i e d by using two-dim-ensional energy a n a l y s i s . I f contours appreciably overlap, then p a r t i c l e i d e n t i f i c a t i o n may be required as w e l l . Another s o l u t i o n i s to perform a t r i p l e coincidence measurement i n conjunction with two-dimensional a n a l y s i s . A d e t a i l e d d e s c r i p t i o n of these techniques requires a complete set of kinematic c a l c u l a t i o n s i n order to deter-mine where two or a l l three of these p a r t i c l e s are to be found, and what energies they would have. An explanation of complete three-body kinematics w i l l be found i n Chapter'.".II and i n the Appendix. From an experimental point of view the f a c t that a co-incidence experiment i s being performed i s u s e f u l i n reducing background events from contaminant reactions. In the past few years a consider-able volume of experimental work has been done on m u l t i p a r t i c l e f i n a l state i n t e r a c t i o n s using two-dimensional a n a l y s i s . The proceedings of the Gatlinburg Conference on Correlations of P a r t i c l e s Emitted i n Nuclear Reactions (1965), contains an excellent summary of t h i s work from both experimental and t h e o r e t i c a l points of view. 6 CHAPTER II THE PROPOSED EXPERIMENT 7Li( 3He,ad) l fHe 1. Symetry Aspects i n Sequential Processes Consider the r e a c t i o n a + b->-D* + d->-e + f + d, which i s i l l u s t r a t e d i n Figure 1. The two-body nature of the f i r s t stage of the r e a c t i o n completely determines the d i r e c t i o n of motion of the r e c o i l system D*, which subsequently breaks up into p a r t i c l e s e and f . I f D* decays i s o t r o p i c a l l y i n i t s own re s t frame ( i . e . the r e c o i l system center-of-mass frame, RSCM), i t can be seen from the fi g u r e that c y l i n d r i c a l symmetry w i l l be obtained about the r e c o i l d i r e c t i o n of D* i n the lab frame. An e f f e c t r e l a t e d to the l i f e t i m e of the intermediate state, and a possible new t o o l which could be used to examine the ground state wave function of the target nucleus and the wave functions of the intermediate states, was discovered i n 1968 by Reimann et. a l . during the i n v e s t i g a t i o n of the three-body reactions, 6 L i ( 3 H e , a ) p , a . A c y l i n d r i c a l asymmetry about the d i r e c t i o n of motion of 5 L i was found i n the breakup of the ground state, which i s an intermediate state i n t h i s r e a c t i o n . I t was found that at an incident 3He energy of 1.25 MeV and at an angle of 30° on opposite sides of the 5 L i r e -c o i l a x i s , the proton y i e l d i n the forward d i r e c t i o n exceeded that i n the backward d i r e c t i o n by a fa c t o r of about two. The asymmetry was defined as the r a t i o of the normalized proton y i e l d s observed at the two a l t e r n a t i v e p o s i t i o n s i n the r e a c t i o n plane at equal angles to and on opposite sides of the 5 L i r e c o i l a x i s . 7 F i g u r e I. The two p o s s i b l e d i r e c t i o n s f o r t h e e m i s s i o n o f p a r t i c l e s e and f i n t h e l a b frame. In c a s e ( a ) p a r t i c l e e i s e m i t t e d a t an a n g l e <{> i n t h e r e c o i l s y s t e m c e n t e r - o f - m a s s frame (RSCM) r e l a t i v e t o t h e d i r e c t i o n o f t h e r e c o i l i n g D* i n t h e l a b o r a t o r y . In (b) e i s e m i t t e d a t $+180 r e l a t i v e t o t h e d i r e c t i o n o f D*. V r s c m i s t h e v e l o c i t y o f i n t h e l a b . f ( l a b ) f ( R S C M ) e(lab) (b) 8 To explain t h i s phenomenon a s e m i c l a s s i c a l model was pro-posed i n which the o r i g i n of t h i s asymmetry i s associated with the short l i f e t i m e of the 5 L i intermediate state, and with the memory retained by the proton during t h i s short l i f e of i t s l o c a l i z a t i o n at the time of formation of 5 L i . Besides t h i s pronounced asymmetry, any s u i t a b l e model must also explain two other observed features. Namely, the dependence of t h i s asymmetry on proton energy, and the r e l a t i v e l y large cross s e c t i o n for the process. The model that was used considered the r e a c t i o n as a direct-delayed sequential process, i n chich a neutron i s transferred very r a p i d l y from 6 L i to 3He. The neutron t r a n s f e r was considered the d i r e c t part of the reac t i o n , and the time taken f o r the reac t i o n products, two alpha p a r t i c l e s with a proton l o o s e l y attached to one of them, to sort themselves out, was c a l l e d the delayed part. The re a c t i o n i s se-que n t i a l , since an alpha p a r t i c l e i s emitted f i r s t , followed by the breakup of 5 L i a f t e r a mean time of about 10 2 1 seconds. The 5 L i l a s t s for a long time compared with the time taken f o r the tra n s f e r of the neutron to He, but the - L i l i f e t i m e i s not long com-pared with the t i m e ' i t takes f o r the lo o s e l y bound proton to move around the 5 L i system. Hence the proton may r e t a i n some memory of where i t was located during the neutron t r a n s f e r . I f t h i s i s true, the geometry of t h i s r e a c t i o n could y i e l d an asymmetry i n the proton y i e l d s at the two a l t e r n a t i v e p o s i t i o n s . The proton v e l o c i t y i n the 5 L i system governs the extent to which the i n i t i a l l o c a l i z a t i o n of the proton i n the alpha-proton system p e r s i s t s . Consequently, protons i n the spectra with higher energies should tend to represent 9 shorter l i v e d intermediate systems, and the asymmetry should i n -crease with increasing proton energy, as the experimental r e s u l t s i n d i c a t e d . The large cross section found f o r t h i s process implies a d i r e c t process i s involved i n which c l u s t e r s are i n t e r a c t i n g much l i k e the compound-cluster model of P h i l l i p s , (1964). A schematic diagram was used to i l l u s t r a t e the model. This i s shown i n Figure 2. The transfer of a neutron i s assumed to take place at the point of c l o s e s t approach of the 3He to The proton i s assumed to be l o c a l i z e d i n one of the three possible p o s i t i o n s shown by the black dot on the shaded hemisphere. The arrows i n d i c a t e the d i r e c t i o n (in the centre-of-mass frame of the reaction) i n which the proton w i l l tend to be emitted. Case A co-rresponds to the proton l o c a l i z e d i n the opposite hemisphere to that from the neutron picked up. Two p a r t i c l e pickup i s represented by B and s i n g l e p a r t i c l e pickup by C. Cases B and C are a l t e r n a t i v e s when the proton i s l o c a l i z e d on the same side of the 6 L i as the neutron at the moment of t r a n s f e r . I t i s assumed that the l o o s e l y bound proton has equal p r o b a b i l i t y of t r a n s f e r r i n g with the neutron (case B) or staying with the o r i g i n a l alpha from 6 L i (case C). A i s assumed to occur 50% of the time, while B and C are each assumed to occur 25% of the time. The geometry.^shown would then favor the forward proton detector by 7 to 1. In the proposed r e a c t i o n , 7Li( 3He,da) l +He, one may i l l -u s t r a t e the pos s i b l e asymmetry by the same model. Using the Cluster Model, one must f i r s t consider what c l u s t e r s of p a r t i c l e s can form 7 L i . This nucleus can be thought of as an alpha core surrounded by • • \ / / 10 DIRECTION OF MOTION OF ALPHA PARTICLE F i g u r e 2. Diagram o f p r i m a r y r e a c t i o n i n t h e c e n t e r - o f - m a s s frame showing n e u t r o n p i c k u p ( s o l i d c u r v e s ) and t w o - p a r t i c l e p i c k u p (dashed c u r v e s ) f o r f i x e d 5 L i r e c o i I d i r e c t i o n. 11 a deuteron and a neutron. There i s , however, evidence suggesting that 7 L i consists of an alpha core and a t r i t o n (Forsyth and Perry, 1965). F i r s t consider the former case, with 7 L i surrounded by a neuteron and a deuteron, uncorrelated. Using the same arguments as those above, the re a c t i o n can proceed by s i n g l e or three p a r t i c l e t r a n s f e r . Case A (figure 3) osrEeagmndG to the deuteron being l o c a l -ized i n the opposite hemisphere to that from which the neuteron i s picked up, and i s assumed to occur 50% of the time. In cases B and C the deuteron i s assumed l o c a l i z e d on the same side of the L i as the neuteron at the time of t r a n s f e r . The l o o s e l y bound deuteron has equal p r o b a b i l i t y of t r a n s f e r r i n g with a neuteron (case B) or staying with the o r i g i n a l alpha from 7 L i . Cases B and C are each assumed to occur 25% of the time. This would give an asymmetry r a t i o n 7 to 1, for the forward deuteron detector p o s i t i o n y i e l d to that of the backward p o s i t i o n , as i n the model used by Reimann et. a l . This a n a l y s i s has t a c i t l y assumed that following the 7 rapid t r a n s f e r of the neutron from the L i system, the remaining two p - s h e l l nucleons can be regarded as a s i n g l e e n t i t y , that i s , e f f e c t i v e l y a "deuteron". The extent to which t h i s i s true would of course modify the p i c t u r e , consequently a f f e c t i n g the asymmetry r a t i o . One may now consider the arguments for 7 L i t r a n s f e r r i n g a t r i t o n i n a s i n g l e stage process (see Figure 4). A t r i t o n can be transferred to 3He to form 6 L i . Forsyth and Perry, (1965), how-ever, also point out that the structure of 6 L i i s of the form 12 DIRECTION OF MOTION OF ALPHA PARTICLE F i g u r e 3. Diagram o f p r i m a r y r e a c t i o n i n t h e c e n t e r - o f - m a s s frame showing n e u t r o n p i c k u p ( s o l i d c u r v e s ) and t h r e e - p a r t i c l e p i c k u p (dashed c u r v e s ) f o r f i x e d 6 L i r e c o i I d i r e c t i on. 13 F i g u r e 4. D i a g r a m o f p r i m a r y r e a c t i o n in t h e c e n t e r - o f - m a s s f rame showing n e u t r o n p i c k u p ( s o l i d c u r v e s ) and t h r e e - p a r t i c l e p i c k u p (dashed c u r v e s ) f o r f i x e d L i r e c o i I d i r e c t i o n . 