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A search for the direct radiative capture rection D(d,[gamma])He⁴ Whalen, Brian Austin 1962

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A SEARCH FDR THE DIRECT RADIATIVE CAPTURE REACTION D ( d , t f ) H e 4 by BRIAN AUSTIN WHALEN B.Sc. U n i v e r s i t y o f W a s h i n g t o n , 1959. THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n t h e D e p a r t m e n t o f PHYSICS We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d . THE UNIVERSITY OF BRITISH COLUMBIA O c t o b e r , 1962. 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 i t 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. B R I A N A U S T I N WHALEN Department of Physics  The University of British Columbia, Vancouver 8, Canada. Date October 9th 1962 ABSTRACT i An experimental method for the detection of the d(Df'J)He4 react ion has been developed. It involves the use of a double focusing magnetic spectrometer in conjunction with a s o l i d state counter mounted in the foca l plane of the spectrometer, the counter determining both the energy and dE/dx of the incident par t i c l e s from the react ion . The design and construction of a p a r t i c l e beam handling system to guide the p a r t i c l e beam from the Van de Graaff generator to the object point of the spectrometer has been completed and tested. Using this beam, the charac-t e r i s t i c s of the spectrometer and s o l i d state counter have been determined and recorded. An attempt was made to detect the d(D ,B )He 4 reaction but no d i r e c t l y useful information on the r e -action crossect ion was obtained. However, u t i l i z i n g the knowledge gained during this experiment, i t should be possible to make a more exacting attempt at the reaction crossect ion determination. - v i -ACKNOWLEDGEMENT Tha a u t h o r w i s h e s t o e x p r e s s h i s g r a t i t u d e t o Dr..B.L.White f o r h i s many l o n g h o u r s o f d i r e c t i o n t h r o u g h o u t h i s r e s e a r c h p r o g r a m . TABLE OF CONTENTS Chapter • Page I INTRODUCTION 1. II BEAM SERVO SYSTEM . 5. General discussion 5. 1 7 ° e l e c t r o s t a t i c switching system. . . . . . 6. Mechanical design . 6. C i r c u i t design of switching system . . . 7. Beam posi t ion servo. . 8. The beam detector 9. Safety precautions 10. The two-dimensional magnetic servo system . . 11. Servo c i r c u i t 12. 6 Volt supply 13. III SURVEY OF THE 6 0 ° DOUBLE FUCU5ING MAGNETIC SPECTROMETER 15. Physical dimensions of the spectrometer . 16. Method of focus survey 17. Primary focusing qual i ty 21 . Counter pos i t ion &. baf f l ing 23. Second order focusing 25. IV COUNTER CHARACTERISTICS 28. General:discussion . . . 28. Counter test ing experimental arrangement 30. - iv -Chapter Page Window thickness . . . . . 33. L inear i ty 33. V. EXPERIMENTAL, D ( d , £ ) H e 4 REACTION . . . . 36. Introduction 36. Time dependent counter background . 37. Heavy Water transmission target s t a b i l i t y 39. Beam scatter ing into spectrometer. . 39. APPENDIX A. D(d,o')He 4 react ion k inet ics 41. APPENDIX B. The 1 7 ° e l e c t r o s t a t i c def lect ion system 44. APPENDIX C. Electromagnetic servo lock-on magnets 46. APPENDIX D. Target thickness c a l i b r a t i o n . . . . 50. APPENDIX E . Estimate of D f d ^ H e 4 Reaction crossect ion 54. LIST OF FIGURES Figure 1. Beam Handling System, 2. E.5 Servo C i r c u i t . 3. . E.S H,T Supply. 4. S t e e r i n g Magnets. 5. S t e e r i n g Magnets C i r c u i t s . 6. Spectrometer Dimensions. 7. Spectrometer Coordinate System. 8 — 1 3 Spectrometer Focus Survey. 14. Focus of°C From D(d ,V)He Reaction. 15. Nomograph 16. Spectrometer Current P r o f i l e . 17-19 Ortec Counter C a l i b r a t i o n . 20. B a r r i e r P e n e t r a t i o n i n Ortec Counter. 