14 4He + d rather than 3He + t, so that t h i s would suggest that such a t r a n s f e r may be i n h i b i t e d , and i f i t did occur, there would be no preferred d i r e c t i o n f or the emission of the deuteron from the mass si x system. Contributions from t h i s process would then tend to lower one maximum asymmetry r a t i o predicted by the simple model. Thus, among other things, the predicted asymmetry w i l l depend on the reaction mechanism and on the r e l a t i v e p r o b a b i l i t y of s i n g l e and three p a r t i c l e t r a n s f e r . Experimental measurements would therefore be of i n t e r e s t i n determining these aspects. 2. Kinematics of the Reaction 7Li( 3He,dct )^B.e The bombardment of 7 L i by 3He leads to a three p a r t i c l e f i n a l state c o n s i s t i n g of two alpha p a r t i c l e s and a deuteron. We may consider the r e a c t i o n proceeding v i a a sequence of the following two reactions: 3He + 7 L i -> 6 L i + 6 L i -> a 2 + d Expressions for three-body f i n a l state kinematics pro-ceeding through an intermediate excited state can e a s i l y be found. The incident energy, the i n t e r n a l state of e x c i t a t i o n of the intermediate state, and the i n t e r n a l s tate of e x c i t a t i o n ( i f any) of the components of the f i n a l system, must be known. In t h i s r e a c t i o n i t i s convenient to l a b e l the detectors oci, « 2 , and d. Thus the f i r s t alpha p a r t i c l e which leaves the 6 L i as a r e c o i l i n g system, i s recorded by detector a i 9 and the other by detector 012. The energies of the f i r s t alpha p a r t i c l e and of the 15 6 L i can be e a s i l y determined from simple two-body kinematic c a l c u l a t i o n s . Since the Q-value of the secondary breakup i s know, the energies and laboratory angles of the second alpha and of the deuteron can then be c a l c u l a t e d . In these c a l c u l a t i o n s we assume that the distance traveled by the intermediate 6 L i system i s neg-l i g i b l e , and that i t does not lose energy to any c o l l i s i o n before i t decays. A computer program, "Kinem", was w r i t t e n to perform these c a l c u l a t i o n s . A d e s c r i p t i o n and a complete l i s t i n g of Kinem i s given i n the Appendix. Figure 5 displays a kinematic phase diagram showing the laboratory energies as a function of laboratory angle for the f i n a l alpha and the deuteron, at fi x e d energy and laboratory angle of the f i r s t emitted alpha. The curves represent the states at 3.56, 4.57 (FWHM =0.35), 5.36 (FWHM = 0.32), and 6.0 MeV e x c i t a t i o n i n 6 L i . These are plo t t e d d i r e c t l y using a modi f i c a t i o n of the Kinem program and a Calcomp p l o t t e r . For excited states which are given a width, the program broadens the curve on the phase diagram i n t o a set of three l i n e s whose outer edges represent the f u l l - w i d t h at half-maximum (FWHM) of the sta t e . Figure 6 shows the energy l e v e l s of 6 L i . Since the Q-value of t h i s r e a c t i o n i s more than 13 MeV, the e f f e c t of bombarding energy i s small on the three-body f i n a l s t a te kinematics. The p o s i t i o n of was chosen to geometrically optimize the a 2 and d detector p o s i t i o n s . The r e s u l t was for example, 75° for aL and -82.2° for the 5 L i r e c o i l . (Figure 7 shows the convention used to i n d i c a t e the laboratory angles). The ^ L i r e c o i l d i r e c t i o n defines an axis of symmetry which also o r\J. F i g u r e 5. K i n e m a t i c phase dia g r a m f o r t h e second a l p h a p a r t i c l e and t h e d e u t e r o n f o r f i x e d a n g l e o f t h e f i r s t a l p h a . 6 L i EXCITED STATES (MeV) a i = 7 5 ° 0.0 A. 3.56 B. 4.57 (FWHM=0.35) C. 5.36 (FWHM=0.32) D. 6.0 NOTE: Primed l e t t e r s r e f e r t o d e u t e r o n c o n t o u r s and un-primed l e t t e r s t o a l p h a c o n t o u r s . -20.0 i 1 r -40.0 -60.0 -80.0 L A B O R A T O R Y A N G L E -1D0.0 . D E G R E E S -120.0 -140.0 -160.0 -1B0.C 17 Figure 6. Energy levels of 6 L i . (From T . Lauritsen and F. Ajzenberg-Selove, Nuclear Physics 78, (1966)I.) 14.0 15.8 J - 8 y///,y/*//Y/y/.>, 6.8 '77/7' 4 ; 5 7 3.562 2.184 ( l " ) ; 0 , '/77/7/r? 1 2 ' ) . 0 //// / 0 » i l 3 * > 0 L i ' l+;0 <*1 BEAM A X I S 6 L i RECOIL DIRECTI ON Figure 7. The two alternative positions for the d and a 2 detectors on opposite sides of the 6Li recoil direction for 04=75 . 19 corresponds to the maximum deuteron energy. The deuteron energy drops as a function of laboratory angle, which l i m i t s the us e f u l range of energy (because of timing and minimum energy considerations) i n which the deuteron can be observed to about 70° on either side of the 6 L i r e c o i l . I f we chose 38° on eit h e r side of the 6L'i r e c o i l to observe the alpha associated with the breakup of 6 L i , then the deuteron w i l l be observed 75° away from the a 2 detector. This means that the angle between the deuteron detector and the ai detector i s always greater than 120°. Consequently, provided that the deuteron detector can d i s t i n g u i s h between deuterons and alpha p a r t i c l e s , there i s no p o s s i b i l i t y of observing the wrong p a r t i c l e f o r a par-t i c u l a r 6 L i excited s t a t e . The experimental problem of i d e n t i f y i n g the deuterons i n the presence of other p a r t i c l e s i s discussed i n the next s e c t i o n . 3. The Experiment An alpha p a r t i c l e spectrum from the re a c t i o n , 7 L i ( 3 H e , a ) 6 L i , was published by A l l e n et. a l . (1960), which showed energy l e v e l s at 2.19, 3.56, 4.5, 5.3, 6.6, 7.4, 8.4. and 9.3 MeV i n 6 L i . The 4.5 and 5.4 MeV l e v e l s had also been found by Galonsky et. a l . (1955), and the -emitting 3.56 MeV st a t e had also been reported by Day and Walker (1952). Then i n 1963 Linck et. a l . published a study of t h i s r e a c t i o n which was i n general agreement with A l l e n et. a l . , except that no l e v e l s above 6 MeV e x c i t a t i o n were seen. In 1968 Cocke also reported f i n d i n g no l e v e l s above 6 MeV e x c i t a t i o n , nor did he f i n d conclusive evidence f o r the 4.57 MeV excited s t a t e . The proposed experiment involves a search for an 20 asymmetric breakup proceeding through the 4.57 MeV °Li excited s t a t e . There are hovever, some experimental problems. One of these i s the p o s s i b i l i t y of contributions from competing modes. This r e a c t i o n may also proceed v i a excited states of 8Be (see Figure 8), 7Be or 9Be, thus: The r e a c t i o n proceeding through 7Be (and then L i ) has a thresh-hold of 1.5 MeV and can be avoided at a bombarding energy of about 1 MeV. The four p a r t i c l e f i n a l state proceeding through 9Be i s experimentally avoided using t r i p l e coincidence techniques and s u i t a b l e p a r t i c l e i d e n t i f i c a t i o n . The only other possible con-t r i b u t i o n to events of i n t e r e s t a r i s e s from the wide (6.7 MeV) 11.4 MeV excited state of 8Be. However, because of energy con-s i d e r a t i o n s , only the outer edge of t h i s state can contribute. Furthermore, by choosing the detector p o s i t i o n s a p p r o p r i a t e l y . t h i s can also be avoided. Contaminant reactions induced from target materials (see Chapter IV) can also be a problem. These are, 3He + 7 L i -> 8Be + d a + a Be + T 9Be + p a + a + n 3He + 1 2 C + a + n C -> d + 1 3 N 3He + 1 9 F •+ d + 2 0Ne 21 F i g u r e 8. Energy l e v e l s o f 8Be. (See r e f . on F i g u r e 6) 2 5 . 2 , J24_01 _ _ jp--,„."-,rH 23.0. ait 21.6 2TTT 20.36 19.9. Jlt>_2* 16,15 17.64. 1 6 . 6 3 : 2 . 9 0 Be 22 However, these alpha p a r t i c l e s and deuteron groups are of s u f f i c i e n t l y low energy, are e a s i l y i d e n t i f i a b l e (see Chapter IV), and are removed by coincidence techniques. Another experimental problem occurs because of other close (within 1 MeV) excited states i n 6 L i . These are the 3.56 MeV and and 5.36 MeV st a t e s . Figure 5 shows the second alpha p a r t i c l e and the deuteron energies as a function of laboratory angle, for these and other states. The 3.56 MeV excited state i s narrow, while the 5.36 MeV state i s 0.32 MeV (FWHM) wide. The excited state of i n t e r -est, 4.57 MeV, i s 0.35 MeV wide. However, These are separ-ated by more than 0.4 MeV taking the d i f f e r e n c e i n energy from the half-width points. A s o l i d state detector with reasonable r e s o l u t i o n (15 keV), can e a s i l y resolve these s t a t e s . The most d i f f i c u l t experimental problem a r i s e s because both alpha p a r t i c l e s and deuterons are received by the detectors. Some means of d i s t i n g u i s h i n g these i s required. One method uses a t o t a l l y depleted detector i n front of one of the detectors and d i s t i n g u i s h e s p a r t i c l e s by dE/dx vs. E a n a l y s i s . For a t o t a l l y depleted transmission detector, AE, T/a = (E + AE) 1 * 7 3 - E 1 * 7 3 , where T i s the thickness of the AE detector, and a depends on the 23 p a r t i c l e type (Ortec, 1966). Separation of various par-t i c l e s - i s based on the rate of energy l e s s , dE/dx, and for a p a r t i c l e of energy, E, i s given by, dE/dx = kmZ2E The product, E dE/dx, i s independent of E and i s proportional to the mass of the p a r t i c l e . This allows i d e n t i f i c a t i o n of p a r t i c l e s when E and dE/dx are recorded. In the proposed experiment i t i s necessary to d i s t i n g u i s h alpha p a r t i c l e s and deuterons whose response to t h i s system would require a t o t a l l y depleted AE detector of between 5.5uin and 7uin. Although such detectors are commercially a v a i l a b l e , they are very d e l i c a t e and expensive, and i t was then decided to pursue the problem from another standpoint. Another w e l l known technique employs time-o f - f l i g h t . However, the usual method uses t i m e - o f - f l i g h t with neutrons-to f i n d the energy of these p a r t i c l e s . Here i t i s proposed to use t i m e - o f - f l i g h t to i d e n t i f y the par-t i c l e s , knowing what energies the p a r t i c l e s should have from the kinematics. In other words, to i n v e s t i g a t e the breakup mode corresponding to e x c i t a t i o n of the 4.57 MeV state of 6 L i , i t was decided to employ a charged p a r t i c l e t i m e - o f - f l i g h t technique to l a b e l the emitted deuterons. Figure 9 shows the t i m e s - o f - f l i g h t of the second alpha as a function of laboratory angle, and Figure 10 shows the d i f f e r e n c e s i n t i m e s - o f - f l i g h t of the second 24 F i g u r e 9. T i m e s - o f - f I i g h t o f second a l p h a p a r t i c l e as a f u n c t i o n of l a b o r a t o r y a n g l e f o r t h e 6 L i e x c i t e d s t a t e s a t 3.56, 4.57, and 5.36 MeV, w i t h t h e f i r s t a l p h a e m i t t e d a t 7 5 . , 1 , r ~ 400 -—I J- 1 1 1--40 - 6 0 -80 -100 -120 Lab A n g l e o f Second A l p h a ( D e g r e e s ) 25 Figure 10. Differences i n t i m e s - o f - f l i g h t for the second alpha — and the deuteron as a function of laboratory angle of the second alpha. The 3.56, 4.57, and 5.36 MeV excited states are shown. The f i r s t alpha i s emitted at 75 deg. LABORATORY ANGLE OF SECOND ALPHA (DEGREES) 26 alpha and the deuteron as a function of laboratory angle for the second alpha.; Coincidence events can be stored, with the energies of these f i n a l two p a r t i c l e s , along with t h e i r d i f f e r e n c e s i n t i m e s - o f - f l i g h t . Knowing the energy of a p a r t i c l e , i t s t i m e - o f - f l i g h t can be found e a s i l y from the r e l a t i o n , f l M. ^ = 71.92 y i/E-^ nanoseconds/meter. t. Furthermore, E . t . 2 = (71.92) 2 M. = k.. x i x x The quantity, E ^ t ^ 2 > 1 S a constant for a p a r t i c u l a r type of p a r t i c l e . In the cases of alpha p a r t i c l e s and deuterons Ka = 2K .'„' Therefore, i f the data {H . , E, , (f. -t,)} i s a' a. a d stored, computing techniques can transform t h i s to { E , E^, E^t_^ 2}. I f one considers f l i g h t paths of about 10 inches, the d i f f -erence i n t i m e s - o f - f l i g h t i s about 10 nsec . for the 4.57 MeV s t a t e . And, by p l o t t i n g the data as E^t_^ 2 vs. E^ the deuterons can be e a s i l y d istinguished from the alpha p a r t i c l e s , as shown i n Figure 11. Moreover, a l l data points can be used, and experimentally undesirable groups, such as low energy p a r t i c l e s , can be r e a d i l y discarded. One would r e -quire, however, a s u f f i c i e n t l y large s c a t t e r i n g chamber; adequate moveable detector holders, would also be needed. 27 E j t f X 10 M e V - ( n s e c ) 2 2.04 2.03 I .02 I .01 a i = 7 5 Deute r o n s E . t ? X I 0 3 M e V l n s e c ) TTTTmP I .30 ,28 0.65 0.64 Ej (MeV) F i g u r e I I. E j t ? as a f u n c t i o n o f Ej f o r a l p h a p a r t i c l e s and d e u t e r o n s . The w i d t h o f t h e band i s due t o t h e n a t u r a l w i d t h o f t h e 4.57 MeV s t a t e . 28 CHAPTER I I I DESIGN OF THE 23 INCH SCATTERING CHAMBER 1. Introduction This chapter describes the design and con-s t r u c t i o n features of the s c a t t e r i n g chamber r e f e r r e d to i n Chapter I I . A v e r s a t i l e aluminum s c a t t e r i n g chamber with i n s i d e diameter of 23 inches and height 17 inches, was constructed. The chamber has around i t s center 20 stan-dard 2 inch ports (18° apar t ) . This c y l i n d r i c a l r i n g with the port flanges and "0"-rings was purchased from and es-p e c i a l l y manufactured by Norton International Inc., with a l l c r i t i c a l surfaces and ports machined to wit h i n ±0.003 inch. Aluminum top and bottom plates of thickness 1~ inches were made, and then f i t t e d to the chamber. The e n t i r e chamber i s mounted d i r e c t l y on i t s own vacuum system, com-ple t e with a s t e e l c a r r i a g e . The chamber i s bolted i n place on an 8 inch standard flange v i a the bottom p l a t e , allowing a 6 inch diameter pumping port through the bottom p l a t e of the chamber, permitting a close, concentric placement for a f a s t pump-out. The vacuum system i s a complete 200 l i t e r / s e c . u nit with a l i q u i d nitrogen b a f f l e d 4 inch o i l d i f f u s i o n pump and associated roughing pump and valves, and i s mounted on the wheelable s t e e l c a r r i a g e . This vacuum system was also purchased from Norton International Inc., i n c l u d i n g 29 i i o n i z a t i o n gauge and c o n t r o l s . A l i q u i d nitrogen automatic feed device was added to maintain the chamber under high vacuum for as long as required. A long c o l l i m a t i o n system was added to the entrance port and a Faraday cup to the ex i t port. The l a t t e r was e l e c t r i c a l l y insulated from the chamber to allow monitoring of the beam with a current i n t e g r a t o r . Arrange-ments i n the Faraday cup provided e l e c t r o n supression, and the i n s i d e of the Faraday cup was l i n e d with tantalum to reduce background a r i s i n g from charged p a r t i c l e induced reactions. Some chamber ports were covered with L u c i t e viewing ports, equipped with l i g h t t i g h t covers. A small l i g h t bulb was also i n s t a l l e d i n s i d e the chamber for viewing purposes, and i s e l e c t r i c a l l y connected by means o f two Covar sea l s , mounted i n one of the blank port flanges. 2. Beam Col l i m a t i o n System Beam c o l l i m a t i o n i s accomplished by means of four tantalum d i s c s placed i n s i d e a ^ inch t h i c k wall brass tube. o Figure 12 shows the arrangement used i n the experimental run, and the method by which the spacing of these d i s c s can be changed to s u i t the experiment. Screw caps on each end hold the parts i n place. The e n t i r e system i s 16 inches long and a l l c r i t i c a l surfaces are machined to within ±0.002 inch. The long c o l l i m a t o r was necessary, since the beam was r e -quired to t r a v e l about 11 inches, and s t i l l be within 1 mm. F i g u r e 12. Layout showing t h e arrangement o f t a n t a l u m c o l l i m a t i n g d i s c s , w i t h v a r i a b l e s p a c i n g (not t o s c a l e ) . 31 of the exact center of the s c a t t e r i n g chamber, regardless of beam i n s t a b i l i t i e s and focussing conditions. Tantalum d i s c s were chosen because of the r e -l a t i v e l y high melting temperature (2000°C) of t h i s metal, and i t s large atomic number (Z * 73), which ensures l i t t l e c o n t r i b u t i o n to background counts i f the bombarding beam i s deuterium. The c o l l i m a t o r tube f i t s i n s i d e an outer vacuum ti g h t jacket, which i s fastened to the outside wall of the s c a t t e r i n g chamber. Evacuation of the beam l i n e and c o l l -imation system was accomplished by mounting the collimator tube on a three-pronged web arrangement at each end, with semicircular b a f f l e s near the center to prevent stray parts of the beam from entering the s c a t t e r i n g chamber. 