21 , Target System. CHAPTER 1. INTRODUCTION The study of the nucleon-nucleon interact ion (or "nuclear force") i s one of the centra l problems of nuc-lear physics . It seems that one of the most d irec t methods of attacking this problem in the low energy (approx, up to 10 Mev,) region is through the study of nuclear s ca t t er -ing and react ions• involv ing only a few nucleons (so that the problem is a "few body" problem, rather than a "Many body" problem). Reactions involving up to 4 nucleons we c a l l "few nucleon" react ions . In this laboratory, the "few nucleon" problem has received some at tent ion, (Warren, G r i f f i t h s et a l p(D,$)He reaction) and i s presently under-3 study (Monier n,p scatter ing and d{D,t)p and d(D,He )n r e » act ions) . This thesis describes some experimental s tudies , also of the D , d f react ion . The reaction to be described is the d irec t r a d -ia t ive capture reaction D(d,tf)He 4. The obvious way to study this reaction is to look for the high energy gamma rays of approximately 25 Mev. A crude ca lcu la t ion ofmthe D(d,y)He crossection , (See Appendix E) , gives a crossection of the -29 -30 2 1 order of 10 or 10 cm . Fowler et a l have set an ex-1. Fowler ,Lauritson,Tol lestrup,Phys ,Rev* T6, 1767, (1949) perirnental upper l i m i t on the crossection of less than. -31 2 10 cm „ However, d i f f i c u l t i e s arise due to the fact that other, highly p r o l i f i c , reactions occur similtaneously and peoduce a very high gamma and nsutron background ac-t i v i t y . The competing reactions are D(d,He )n and D ( d , t ) p „ and the crossections for these reactions are of the order -27 2 of 10 cm . Also any target backing that i s used w i l l produce gamma a c t i v i t y and contribute to the background. It i s evident that to study this reaction through gamma measurements would require the measurement of a very low gamma a c t i v i t y in a very high background which would tend to give spurious counts in the relevant energy region in the gamma ray spectrometer. Therefore a second method of treat ing the problem has been considered. The other approach i s to look for the r e c o i l Helium ions which resul t from D(d,2nHe4. These ions w i l l be mainly in the ++ state and w i l l henceforth be ca l l ed alphas. If the kinematics of the reaction are considered, as in the -Appendix A, i t i s found that for a 3 Mev. beam of incident deutrons, a l l the r e c o i l alphas w i l l emerge in a cone at an angle of less than 1 5 ° with respect to the incident beam. Using the 60° double focusing magnet spectrometer with a s o l i d state detector at the image focus, i t i s possible to measure over acceptance angles of between 5° and 15° with respect to the beam. This avoids the danger of swamping the r e c o i l alpha counter with coulomb scattered deuterons from the beam when the - 3 -r e c o i l p a r t i c l e s are detected at smell angles to the i n c i d -ent beam, since the e l a s t i c a l y s c a t t e r e d deuterons do not have the same t r a j e c t o r y i n the spectrometer as the r e c o i l alphas and t h e r e f o r e do not reach the counter a \ the s p e c t -rometer focus. Other charged p a r t i c l e s , f o r example protons with the same momentum to charge r a t i o as the alphas have the same t r a j e c t o r y i n the spectrometer, but with a s o l i d s t a t e counter at the focus the energy of the p a r t i c l e s may be measured and thus i t i s p o s s i b l e to d i f f e r e n t i a t e between these p a r t i c l e s and the r e c o i l i alphas, Upon i n s p e c t i o n of p a r t i c l e t r a j e c t o r i e s i n the spectrometer, ( r e f e r to Ap-pendix D.), i t i s evident that a proton and alpha of the same energy have the same t r a j e c t o r y i n thei spectrometer, so that a method must be devised to d i f f e r e n t i a t e between the two p a r t i c l e s of the same energy. This i s accomplished using a dE/dX technique by using a s o l i d s t a t e counter with a low r e s i s t i v i t y and applying a low bias voltage to i t . This makes the a c t i v e region of the counter small enough that the alphas are completely stopped i n i t and lo s e a l l t h e i r energy while the protons of the same energy penetrate through the a c t i v e region and