3. Detector Holder Assemblies The s c a t t e r i n g chamber has three 360° r o t a t a b l e detector holders, two of which can be rotated e x t e r n a l l y , while the chamber i s under high vacuum. These two detector holders are positioned by two "rotary feed-through" devices, with a gear assembly i n s i d e . These detector holders are fastened on two aluminum p l a t e s , 44cm and 48cm i n diameter, each with a b i c y c l e chan f i t t e d to i t s edge, and geared to the rotary feed-through on the bottom cover, The two plates are held i n place v i a Nylatron dry bearings, and are positioned c o n c e n t r i c a l l y around the pumping port. The t h i r d detector holder i s not movable from the outside, but can be positioned on a r i n g engraved i n i n t e r v a l s of i° from 32 0 to 360 . This i s mounted i n s i d e another r i n g suspended from the i n s i d e wall of the chamber by three supports. .Each detector holder consists of a movable carriage which allows p o s i t i o n i n g of the detector at 5cm. to 25cm. from the center of the chamber. Detectors are mounted on Micro-dot detector mounts fastened to the movable carriage and provisions are made for v e r t i c a l adjustment. A penta-prism i s mounted near one of the l u c i t e covers on one of the ports, and allows the experimenter to view the markings on the movable p l a t e s . The plates are engraved i n i n t e r v a l s of |° from 0° to 360°, which allows external p o s i t i o n i n g of these two detectors to with i n ±^°» This i s f a c i l i t a t e d by a pointer system d i r e c t l y above the engraved p l a t e s . Other detectors can be mounted d i r e c t l y on the remaining ports (18° i n t e r v a l s ) , allowing f o r example a Rutherford e l a s t i c s c a t t e r i n g monitor to be placed at such backward angles as ±162° or ±144°, etc. Other 360° movable detectors can also be mounted i n s i d e the chamber by mounting these on d i f f e r e n t diameter r i n g s , as the t h i r d detector holder mentioned above. I t i s poss i b l e to make these extern-a l l y movable by adding s u i t a b l e feed-through devices and gears to the top l i d . Microdot detector mounts are connected to ports with Microdot 100 ohm, low capacitance (12pf./ft.) 33 coax i a l cable. E l e c t r i c a l connection to the outside i s made using s p e c i a l Microdot vacuum feet-through connectors. Spec-i a l precautions were made to allow r o t a t i o n of the two de-tect o r s through 360° without these cables becoming caught i n the apparatus. 4. Target Holders and Assembly Targets are inserted into the center of the sc a t t e r i n g chamber from the top plate using a "rotary push-p u l l " vacuum feed-through. The target holders are attached to the feed-through and co n s i s t of four to s i x holes d r i l l e d i n a j-^ inch t h i c k copper s t r i p . Provisions are made on the target holder f o r a piece of quartz to f a c i l i t a t e beam focussing, or a small mirror to a s s i s t i n chamber alignment. Targets can be selected e x t e r n a l l y and guided into p o s i t i o n by an assembly attached to the top l i d . The shaft of the rotary feed-through i s connected to a dis c with a pointer, which f i t s i n s i d e a brass p l a t e graduated from 0° to 360°. Figures 13 and 14 depict the parts of the sc a t t e r i n g chamber, with important parts being marked as shown. 3 4 A Scattering Chamber B Faraday Cup C Collimation System D Pumping Unit E Target Holder Assembly F i g u re 13 35 (Center Detector Holder and Top Lid Removed) A Externally Movable Detector Holder B Pointer and Gear Arrangement C Pumping Port F i g u r e 14 36 CHAPTER IV THE REACTION 7Li(p,a)tfHe TO INDICATE CHAMBER SYMMETRY 1. Introduction As a means of checking the scattering chamber for performance under actual experimental conditions, the reaction 7Li(p,a)1+He was chosen primarily because two alpha particles are emitted 180° apart in the center-of-mass system. These would show the experimenter the degree to which the chamber collimation system, target holders, and detector holders are geometrically aligned and machined. Very slight deviations in workmanship would be multiplied over large distances. In this case some deviations multiplied over 23 inches could be ex-tremely significant, and experimentally undesirable. By rotating the two movable detectors one could determine even more precisely how symmetrical the chamber is, when the two alpha particles are observed in coincidence. The proton beam from the U.B.C. Van de Graaff accelerator is also one of the easiest of its various beams with which to work. This reaction, 7Li(p,a)lfHe, which has been studied extensively (see for example, Freeman et. al. 1958; or more recently Duggan, 1968; and Lerner and Marion, 1969), could also test, at various beam intensities, the thin targets made by evaporating lithium fluoride onto a thin carbon backing. These targets will also be used 37 i n the i n v e s t i g a t i o n of the rea c t i o n , 7Li( 3He,dct) t tHe, as outlined i n Chapter I I . 2. Detector Positions In the i n v e s t i g a t i o n of 7Li(p,cO^He i t i s con-venient to c a l l one detector ai and the other, a 2 , as i t i s shown i n Figure 15. The two alpha p a r t i c l e s share the Q-value of the r e a c t i o n and the bombarding energy i n a manner shown i n the kinematic diagram of Figure 16, where the two-body kinematics were calculated from the computer program, Kinem, which i s equally u s e f u l f or three-body kinematics. The large p o s i t i v e Q-value of 17.35 MeV makes measurements p a r t i c u l a r l y convenient, e s p e c i a l l y at a bombarding energy of 1.5 MeV, which was chosen because the cross section v a r i e s smoothly with energy i n t h i s region. To measure accurately and eliminate background, i t was decided to perform a coincidence measurement using the two-dimensional analysis technique mentioned i n Chap-ter I, with detectors placed at 45° and -126.1° i n the rea c t i o n plane. Since t h i s r e a c t i o n i s a two-body pro-cess, the alpha p a r t i c l e energies are well defined, being 10.67 MeV and 8.17 MeV r e s p e c t i v e l y . The coincidence spectrum w i l l then appear as an intense point on the two-dimensional energy plane. Deviations i n symmetry of the chamber can be checked by comparing the experimentally obtained energies with those predicted by the kinematics 38 LABORATORY ANGLE (DEGREES) Figure 16. Theoretical energies plotted as a function of lab angle f o r the f i r s t alpha, with bombarding energy of 1.5 MeV. 40 (allowing f or energy los s c o r r e c t i o n s ) , and a more sen-s i t i v e t e s t , by looking f or s h i f t s i n the energy spectra when the two detectors are interchanged. It i s also necessary to place f o i l s i n front of both detectors to stop e l a s t i c a l l y scattered protons from the reactions 7 L i ( p , p ) 7 L i , 1 9 F ( p , p ) 1 9 F , 1 2 C ( p , p ) 1 2 C , and 1 3 C ( p , p ) 1 3 C . For t h i s purpose 40uinch f o i l s were chosen. 3. Targets Since t h i n targets (of order, 10ugm/cm2 t h i c k -ness) w i l l be required for the i n v e s t i g a t i o n of the rea c t i o n , 7Li( 3He,da)^He, i t was decided to use them for the s c a t t -ering chamber i n v e s t i g a t i o n experiment. These targets give a reasonable y i e l d , are s e l f supporting (with a strong backing m a t e r i a l ) , yet are t h i n enough so that the r e a c t i o n products can be observed through the target with l e s s than 10 keV energy l o s s . Since l i t h i u m metal has a great a f f i n i t y f o r both water and oxygen, targets made from free l i t h i u m d e t e r i o r a t e very r a p i d l y . For t h i s reason a l i t h i u m s a l t was decided upon. The most u s e f u l of these i s L i F , which i s perhaps one of the easiest s o l i d s to evaporate. However, these targets require a strong back-ing m a t e r i a l , since they are not se l f - s u p p o r t i n g . Some experimenters use very t h i n metal f o i l s , such as n i c k e l (Cocke, 1968) and others use carbon (Dearnaley, 1960). Owing to the smaller energy losses involved, carbon f o i l s 4 1 w e r e u s e d . T h e y a r e r e l a t i v e l y e a s y t o p r e p a r e , a n d a r e a d e q u a t e l y t h e r m a l l y a n d e l e c t r i c a l l y c o n d u c t i v e , a n d c a n w i t h s t a n d t e m p e r a t u r e s o f a l m o s t 9 0 0 ° b e f o r e m e l t i n g . A l t h o u g h a t a r g e t o f n a t u r a l L i F p r e p a r e d o n a c a r b o n b a c k i n g w i l l p r o d u c e b a c k g r o u n d n u c l e a r r e -a c t i o n s w i t h 1 2 C , 1 3C, a n d 1 9 F , s e v e r a l a d v a n t a g e s a r e o b t a i n e d . T h e o n e - t o - o n e r a t i o o f l i t h i u m t o f l u o r i n e n u c l e i p e r m i t s t h e u s e o f a m o n i t o r d e t e c t o r b y o b s e r v i n g t h e y i e l d o f e l a s t i c a l l y s c a t t e r e d beam p a r t i c l e s f r o m f l u o r i n e n u c l e i . I f t h e c o u l o m b b a r r i e r i s s u f f i c i e n t l y h i g h s o t h a t n u c l e a r e f f e c t s c a n b e n e g l e c t e d , t h e a b -s o l u t e c r o s s s e c t i o n f o r t h e p r o c e s s u n d e r s t u d y c a n b e e v a l u a t e d b y n o r m a l i z i n g t o t h e w e l l k n o w n R u t h e r f o r d 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 t h e y i e l d i n t h e m o n i t o r . T h i s h a s t h e a d d i t i o n a l a d v a n t a g e t h a t n o n - u n i f o r m i t i e s i n t h e t a r g e t c o m p o s i t i o n a r e a u t o m a t i c a l l y a c c o u n t e d f o r . T h e p r e p a r a t i o n o f t h e s e t h i n t a r g e t s i s e s s e n t i a l l y a two s t a g e p r o c e s s , c o n s i s t i n g o f t h e e v a p o r a t i o n o f c a r b o n , a n d t h e n t h e e v a p o r a t i o n o f l i t h i u m f l u o r i d e o n t o t h e c a r b o n b a c k i n g s . C a r b o n f o i l s w e r e p r e p a r e d i n a v a c u u m o f a b o u t 10 6 T o r r i n a s t a n -d a r d b e l l - j a r e v a p o r a t o r . P r e c l e a n e d s t a n d a r d m i c r o s c o p e g l a s s s l i d e s w e r e p l a c e d a b o u t 1 0 c m . a b o v e t w o c a r b o n r o d s , o n e o f w h i c h was p l a c e d h o r i z o n t a l l y w i t h t h e end 42 cut to a 45 angle, and the other rod was sharpened to a point and placed at an angle of 30° to the h o r i z o n t a l , much l i k e the arrangement used by Makosky (1969). The two rods were held i n contact by l i g h t