expend only part of t h e i r energy i n i t . The r e s u l t i s that the cu r r e n t s i g n a l r e c e i v -ed from the counter due to the protons can be made to be smaller than the s i g n a l due to the alphas of the same energy. Using t h i s combination of s o l i d s t a t e counter and s p e c t r o -meter, the search f o r the r e c o i l alphas now becomes f e a s i b l e . - 4 -Before c a r r y i n g out the above described ex-periment, three p r e l i m i n a r y pieces of work had to be com-p l e t e d . F i r s t , a high f l u x (approx.10 micro-amps) beam of deuterons had to be guided from the Van de Graaff generator, to the t a r g e t at the object point of the spectrometer. This r e q u i r e d the c o n s t r u c t i o n of a beam handling system compri-sed of two servo systems, namely a 17° e l e c t r o s t a t i c de-f l e c t i o n system beam switcher followed by a two dimensional magnetic servo lock-on system. Secondly, an exact determin-a t i o n of the p a r t i c l e t r a j e c t o r i e s i n the spectrometer and i t s f o c u s i n g c h a r a c t e r i s t i c s was necessary to allow the • . mounting of the s o l i d s t a t e counter at the optimum p o s i t i o n f o r d e t e c t i n g the r e c o i l alphas. Also, a b a f f l i n g system had to be designed to keep s c a t t e r e d p a r t i c l e s from reach-' ing the counter. F i n a l l y , the c h a r a c t e r i s t i c s of the s o l i d < s t a t e c o u n t e r and a m p l i f i e r had to be determined so that d i f f e r e n t i a t i o n between alphas and protons could be acc-omplished. In Chapter 5 a d e s c r i p t i o n of the experimental apparatus and procedure i s recorded. Although no u s e f u l d e t a i l s on the r e a c t i o n c r o s s e c t i o n were obtained, i n f o r m a t i o n as to ta r g e t t h i c k n e s s and s t a b i l i t y , counter response and time de-pendant background w i l l be u s e f u l i n any f u t u r e attempt at the, c r o s s e c t i o n measurement. With s i m i l a r background c o n d i t i o n s , assuming there w i l l be no e l a s t i c a l l y s c a t t e r e d beam reaching the counter with good b a f f l i n g , i t should be p o s s i b l e to meas--32 2 ure a c r o s s e c t i o n of ^ .10 cm with the present apparatus. % CD z rn r n 0 x _ > •n •n F I G U R E I - 5 -CHAPTER IT BEAM SERVO SYSTEM The p a r t i c l e beam p r o d u c e d by t h e U.B.C. Van de G r a f f g e n e r a t o r i s t o be g u i d e d by means o f e l e c t r o s t a t i c and m a g n e t i c s e r v o d e f l e c t i o n s y s t e m s and f o c u s e d by e l e c t r o -s t a t i c and m a g n e t i c q u a d r u p o l e l e n s e s t o t h e o b j e c t p o i n t o f t h e s i x t y d e g r e e d o u b l e f o c u s i n g m a g n e t i c s p e c t r o m e t e r . The beam emerges f r o m t h e a n a l y s i n g magnet a t t h e base o f t h e Van de G r a f f and i s f o c u s e d on t h e e n t r a n c e o f t h e 17° d e f l e c t o r by a m a g n e t i c q u a d r u p o l e l e n s . I t i s t h e n d e f l e c t e d i n t h e d i r e c t i o n o f t h e s p e c t r o m e t e r o b j e c t p o i n t by t h e 17° e l e c t r o s t a t i c d e f l e c t i o n s y s t e m and p a s s e s t h r o u g h t h e two s e r v o s t e e r i n g magnets w h i c h l o c k t h e beam o n t o t h e t a r g e t a t t h e o b j e c t p o i n t o f t h e s p e c t r o m e t e r ; t h e s t e e r i n g magnets i n c r e a s e v e r y c o n s i d e r a b l y t h e l a t i t u d e a l l o w a b l e i n t h e t o l -e r a n c e s on beam h a n d l i n g e q u i p m e n t p r e c e d i n g them. Two q u a d -r u p o l e l e n s e s a r e p l a c e d between t h e d e f l e c t i o n magnets and th e t a r g e t t o c o n s e r v e t h e beam i n t e n s i t y . The p o s i t i o n i n g o f t h e components o f t h e s e r v o s y s t e m i s shown i n F i g u r e 1. The a p p r o x i m a t e o v e r a l l d i s t a n c e o f t r a v e l f o r t h e beam i s 34 f t . The d i s t a n c e o f t