springs fastened to water cooled brass mounts. A corrent of 200 amps was passed through the rods i n 8 to 10 bursts, each burst l a s t i n g about 2 seconds, with the apparatus being allowed to cool f o r about one minute between bursts. The edges of the glass s l i d e s were then scraped and the carbon layer was cut into squares large enough to cover the target holder holes. The s l i d e s were placed i n a tray at an angle of 30° to the h o r i z o n t a l , and warm water was used to f l o a t the fil m s o f f by allowing the water to r i s e slowly i n the tray. Two types of glass s l i d e s were used, the precleaned s l i d e s g iving the best r e s u l t s . S l i d e s coated with Tepol, a very highly soluable detergent-, produced excellent f o i l s as we l l , although some tended to break while being f l o a t e d o f f . The target holders c o n s i s t i n g of s i x inch holes d r i l l e d i n a copper s t r i p , were placed into the water bath, and the f o i l s were f l o a t e d over the holes of the target holder consecutively, beginning at one end. The target holders with the carbon f o i l s were next placed i n a v e r t i c a l p o s i t i o n and allowed to dry for a day. Each target holder was placed h o r i z o n t a l l y i n an evaporator, and held 15cm. above a tantalum boat containing 43 about one gram of the L i F s a l t . The L1F was evaporated onto the carbon backings i n about 5 minutes by allowing 50 amps of corrent to pass through the boat, under a vacuum of almost 10 6 Torr. This procedure gave 4 or 5 excellent targets per target holder of 10 to 15ugm/cm2 thickness of L i F on a backing of 15 to 30ugm/cm2 of carbon. Such targets t y p i c a l l y have energy losses of only a few keV for a 10 MeV alpha. 4. Detectors Two s i l i c o n surface b a r r i e r s o l i d state detectors were chosen as the two alpha p a r t i c l e detectors. These are large-area p-n diodes comprised of an extremely t h i n p-type l a y e r on the s e n s i t i v e face of a high p u r i t y n-type s i l i c o n wafer. E l e c t r i c a l contact i s made to the p-type surface by a t h i n gold f i l m , t y p i c a l l y 40ugm/cm2 t h i c k , and to the n-type s i l i c o n by means of a no n - r e c t i f y i n g metal contact on the back surface. Upon a p p l i c a t i o n of an e x t e r n a l l y applied reverse bias voltage, a region known as the depletion region i s obtained, which v a r i e s i n depth as the square root of the applied voltage. The depletion region i s the por t i o n of the n-type s i l i c o n which contains the e l e c t r i c f i e l d ( r e s u l t i n g from the reverse b i a s ) . Free charge c a r r i e r s are created i n t h i s region by the i o n i z i n g r a d i a t i o n , and these are separated 44 by the influence of the e l e c t r i c f i e l d , and the r e -s u l t i n g net current represents, the basic source of information about the number of charge c a r r i e r s created by the incident charged p a r t i c l e r a d i a t i o n . These diodes are then mounted i n metal c y l i n d e r s on which conn-ection can be made with B.N.C. or Microdot connectors. The two detectors used were supplied by Oak Ridge Tech-n i c a l Enterprises Corporation (ORTEC), and t y p i c a l l y have an alpha p a r t i c l e energy r e s o l u t i o n of l e s s than 60 keV for an 2 1 + 1Am(5.477 MeV) alpha source and a very low noise amplifying sytem. Range-energy curves for s i l i c o n (Ortec, 1967) show that 12 MeV alpha p a r t i c l e s t y p i c a l l y t r a v e l 100 microns i n s i l i c o n before being stopped. Consequently, the two detectors were operated at depletion depths of 110 microns, to ensure a l l alpha p a r t i c l e s of i n t e r e s t were completely stopped within the depleted region. Nickel f o i l s of 40yinch thickness were placed i n front of the detectors to stop the e l a s t i c a l l y s c a t t -ered protons, and these were l e f t on during the energy c a l i b r a t i o n procedure. These f o i l s were placed i n s i d e the dete Q:or c o l l i m a t o r s , which consisted of c y l i n d e r s which f i t over the detectors, and are held i n place by small locking screws. The co l l i m a t o r faces had holes 1 3 d r i l l e d i n them which were g- inch and ——• inch i n diameter. 45 Each detector was placed at 20cm ±0.1cm from the target axis (the center of the chamber), with the •5- inch diameter c o l l i m a t o r on the 45° detector and the . o T T - inch c o l l i m a t o r on the -126.1° detector (Figure 15). lb Thus the angles subtended by the two alpha detectors were 0.9° and 1.4° r e s p e c t i v e l y . Alpha p a r t i c l e s are de-tected by the 45° detector, within i t s s o l i d angle. One must be c e r t a i n that the corresponding alpha p a r t i c l e which share the energy with those recorded by the 45° detector, and which are i n the v i c i n i t y of the -126.1° detector, are a l l recorded by t h i s second detedtor. For an angle subtended by the 45° detector of 0.9° kinematic c a l c u l a t i o n s show that the -126.1° detector must.subtend an angle of 1.1°, due to kinematic spreading Hence i n double coincidence, i f the -126.1° detector subtends an angle of 1.4°, we can be c e r t a i n that a l l corresponding alpha p a r t i c l e s are detected, provided of course, that the chamber and detectors etc. are a l l i n reasonable alignment. 5. Scattering Chamber Alignment Alignment of the s c a t t e r i n g chamber, incl u d i n g beam co l l i m a t o r , target assembly, and detectors, was done o p t i c a l l y . A continuous helium-neon gas l a s e r was placed i n the beam p o s i t i o n , approximately 10 feet from the chamber entrance port. The Faraday cup was removed 46 and a s p e c i a l alignment flange, with a — inch hole d r i l l e d through i t s center and which f i t s the port within 0.003 inch, was i n s t a l l e d . The chamber was then c a r e f u l l y leveled and aligned by observing the l a s e r beam on a wall a f t e r i t had passed through the beam col l i m a t o r system and the alignment flange. To check the target holder assembly with respect to the chamber, masking tape was placed over the s i x holes of the target holder, through the center of which p i n holes were pierced. The target feed-through device was moved v e r t i c a l l y and the l a s e r beam spot was again observed on the wall a f t e r i t had passed through each of the p i n holes and the alignment flange, showing the p r e c i s i o n by which the top p l a t e of the s c a t t e r i n g chamber and the target holder assembly had been constructed. A small mirror was i n s t a l l e d on the upper portion of the target holder, where care was taken to ensure that the r e f l e c t i n g surface of the mirror was on the c e n t r a l chamber a x i s . The detectors were aligned by r e f l e c t i n g the l a s e r spot into the detector c o l l i m a t o r holes i n several backward angles, where both detectors were rotated. The target assembly was retracted and the two detectors were i n turn rotated to the 0° p o s i t i o n where the l a s e r spot was seen i n s i d e the detector c o l l -imator holes. As a f i n a l check, the target was inserted 47 and the l a s e r beam was r e f l e c t e d backward upon i t s e l f , as a l a s t t e s t of o p t i c a l alignment. 6. E l e c t r o n i c s The e l e c t r o n i c arrangement consisted of stan-dard commercially a v a i l a b l e u n i t s (see Table 1), with the exception of the preamplifiers whose operation i s described by Whalen (1965). These are well suited for use with the d e l a y - l i n e clipped main a m p l i f i e r s , since these charge s e n s i t i v e nuvistor preamplifiers have a f a s t r i s e t i m e (<15nsec.), are low ,noise ( r e s o l u t i o n <10 keV), and have a slow decay time ('vLOOusec.). A block diagram of the a m p l i f i c a t i o n and co-incidence system i s shown i n Figure 17. Pulses from the nuvistor preamplifier, which correspond to the de-t e c t i o n of a charged p a r t i c l e , are double d e l a y - l i n e c l i p p e d by the main a m p l i f i e r , whose prompt output t r i g g e r s the s i n g l e channel analyzer at the zero-cross-over point, provided the pulse f a l l s w i t h i n the desired voltage range. The outputs from the two s i n g l e channel analyzers are presented to the inputs of the Canberra f a s t coincidence u n i t . Negative output pulses from the coincidence unit are recorded by a s c a l e r to count co-incidence events, while p o s i t i v e pulses are delayed and then stretched to produce the c o r r e c t gating pulses for the ND-160 analyzer, operated i n coincidence mode. A A8 T a b l e I Commercial E l e c t r o n i c U n i t s R e f e r r e d t o by t h e Numbers i n t h e b l o c k Diagram o f F i g u r e 17. 1) C l Model 1410 L i n e a r A m p l i f i e r ( C a n b e r r a I n d u s t r i e s I n c . , M i d d l e t o w n , Conn.) 2) C l Model 1435 T i m i n g S i n g l e Channel A n a l y z e r 3) C l Model 1470 S c a l e r 4) C l Model 1441 C o i n c i d e n c e U n i t 5) ORTEC Model 427 Del a y A m p l i f i e r (Oak R i d g e T e c h n i c a l E n t e r p r i s e s C o r p . , O a k r i d g e , Tenn. 6) ORTEC Model 416 Gate and D e l a y G e n e r a t o r 7) ORTEC Model 411 P u l s e S t r e t c h e r 8) NUCLEAR DATA Model ND-160 Dual P a r a m e t e r A n a l y z e r ( N u c l e a r Data I n c . , P a l a t i n e I l l i n o i s ) Preamp Preamp. 2. SCA i 1. LA 2. TSCA 2. TSCA LA 1. 3. Scaler Delay 4. Coinc. G & D Scaler PS Delay N D 1 6 0 •P-Figure 17. Block Diagram of E l e c t r o n i c Arrangement (numbers r e f e r to units given i n Table 1.) 50 s c a l e r and a s i n g l e channel analyzer were also added to one of the l i n e a r a m p l i f i e r s i n order to compare coincidence counts from various experimental runs. The primary purpose of the e l e c t r o n i c arrangement was to count coincidence events from the two detectors which s a t i s f y the energy requirements, and which f a l l w i t h i n the coincidence r e s o l v i n g time of 50nsec. Dual parameter analysis was provided by taking prompt outputs from the l i n e a r a m p l i f i e r s , delaying them, and feeding to the X and Y inputs of the ND-160 dual parameter ana-l y z e r , where they were accumulated i n a 64 X 64 array. (This d i s p l a y was used only to show the region i n which the p a r t i c l e s of t h i s energy would l i e , as well as to i n d i c a t e to some degree what random coincidences might have occurred.) A l l of the analyzing equipment could be started and stopped by remote c o n t r o l . Not shown i n Figure 17 are the Ortec detector bias supply, and the t e s t pulse generator. 7. E l e c t r o n i c s C a l i b r a t i o n The e l e c t r o n i c system was c a l i b r a t e d using an 2 l t lAm alpha source, of which the major alpha p a r t i c l e group has an energy of 5.477 MeV. By applying various t e s t pulses i t i s p o s s i b l e to determine the pulse height necessary to simulate p a r t i c l e s of any desired energy i n the experiment. 51 The 2 4 1Am source was attached to the target holder assembly and both detector-amplifier systems were c a l i b r a t e d by turning the source to face the desired detector. The c a l i b r a t i o n was c a r r i e d out with the 40yinch f o i l s , used to stop e l a s t i c a l l y scattered protons, placed i n front of the detectors, as these would be i n place during the experiment. As a check, c a l i b r a t i o n was compared with the absence of f o i l s , 75yinch of f o i l , and 175uinch of f o i l , using the 2ltlAm source. The a m p l i f i e r gains were adjusted so that peaks corresponding to 5.477 MeV alpha p a r t i c l e s were i n a convenient p o s i t i o n i n the pulse height analyzer. The baselines and window widths or the s i n g l e channel ana-ly z e r s were adjusted so as not to allow events other than those corresponding to the energy regions of i n t e r e s t . This was accomplished by applying t e s t pulses c o r r e s -ponding to the required energies using the c a l i b r a t i o n curves, and then checking these by observing s i n g l e par-t i c l e energy spectra from each of the two detectors, at the desired laboratory angles. The coincidence r e s o l v i n g time was determined by varying the delay i n the ot2 channel, using the timing portion of the timing s i n g l e channel analyzers, then p l o t t i n g the number of coincidence events vs. delay time i n the a 2 channel. A p l a t e a u - l i k e curve r e s u l t e d , where 52 the r e s o l v i n g time was found from the width of t h i s curve, and the optimum delay i n the a 2 channel was taken at the center of t h i s plateau. Thus, the co-incidence u n i t generated an output l o g i c pulse when the simultaneous energy and time requirements were met. 8. Experimental Results Data was accumulated using the 3 MeV U.B.C. Van de Graaff accelerator, and a 1.5 MeV proton beam from the accelerator was analyzed by a 90° d e f l e c t i n g magnet, then focussed to a spot about 2mm. i n diameter on a L i F target i n the 23 inch s c a t t e r i n g chamber. The beam current was monitored i n the Faraday cup using a current i n t e g r a t o r , and was t y p i c a l l y 0.3uamp. Single p a r t i c l e energy spectra were accumulated at several laboratory angles f o r both surface b a r r i e r detectors. This was accomplished by operating the el e c t r o n i c s i n si n g l e coincidence mode. E l a s t i c a l l y scattered protons were found to be completely absorbed by the n i c k e l f o i l s i n front of the detectors. Shown i n Figures 18 and 19 are s i n g l e p a r t i c l e energy spectra for the laboratory angles of 45° and -126.1° r e s p e c t i v e l y , with the chamber geometry as indicated i n Figure 15. The most s t r i k i n g feature of these two si n g l e p a r t i c l e spectra i s the presence of the two lower energy alpha groups. These are a t t r i b u t e d to the alpha decay Q f 2 0Ne t o U 600 h 500 400 •300 200 h- IOO F i g u r e 18. S i n g l e P a r t i c l e Energy Spectrum, aj= 45° " * 1 9 F ( p , a ) 1 60 1 9 F ( p , a Q ) 1 6 0 6 7 8 9 P a r t i c l e Energy (MeV) 7Li(p^ajJ^He I 12 Particle Energy (MeV) 55 the ground and f i r s t excited states of l e 0 , since they s a t i s f y a l l phy s i c a l and energy requirements. The bombardment of 1 9 F by protons forms 2-°Ne i n excited states, which show a very high prob-a b i l i t y of decaying by alpha emission to states of l 5 0 (Ask, 1960). This decay can give f i v e groups of alpha p a r t i c l e s i n the t r a n s i t i o n s to the ground state and four excited states of 1 6 0 . The two most energetic of these are denoted ctQ and a^, which leave 1 6 0 i n the ground state and f i r s t excited n u c l e a r - p a i r -emitting state r e s p e c t i v e l y . (The presence of 1 9 F i s of course due to the L i F used to make the t a r g e t s ) . These reactions, 1 9 F ( p , a 0 ) 1 6 0 and 1 9 F ( p , a ) 1 6 0 have been observed by Lerner and Marion (1969), Telepov et. a l £1961), and many others. The r e l a t i v e i n s t e n i t i e s observed were also i n agreement with these authors. The Q-values f o r these two reactions are 8.12 MeV and 2.06 MeV r e s p e c t i v e l y . Ranken et. a l . (1958), showed that i n t h i s energy region the main r e a c t i o n mechanism i s a process associated with the formation of an i n t e r -mediate compound nucleus, i n t h i s case 2 0Ne. To eliminate these two unwanted lower energy alpha groups i t was necessary to set the a\ and a 2 s i n g l e channel analyzers to allow only pulses c o r r -esponding to alpha p a r t i c l e s from the primary r e a c t i o n , 7 L i ( p , a i ) a 2 , to be analyzed. This was accomplished by using the test pulse generator and applying various 56 tes t pulses, then adjusting the baselines of the s i n g l e channel analyzers u n t i l the unwanted pulses were elim-inated. Once the e l e c t r o n i c s were properly adjusted, ai-012 coincidences were counted using the ±45° side of the e l e c t r o n i c s as a monitor (Figure 17). The detector p o s i t i o n s were f i r s t , 0 4 at 45° and a 2 at -126.1°, where 500 coincidences were accumulated, with appropriate output cables being reversed. Measurements were r e -peated, t h i s time by r o t a t i n g the two detectors to opposite sides of the beam axis, 0 4 being placed at -45° and a 2 at 126.1°. F i n a l l y , a i was placed at -126.1° and a 2 at 45°, and the procedure repeated. The l a r g e r detector c o l l i m a t o r was i n each case a t t -ached to the detector at the backward angle, and the monitor count was recorded for each of the four runs. Results are summarized i n Table 2. The coincidence y i e l d per monitor counts were compared for each of the four cases. Cases A 7 and B/ can be added to cases A and B, since no detector d i f f e r e n c e e f f e c t s were seen. Dual parameter analysis displayed the two-dimensional energy region i n each case (as well as a.few random coincidences), where t h i s region consisted of a few points around a dense c e n t r a l point. Theor-e t i c a l l y , t h i s "contour" would consist of only a s i n g l e point. But, because of the f i n i t e target T a b l e 2. C o i n c i d e n c e and m o n i t o r c o u n t s f o r t h e f o u r d e t e c t o r c o n f i g u r a t i o n s . Case 04 Lab An g l e o i 2 Lab Ang 1 e d l - C l 2 Coi nc i dences Mon i t o r Counts C o i n c i d e n c e s p e r M o n i t o r w i t h S t a t i s t i c a l E r r o r X i 0 _ l + A 45° -126.1° 500 967083 5.238±0.236 B -45° 126.1° 500 964005 5.I89±0.237 A' -126.1° 45° 500 961718 5.20010.237 B' 126.1° -45° 500 954552 5.23710.238 '. A" 1000 1928801 5. 18510.168 B" 1000 1918557 5.21210.169 58 thickness, r e s o l u t i o n of the detectors, and kinematic spreading due to a s o l i d angle subtended at the t a r -get by the detectors, t h i s contour can appear as a c l u s t e r of a few points around the primary point c o r r -esponding to the alpha p a r t i c l e s of energies 10.7 MeV and 8.17 MeV. The peak po s i t i o n s of s i n g l e p a r t i c l e spectra did not appear to s h i f t more than ^ of a channel, on the a l t e r n a t i v e sides of the beam a x i s . 