r a v e l f r o m d e f l e c t o r t o t a r g e t i s a b o u t 25 f t . and t h e r e q u i r e d s t a b i l i t y o f t h e beam on t a r g e t i s 1/25". T h i s i s an a n g u l a r s t a b i l i t y o f 1/100 d e g r e e o r a s t a b i l i t y o f t h e 17° d e f l e c t i o n s y s t e m o f a b o u t one p a r t i n two t h o u s a n d . The c o n t r o l c i r c u i t o f - 6 -t h a t s y s t e m was d e s i g n e d t o g i v e t h i s s t a b i l i t y . The h o r i z o n -t a l and v e r t i c a l s t e e r i n g magnets w i l l d e f l e c t the beam up t o 1 ° i n e i t h e r d i r e c t i o n and t h e g a i n - f e e d b a c k o f t h e l o c k -on s y s t e m i s s u f f i c i e n t a l s o to g i v e a t a r g e t p o s i t i o n s t a b -i l i t y o f 1 / 2 5 " . i 1 7 ° E l e c t r o s t a t i c S w i t c h i n g S y s t e m M e c h a n i c a l D e s i g n : The e l e c t r o s t a t i c d e f l e c t i o n s y s t e m c o n s i s t s o f two c o n c e n t r i c s t a i n l e s s s t e e l p l a t e s , s e p a r a t e d a d i s t a n c e o f 0 . 3 7 5 " by l u c i t e s p a c e r s . T h e s e p l a t e s f o r m a s e c t i o n o f c o n c e n t r i c c y l i n d r i c a l c o n d e n s e r w i t h a r a d i u s o f c u r v a t u r e 1 6 1 " and an a r c l e n g t h f o u r f e e t . The e l e c t r o s t a t i c f i e l d between t h e p l a t e s , when a p o t e n t i a l d i f f e r e n c e i s a p p l i e d , v a r i e s as t h e r e c i p r o c a l o f t h e r a d i u s ; t h e r e f o r t h e f r a c t i o n -a l v a r i a t i o n i n t h e e l e c t r i c f i e l d between t h e p l a t e s i s j u s t t h e r a t i o o f t h e p l a t e s e p a r a t i o n to t h e r a d i u s o f t h e c u r -v a t u r e . T h i s amounts t o a b o u t one p a r t i n 5 0 0 . The d e f o c u s -i n g e f f e c t t h i s has on t h e beam i s e a s i l y c o r r e c t e d by t h e q u a d r u p o l e l e n s w h i c h f o l l o w s . Thus t h e e l e c t r i c f i e l d i n -s i d e t h e p l a t e s c a n be c o n s i d e r e d c o n s t a n t f o r the p u r p o s e o f c a l c u l a t i n g p a r t i c l e t r a j e c t o r i e s be tween the p l a t e s . The s y s t e m i s d e s i g n e d t o d e f l e c t up t o 3 . 5 Mev p a r t i c l e s f r o m t h e Van de G r a f f a c c e l e r a t o r . The v o l t a g e ' w h i c h must be a p p l i e d between t h e p l a t e s o f t h e d e f l e c t o r t o a c c -4- 300 V 10 K< <IOK FIGURE 2. - 7 -o m p l i s h t h i s i s 16.2 Kev ( r e f e r t o A p p e n d i x C ) , I t may be n o t e d f r o m t h e a p p e n d i x t h a t t h e v o l t a g e a p p l i e d t o t h e p l a t e s t o p r o d u c e a d e f l e c t i o n w i l l be d i r e c t l y p r o p o r -t i o n a l t o t h e Van de G r a a f f p o t e n t i a l and i n d e p e n d a n t o f t h e t y p e o f p a r t i c l e b e i n g a c c e l e r a t e d . C i r c u i t D e s i g n o f S w i t c h i n g S y s t e m ; The e l e c t r i c a l s y s t e m a s s o c i a t e d w i t h t h e E l e c t r o s t a t i c d e f l e c t o r c o n s i s t s o f two p a r t s ; one, t h e s e r v o s y s t e m , w h i c h d r i v e s , t h e o t h e r , t h e h i g h v o l t a g e s u p p l y f o r t h e d e f l e c t o r p l a t e s . The s e r v o s y s t e m i s a c t -i v a t e d by a s i g n a l g e n e r a t e d when t h e p a r t i c l e beam s t r i k e s one o f t h e beam p o s i t i o n d e t e c t o r s ( " s n i f f e r s " - see f i g u r e 1 ) . The s i g n a l i s a m p l i f i e d and f e d i n t o t h e c o n t r o l s y s t e m o f t h e h i g h v o l t a g e g e n e r a t o r , where i t c o n t r o l s the v o l t -age a p p l i e d t o t h e p l a t e s o f t h e d e f l e c t o r . The s e r v o s y s t e m i t s e l f i s made up o f two p a r t s ( r e f e r t o F i g u r e 2 ) . One p a r t i s a beam d e t e c t o r and the s e c o n d a beam p o s i t i o n s e r v o . The beam d e t e c t o r i n i t i a t e s t h e a c t i o n o f t h e c i r c u i t d r v i n g up