9. Conclusions In view of the experimental conditions imposed on the alignment and construction of the 23 inch s c a t t -ering chamber, i t i s safe to say that i t i s well suited for m u l t i p a r t i c l e experiments, well machined and aligned, and extremely v e r s a t i l e . The long 16 inch c o l l i m a t i o n system proved to be highly successful i n keeping the beam spot on the target, regardless of beam i n s t a b i l i t i e s . In f a c t i t was estimated to have moved l e s s than mm. over a period of several hours. The t h i n targets which w i l l be used i n the i n v e s t i g a t i o n of the rea c t i o n , 7Li( 3He,da) 1*He, proved to be able to withstand beam currents of more than 0.4uamp over periods of a h a l f hour, without appreciable damage. The excellent vacuum system permitted the experimenter to pump the sc a t t e r i n g chamber down to pressures of 10 6 Torr i n a few minutes. The only disadvantage found i n using t h i s large s c a t t -ering chamber and i t s systems, was i t s great s i z e and 59 weight, making assembly and moving d i f f i c u l t , but t h i s appeared to be outweighed by the f a c t that the i n i t i a l i n s t a l l a t i o n and alignment would l i k e l y not require adjustment for some time. 60 CHAPTER V OTHER WORK 1. Other Experiments Two other sequential processes i n which mass f i v e n u c l e i are formed are presently under i n v e s t i g a t i o n by Heggie et. a l . (1969). These are: d + 7 L i 5He + a (a + n) + a 3He + T -> 5 L i + n (a + p) + n These two reactions are of current i n t e r e s t because of the p o s s i b i l i t y of f i n d i n g asymmetries about the r e c o i l d i r e c t i o n s of the mass f i v e intermediate states, and to further study the mechanisms involved i n these sequential processes. 2. Future Work With the 23 Inch Scattering Chamber As was mentioned i n Chapter I I , A l l e n et. a l . (1960) and Cocke (1968) found no evidence for l e v e l s above 6.0 MeV e x c i t a t i o n i n ^ L i . Consequently, besides the proposed search for an asymmetry i n the deuteron y i e l d about the 6 L i r e c o i l d i r e c t i o n i n the r e a c t i o n 7Li( 3He,da)^He, some work may be u s e f u l to e s t a b l i s h some of the dubious excited states of 6 L i . In the i n v e s t i g a t i o n of the asymmetry found by Reimann et. a l . a p l o t of cross section as a function of center-of-mass angle showed a d i s t i n c t d i s c o n t i n u i t y i n the cross s e c t i o n curve f o r the forward and a f t p o s i t i o n s of the proton detector, 61 on opposite sides of the 5 L i r e c o i l d i r e c t i o n . This curve drops as a function of center-of-mass angle f o r the forward proton detector p o s i t i o n s , except for the l a s t point which suggests that the c r o s s - s e c t i o n a c t u a l l y r i s e s . Because of t h e i r small s c a t t e r i n g chamber, the geometry forced the use of the a f t detector p o s i t i o n s , and t h i s i s where the asymmetry was discovered. A Distorted Wave Born Approximation c a l c u l a t i o n by Deutchman (1969) suggests that the cross s e c t i o n drops as a function of center-of-mass angle. Since the large s i z e of t h i s s c a t t e r i n g chamber allows further i n v e s t i g a t i o n of forward de-t e c t o r p o s i t i o n s , with the use of annular detectors, several more forward posi t i o n s may be used. This might-enable one to a s c e r t a i n i f the c a l c u l a t i o n by Deutchman i s compatible with the experiment data. To help explain the asymmetry observed i n the breakup of 5 L i ground state, an experiment i n -v o l v i n g the f i r s t excited state of t h i s system i s also proposed. Since the f i r s t excited state i s wider, and hence shorter l i v e d , t h i s possible asymmetry should be l a r g e r . 62 APPENDIX KINEMATICS CALCULATIONS A computer program, "Kinem", was wr i t t e n to carry out the relevant c a l c u l a t i o n s i n v o l v i n g three-body sequential kinematics. The program was written as general as possible to allow the kinematics of almost any such r e a c t i o n to be ca l c u l a t e d (non-r e l a t i v i s t i c ) , and has as input v a r i a b l e s , the masses of the s i x (or fewer) p a r t i c l e s , the laboratory angles of i n t e r e s t , the bombarding energy of the p r o j e c t i l e , the Q-values of the two sequential processes, and the e x c i t a t i o n energies and natural widths (FWHM) of the intermediate state. A modi f i c a t i o n of t h i s program w i l l p l o t d i r e c t l y the kinematic phase diagrams showing p a r t i c l e energy as a function of laboratory angle, for the f i n a l two p a r t i c l e s , f o r a fixed laboratory angle and energy of the f i r s t emitted p a r t i c l e . (See Figure 20) The program c a l c u l a t e s the following: f o r a s p e c i f i c angle of emission of the f i r s t p a r t i c l e (which can be automatically v a r i e d ) , i t w i l l c a l c u l a t e i t s energy and the angle and energy of the fourth p a r t i c l e (intermediate state i n most cases). I f t h i s fourth p a r t i c l e decays into two more p a r t i c l e s , i t w i l l c a l -c u late the energies as a function of angle f o r the center-of-mass and repeat the c a l c u l a t i o n s . The program 63 w i l l also c a l c u l a t e the t i m e s - o f - f l i g h t of a l l three emitted p a r t i c l e s , i n nanoseconds per meter. Table 3 gives a d e f i n i t i o n of the input and output symbols. For s i m p l i c i t y data i s read with one number per card i n F 10.6 format, i n the following order: DELTA1, DELTA2, LIM1, LIM2, LIM3, LIM4, Ml, M2, M3, M4, M5, M6, E l , Ql, Q20. This i s followed by pai r s of cards f o r each of the excited states of i n t e r e s t . The f i r s t of the p a i r i s the excited state, and the second i s the width of that s t a t e . (For the ground state and for very sharp states, the cards must be zero or blank). The l a s t card a f t e r the data cards can be $ENDFILE. A l i s t i n g of Kinem follows Table 3, and i s written i n Fortran IV (and was rewritten f o r the I.B.M. 360/67). Figure 20 shows the various p a r t i c l e s and the names of t h e i r respective laboratory angles. 20. S c h e m a t i c d i a g r a m showing t h e t h r e e f i n a l s t a t e p a r t i c l e s M3, M5, and M6 and t h e i r lab a n g l e s PS I, THETA5, and THETA6 r e s p e c t i v e l y . 65 Table 3 D e f i n i t i o n of Output Symbols From "Kinem" Ml: mass of the bombarding p a r t i c l e M2: mass of target nucleus M3: mass of the f i r s t emitted p a r t i c l e M4: mass of r e c o i l nucleus (intermediate state) M5: mass of second emitted p a r t i c l e M6: mass of t h i r d emitted p a r t i c l e E l : bombarding energy Ql: Q of f i r s t r e a c t i o n . Q20: Q of breakup of r e c o i l nucleus . •" LIM1: the smallest angle of i n t e r e s t f o r the f i r s t emitted p a r t i c l e , M3. This i s incremented by DELTAlvomtil the l a r g e s t angle at which M3 i s observed, i s reached, which i s LIM2. LIM3: the smallest angle of i n t e r e s t f o r the second emitted p a r t i c l e , M5. This i s incremented by DELTA2 u n t i l the la r g e s t angle at which M5 i s observed, i s reached, which i s LIM4. The natural width (FWHM) of the excited states of the r e c o i l i s incorporated into the c a l c u l a t i o n and i s denoted by I. Where 1 = 1 , 0, +1, representing the upper middle and lower middle and lower l i n e contours r e s p e c t i v e l y , of the f i f t h emitted p a r t i c l e , M5. If the state has no width, 1 = 0 . PSI: the laboratory angle of M3 ZETA4: the laboratory angle of M4 66 E3: the energy of M3 E4: the energy of M4 T3: the t i m e - o f - f l i g h t of M3 T4: The t i m e - o f - f l i g h t of Mr THETA5, E5, T5: The laboratory angle, energy, and time-o f - f l i g h t of M5, r e s p e c t i v e l y . THETA6, E6, T6: the laboratory angle, energy, and time-o f - f l i g h t of M6, r e s p e c t i v e l y . THETAR5, THETAR6, ER5, ER6, TR5, TR6: the laboratory angles, energies, and t i m e s - o f - f l i g h t of the f i f t h and s i x t h p a r t i c l e s reversed i n i d e n t i t y i n the centre-of-mass frame. $LIS KINEM > 1 C * * * * L A B S Y S T E M * * * * > 2 C > 3 REAL M1 /M2 /M3 /M4 /M5,M6 /LIM1 /LIM2 /LIM3 /LIMU /MZETU /MZMAX > k LOG 1CAL ROOT2,ROOT3,NOMAX,NOMAX6 > 5 ROOT2 =.FALSE. > 6 XXX =360. > 7 XX =0. > 8 c R E A D I N A N D W R I T E D A T A > 9 READ(5 /10)DELTA1,DELTA2,LIM1,LIM2 /LIM3,LIM4 > 10 WRITE(6 /12)DELTAl /DELTA2 /LIMl /LIM2 /LIM3 /LIMlt > 11 READ(5,10)Ml,M2,M3,Mli,M5,M6, El/Q1/Q20 > 12 WRITE(6,13)M1,M2,M3,MU,M5,M6,E1,Q1,Q20 > 13 I F ( M 3 . L E . 0 . ) M 3 » 1 . E - 1 5 > lk 7 READ(5,10)EX,W > 15 WRITE(6,305) > 16 305 FORMAT(lHl) > 17 WRITE(6/li*)EX/W > 18 10 FORMAT(F10.6) > 19 12 FORMAT( 1X,8HDELTA1 = /F8.3,2X,8HDELTA2 =,F8.3,2X,6HLIM1 =,F8.3,2X > 20 1,6HLIM2 =,F8.3,2X,6HLIM3 -,F8.3,2X,6HLIMlr =,F8.3,/) > 21 13 FORMATCIX,UHM1 =,F10.6,2X,UHM2 = , F10. 6, 2X, l*HM3 = , F10 . 6, 2X,l*HMlt = , > 22 1F10.6,2X,4HM5 =,F10.6,2X,UHM6 =, F10. 6, 2 X , / 7 , I X , 4HE1 =,F9.5,2X > 23 2WI =,F9.3,2X,5HQ20 =,F9.3,/ ) > 2k lk FORMAT(10X,29HEXC1TATION ENERGY OF RECOIL =,F9.3,2X,13HMEV ,FWHM > 25 1 =,F9.3,2X,3HMEV ) > 26 C ************************************************************ > 27 LL = 0 > 28 LM = 2 > 29 IF(W.EQ.0.0)GO TO 9 > 30 GO TO 8 > 31 9 LL = 1 > 32 LM-1 > 33 8 DO 5 J=LL,LM > 3k 1 =J-1 > 35 Q =Q1-EX+FL0AT(I)*W/2. > 36 Q2=Q20+EX-FLOAT(1)*W/2. > 37 WRITE(6,15)0,02 > - 38 15 FORMAT(////,2X/3HQ =,F9.3,2X,4HQ2 =,F9.3,2X,10H########## ,/) > 39 IF(I)17,18,19 > kO 17 WRITE(6,171)1 > hi 171 FORMAT(IX,3H1 =,13,2X,11HUPPER ) > hi GO TO 16 > 1*3 18 WRITE(6,181)1 kh - - 181 F0RMAT(1X,3HI =,13,2X,6HM1DDLE ) > kS GO TO 16 > 1*6 19 WRITE(6,191)1 > - - hi 191 F0RMAT(1X,3HI =,13,2X,11HL0WER ) > hZ C **************************************************** * ************ > 49 16 C1=M4*(M2*E1 +Q*M2 +Q*M1)/(M1*M3*E1) > 50 PS 1 MAX = 360. > 51 IF(C1.LT.O.O)GO TO 5 > 52 B=M1*M3*E1/((M1+M2)*(M3+Mn0) > 5 ^ C = M 2 * M 3 * ( 1 . + M 1 * Q / M 2 / E T ) / ( M 1 + M 2 ) / ( M 3 + M l r ) > 55 A = M 1 * M U * E 1 / E T / ( M 1 + M 2 ) / ( M 3 + M l r ) > 5 6 C T E S T F O R P S I M A X I M U M > 57 C T E S T F O R T W O V A L U E S O F E 3 > 58 I F ( C 1 - 1 . ) 2 0 , 2 0 , 3 9 > 5 9 20 R P S I M X = A R S I N ( S Q R T ( C D ) > 60 P S I M A X = R P S I M X * 5 7 . 2 9 5 7 > 61 ROOT2 = . T R U E . > 62 W R I T E ( 6 , 2 2 ) P S I M A X > 63 22 F O R M A T ( / , 1 0 X , 2 7 H T H E R E IS A MAXIMUM ANGLE OF F 9 . l r , 2 X , 5 1 H D E G R E E S FOR > .6U 1 PSI AND TWO V A L U E S FOR THE E N E R G I E S ) > 65 C > 66 C ************************************** > 67 C > 68 L I M 2 = P S I M A X > 69 3 9 P S I = L I M 1 > 70 C I N C R E M E N T P S I > 71 1*0 P S I = D E L T A 1 + P S I > 72 IF(PSI.GT.LIM2)GO TO 5 > 73 RPSI=PSI/57.2957 > 7k C M A X . A S Y M M E T R Y E N E R G Y O F M 3 > 75 E3SYMM=ET*(1.-A-C) > 76 WRITE(6,24)E3SYMM > 77 2** FORMAT(//2X/32HMAXIMUM ASYMMETRY ENERGY OF M3 = ^ 9 . 3 , / / ) > 78 ZMAX =180. > 79 ZMAX6 =360. > 80 ROOT3 =.FALSE. > 81 NOMAX6=.FALSE. > 82 C3=COS(RPSI) > 83 AE3=C3 + SQRT(C1-1. + C3*C3) > 81* E3=B*AE3*AE3 > 85 El* = El + Q-E3 > 86 IFCE**. LT.0.0)GO TO 5 > 87 XM =SQRT(M3*E3/(M1**E1*))*SIN(RPSI ) > 88 IF(ABSCXM) . G E . l . )GO TO 1*0 > 89 RZETAI*=ARSIN(XM) > 90 ZETA4 =RZETAi+*57.2957 > 91 C T E S T A R C S I N O F Z E T A l( > 92 PI =SQRT(2.*M1*E1) > 93 P3 =SQRT(2.*M3*E3) > 9k DEL =P1-P3*C0S(RPSI) > 95 1 F (DEL. LT. 0. ) Z E T A U = 180. - Z E T A I T > 96 LR05 =ZETA4 > 97 R05 = Z E T A I +-FL0AT(LR05) > 98 T3 =71.92*SQRT(M3/E3) > 99 Tk =71.92*SQRT(M4/Ei,) > 100 c -> 101 IF(ROOT2) GO TO kl > 102 MZETtt =-ZETAU > 103 WRITE(6,U)PSI ,MZ£.Tk,£l,£k,T5,Tk > 10k kl FORMAT(/,1X,10HFOR PSI = ,F10.k,2X,13HDEG. ZETAk « ,F9 . * f ,2X , l rHE3 > 105 lF9.kf 2X,7HAND EI*=,F9.lr,2X,lfHT3 = ,G9. k, 2X,kHTk - , G 9 . U , / ) > 106 GO TO 49 > 107 c > 108 42 AE32 =C3 -SQRTCC1-1. + C3*C3) > 109 E32 =B*AE32*AE32 > 110 E42 =E1 + Q - E32 > 111 " IF(E42.LT.0.0)GO TO 5 > 112 XN =SQRT(M3*E32/(M4*E42))*SIN(RPSI) > 113 IF(ABS(XN).GE.1.)G0 TO 40 > 114 RZETA2=ARS I M (XN) > 115 ZETA42=RZETA2*57.2957 > 116 P32 »SQRT(2 .*M3*E32) > 117 ' DEL2 =P1-P32*C0S(RPSI) > 118 IF(DEL2.LT.0.)ZETA42=180.-ZETA42 > 119 T32 =71.92*SQRT(M3/E32) > 120 "" T42 =71.92*SQRT(M4/E42) > 121 WRITE(6,43)PSI,ZETA4,ZETA42,E3,E32,T3,T32, E4,E42,T4,T42 > 122 43 FORMAT(9X,9HFOR PS I -,F8.1t,5X,36HDEGREES,THE TWO VALUES OF ZETA4 A > 123 1RE- / 2(F9.3 / 3X) / / / 9X,25HTHE TWO VALUES OF E3 A R E - , 2 ( F 9 . 3 , 3 X ) , / , 9 X , > 124 225HTHE TWO VALUES OF T3 ARE,2(G9.3 / 2X) / / / 9X / > 125 325HTHE TWO VALUES OF E4 ARE,2(F9 .3 ,2X) ,/ ,9X , > 126 425HTHE TWO VALUES OF T4 ARE,2(G9.3, 2X ) , / ) > 127 .... IF((M5.EQ.0.0).OR.(M6.EQ.0.0))GO TO 40 > 128 WRITE(6 / 44)E3 > 129 44 FORMAT(10X,19HF0R THE LARGER E3 - , E 9 . 3 , / ) > 130 ... 49 ... IF((M5.EQ.0.0).OR.(M6.EQ.0.0))GO TO 40 > 131 C ***************************************** > 132 C T E S T F O R Z E T A 6 M A X I M U M 133 ... . . . . 1 F ( ( M 5 * Q 2 / M 6 / E 4 ) - 1 . ) 6 0 0 / 6 0 0 / 6 2 > 134 600 RZMAX6=ARSIN(SQRT(M5*Q2/M6/E4)) > 135 ZMAX6 =-RZMAX6*57.29578 136 .. ._ ... NOMAX6 = .TRUE. > 137 WRITE(6,61)ZMAX6 > 138 61 FORMAT(/,10X,28HTHERE IS A MAXIMUM ANGLE OF ,F9.3,2X,9HFOR ZETA6) . 139 . 62 ... TEST =M6*Q2/M5/E4 > 140 NOMAX =.TRUE. > 141 C T E S T F O R Z E T A 5 M A X I M U M > . 142 - - .. IF (TEST-1.570,70,54 > 143 70 RZMAX =ARS1N(SQRT(TEST)) > 144 NOMAX =.FALSE. > 145 ZMAX =RZMAX*57.29578 > 146 ROOT3 =.TRUE. > 147 MZMAX =-ZMAX > 148 WRITE(6,72)MZMAX > 149 72 FORMAT(/,10X/28HTHERE IS A MAXIMUM ANGLE OF , F 9 . 3 , 2 X , 9HFOR ZETA5) > 150 C > 151 LIM4 =ZMAX > 152 C > 153 c *********************************** > 154 54 ZETA5 =-LIM3+R05 > 155 IJR1 TEC 6, 50) > 156 50 FORMATC 5X,120H*THETA5 ***** E5 *** THETA6 ***** E6 ******** T5 *** > 157 1* T6 *** THETR5 ***** ER5 ** THETR6 ***** ER6 ***** TR5 ****** TR6 > 158 2 *) > 159 Wl =ZETA4-90. > 160 W2 =ZETA4+90. > 161 C C A R D S F O R T H E T A 5 , E 5 , E T C . > 162 55 RZETA5=ZETA5/57.2957 > 163 IF(LIM4.EQ.ZMAX)ROOT3=.TRUE. >... -. 164 . . . . . . IF((ZETA5.LT.0.0).AND.(ABS(ZETA5).GE.ZMAX))GO > 165 IF(ZETA5.GT.ZMAX)GO TO 40 > 166 C5 =COS(RZETA5) > 167 AE5 =C5+SQRT(TEST-1.+C5*C5) > 168 56 E5 =E4*AE5*AE5*M5/M4 > 169 E6 =Q2+E4-E5 170 IF(E6.LE.0.0)GO TO 90 > 171 57 XL « S Q R T ( M 5 * E 5 / ( M 6 * E 6 ) ) * S I N ( R Z E T A 5 ) > 172 IF(ABS(XL).GT.l .)GO TO 94 > . . . 173 - RZETA6=1.5707963-ARCOS(XL) > 174 ZETA6 =RZETA6*57.2957 > 175 THETA5 =ZETA4-ZETA5 > ... 176 - IF(THETA5.GE.360.)GO TO 60 > 177 IF(ROOT3.0R.NOMAX)XX=XXX > 178 570 THETA6=ZETA4+ZETA6 > 179 C Z E T A 6 A R C S I N C O R R E C T I O > 180 IF((NOMAX6).AND.(THETA6.LT.(ZETA4+ZMAX6)))GO TO 94 > 181 IF((NOMAX6).AND,(THETA6.GT.(ZETA4-ZMAX6)))GO TO 94 > 182 I =0 > 183 IF(NOMAX6)GO TO 575 > 184 I F(NOMAX)ROOT3 = .TRUE. > 185 !F(ROOT3)XXX=THETA6 > 186 IF((THETA5.GT.ZETA4).AND.(R00T3).AND.(THETA6.GT.W1).AND.(XX.GT. > • 18 7 1THETA6))I=-10 -> 188 IF((THETA5.LT.ZETA4).AND.(R00T3).AND.(THETA6.LT.W2).AND.(XX.LT. > 189 1THETA6))I=10 > - 190 IF((THETA6.GT.ZETA4).AND.(NOMAX).AND.(THETA6.LT.W2).AND.(XX.LT. -> 191 1THETA6))I=10 ^ > 192 IF((THETA6.LT.ZETA4).AND.(NOMAX).AND.(THETA6.GT.Wl).AND.(XX.GT. > 193 - 1THETA6)) I =-10 > 194 IF(I.LT.0)THETA6=2.*W1-THETA6 > 195 IF CI.GT.0)THETA6=2.*W2-THETA6 > 196 575IF(N0MAX)R00T3=.FALSE. > 197 IF(THETA5.LE.LIM3)GO TO 40 GO BACK FOR ANOTHER PS I THETA5,THETA6,ZETA5,ZETA6,ARE ALL MEASURED BELOW THE AXIS AND ARE ALL NEGATIVE WITH RESPECT TO PS I XLR1 =SQRT(M4*E5/M6/Q2)*SIN(RZETA5) IF(ABS(XLRl).GT.l . )GO TO 94 RTHE5 =ARSIN(XLR1) ER5 =M6*E4/M4 +2.*SQRT(M5*M6*E4*Q2/M4/M4)*COS(RTHE5) + M5*Q2/M4 ER6 = E4 + Q2 - ER5 IF(ER6.LT.0.0)GO TO 94 XLR2 =SQRT(M5*Q2/M4/ER5)*SIN(RTHE5) IF(ABS(XLR2).GT.l.)GO TO 94 RZETR5=ARSIN(XLR2) XLR3 =SQRT(M6*Q2/M4/ER6)*SIN(RTHE5) IF(ABS(XLR3).GT.l.)GO TO 94 RZETR6=ARSIN(X LR3) ZETR5 = RZETR5*57.29578 ZETR6 = RZETR6*57.29578 THETR5=ZETA4-ZETR5 > 216 THETR6=ZETA4+ZETR6 > 217 IFCI .LT.0)THETR6=2.*W1-THETR6 > 218 IF(I .GT.0)THETR6=2.*W2-THETR6 > 219 A3 =-THETA5 " ' ' > 220 A4 =-THETA6 > 221 A5 =-THETR5 222 - •• " A6 =-THETR6 > 223 T5 =71.92*SQRT(M5/E5) > 224 T6 -71.92*SQRT(M6/E6) > — 225 TR5 =71.92*SQRT(M5/ER5) > 226 TR6 =71.92*SQRT(M6/ER6) > 227 C > 228 1FCTHETA5.GT.190.)GO TO 93 > 229 WRITE(6,58)A3,E5,A4,E6,T5,T6,A5,ER5,A6,ER6,TR5,TR6 > 230 58 F0RMAT(5X,4(F8.3,2X) ,2(F9.2,1X) ,4(F8.3,2X) ,2(F9.2,1X) ) > 231 93 • IF(R00T3)G0 TO 90 > 232 C IF ZETA5 IS POSITIVE INCREMENT WITH A POSITIVE VALUE, DELTA2 > 233 C IF ZETA5 IS NEGATIVE,SUBTRACT DELTA2 EACH TIME UNTIL ZETA5 IS > 234 C LESS THAN OR EQUAL TO LIM3 > 235 94 IF(ZETA5,GE.0.0)GO TO 65 > 236 ZETA5=ZETA5-DELTA2 > 237 C TEST FOR THE CHANGE OF INCREMENT > 238 GO TO 55 > 239 59 IF(ZETA5.GT.0.0)GO TO 40 > 240 ZETA5 =LIM3+R05 > 241 THETA6=0. > 242 GO TO 55 > 243 65 ZETA5 =ZETA5 + DELTA2 > 244 GO TO 55 > 245 C ****************************************** > _. 246 100 IF (.NOT.ROOT2) GO TO 40 > 247 E4 =E42 > 248 ZETA4 =ZETA42 . 24 9 WRITE(6,45)E32 > 250 45 FORMATQOX^OHFOR THE SMALLER E3 - , £ 9 . 3 ) > 251 ROOT2 =.FALSE. > 252 GO TO 49 > 253 C *************************************** > 254 90 IF(.NOT.ROOT3)GO TO.94 > 255 AE5 =C5-SQRT(TEST-1.+C5*C5) > 256 E5 =E4*AE5*AE5*M5/M4 > 257 E6 =Q2+E4-E5 > 258 IF(E6.LE.0.0)GO TO 94 > 259 ROOT3=.FALSE. > 260 GO TO 57 > , 261 5 CONTINUE > 262 GO TO 7 > 263 1000 STOP > 264 END # END OF FILE 8 2 B i b l i o g r a p h y A l l e n , K. W., A l m q v i s t E., and Bigham, C. B. 1960. Procedures o f the P h y s i c a l S o c i e t y 75,913. Ask, L. 1961. A r k i v f o r F y s i k 1 9 , 2 1 9 . Cocke, C. L. 1968. N u c l e a r P h y s i c s A L I O , 3 2 1 . Day, R. B. and Walker, R. L. 1952. P h y s i c a l Review 85,582. Dearnaley, G. I960. Review of S c i e n t i f i c Instruments 31,197. Deutchman, P. 1969. P r i v a t e Communication. Duggan, J . L. L968. J o u r n a l o f N u c l e a r P h y s i c s 67,517. F o r s y t h , P. D. and P e r r y , R. R. 1965. N u c l e a r P h y s i c s 67,517. Freeman, J . M., Hanna, R. C , and Montague, J . H. L958. N u c l e a r P h y s i c s 5,148. Galonsky, A. and M c E l l i s t r e m , M. T. L955. P h y s i c a l Review 98,590. G a t l i n b u r g Conference on C o r r e l a t i o n s of P a r t i c l e s E m i t t e d i n N u c l e a r R e a c t i o n s , Tennessee, 1964. Reviews o f Modern P h y s i c s , 37,327. Heggie, J . C. P., M a r t i n , P. W., and Omar, H. M. L969. P r i v a t e Communication. L e r n e r , G. M. and Marion, J . B. L969. N u c l e a r Instruments and . Methods 69,115. L i n c k J . , N i c o l a s - L i n c k , I . , BiLwes, R., and M a g n e t t e - V a l e t t e , D. 1963. J o u r n a l o f P h y s i c s and R a d i a t i o n 24,983. Makosky, L. 1969. MSc. T h e s i s , U n i v e r s i t y o f B r i t i s h Columbia. 83 P h i l l i p s , G. C. 1964. Reviews of Modern Physics 36,1085. Ortec, 1966. I n s t r u c t i o n Manual f o r the 423 P a r t i c l e I d e n t i f i e r , Oakridge, Tennessee. Ortec. 1967. S o l i d State Detector Manual, Oakridge, Tennessee. Ranken, W. A., Bonner, T. W., and McCrany, J . H. 1958. P h y s i c a l Review 109,1646. Reimann, M. A., M a r t i n , P. W., and Vogt, E. V/. 1968. Canadian -J o u r n a l of Physics 46,2241. Teplov, I . B., Shevchenko, 0. P., and Ruuge, E. K. 1961. S o v i e t P h y s i c s , JETP, 12,640. Watson,. ?K. W. 1952 . P h y s i c a l Review 88,1163 . Whalen, B. A., 1965. Ph.D T h e s i s , U n i v e r s i t y of B r i t i s h Columbia. 

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