t h e d e f e l e c t o r p l a t e v o l t a g e . When t h e v o l t a g e r e a c h e s t h e c o r r e c t m a g n i t u d e , t h e p o s i t i o n s e r v o s y s t e m i s a c t i v a t e d and c o n t r o l s t h e p l a t e v o l t a g e f r o m t h e n on. B o t h p a r t s a r e b u i l t a r o u n d t h e op-e r a t i o n o f t h e 12AX7 d o u b l e t r i o d e i n a " l o n g t a i l e d p a i r " c o n f i g u r a t i o n . When a v o l t a g e d i f f e r e n c e i s a p p l i e d between t h e two g r i d s t h e 12AX7 o p e r a t e s as a d i f f e r e n c e a m p l i f i e r 220C\Q son 5 0 0 p F . 500pF "2TO co T ^ CC CM y r- U . 5 0 0 p F ' 20. M A A V >900M 5 0 0 p F . lOOOpF A A A / — o 20 M FIGURE 3 . - 8 -and t h e a m p l i f i e d v o l t a g e d i f f e r e n c e a p p e a r s a c r o s s r e s i s t o r R^ and i n t u r n a c r o s s t h e o u t p u t AA', minus t h e e m i t t e r - b a s e v o l t a g e o f t r a n s i s t o r T^. The b r i d g e and f i l t e r c o n d e n s e r s u p p l y t h e power n e c e s s a r y t o o p e r a t e t h e t r a n s i s t o r s as d e s -c r i b e d , t h a t i s a t 12 v o l t s d.c., and 2 amps. The o u t p u t v o l t a g e AA' i s f e d i n t o t h e i n p u t o f t h e s a t u r a b l e c o r e m u l t i v i b r a t o r ( F i g u r e 3 ) . T h i s m u l t i -v i b r a t o r i s d e s i g n e d t o o p e r a t e a t a f r e q u e n c y o f 15.4 K.C, and t u r n s o u t a peak v o l t a g e o f 3.5 K.V., f o r an i n p u t o f 10. S i v . v o l t s d .c. T h i s a . c . v o l t a g e i s t h e i n p u t t o a s t a n d a r d q u a d r u p l e r w h i c h p r o d u c e s a d.c. o u t p u t o f 14 K.V. T h i s , i n t u r n , p a s s e s t h r o u g h an R.C. f i l t e r and s u p p l i e s t h e r e q u i r e d h i g h v o l t a g e t o t h e p l a t e s o f t h e d e f l e c t o r . The r i p p l e on t h e o u t p u t o f t h e f i l t e r was measured t o be 24 v o l t s w h i c h i s a b o u t 2%. Beam P o s i t i o n S e r v o O p e r a t i o n : The beam p o s t i o n s e r v o i s a c t i v a t e d by t h e beam s t r i k i n g two " S n i f f e r s " w h i c h a r e h a l f - m o o n s h a p e d p i e c e s o f s t a i n l e s s s t e e l (5ee F i g u r e 1) s i t u a t e d a b o u t 4" p a s t t h e e x i t o f t h e d e f l e c t i o n p l a t e s and e l e c t r i c a l l y i n s u l a t e d f r o m g r o u n d . T h e i r s t r a i g h t edges e x t e n d a p p r o x i m a t e l y 1/16" i n -s i d e t h e r e g i o n d e f i n e d by t h e p l a n e s t a n g e n t t o t h e f a c e s o f t h e d e f l e c t o r p l a t e s a t t h e e x i t o f t h e d e f l e c t o r . When t h e p a r t i c l e beam f r o m t h e Van de G r a a f f i s p a s s i n g c o r r e c t l y t h r o u g h t h e d e f l e c t o r , t h e d e f l e c t o r p l a t e v o l t a g e V w i l l be - 9 -s u c h t h a t e q u a l beam c u r r e n t w i l l be f a l l i n g on e a c h " S n i f f e r " . I f V q d r o p s , t h e beam w i l l move o n t o t h e l o w e r " S n i f f e r " . T h i s w i l l c a u s e a l a r g e r v o l t a g e t o a p p e a r a t g r i d g^ ( R e f e r t o F i g u r e 2 ) . As d e s c r i b e d p r e v i o u s l y , t h i s v o l t a g e r i s e w i l l c a u s e V q t o i n c r e a s e and r e - e s t a b l i s h e q u i l i b r i u m . S i m i l a r l y , i f t h e p l a t e v o l t a g e r i s e s t o o h i g h , t h e beam w i l l s t r i k e t h e u p p e r " S n i f f e r " ' - a n d c a u s e V t o f a l l . In t h i s manner t h e d e f l e c t o r o p l a t e v o l t a g e i s h e l d s u c h t h a t t h e beam p a s s e s between t h e " S n i f f e r s " . The Beam D e t e c t o r : The beam d e t e c t o r i s an e l e c t r i c a l l y i n s u l a t e d e n t -r a n c e a p e r t u r e t o t h e r e g i o n between t h e d e f l e c t i o n p l a t e s . I t s f u n c t i o n i s t o s u p p l y a s i g n a l w h i c h d r i v e s t h e d e f l e c t o r p l a t e v o l t a g e up. The m a j o r p o r t i o n o f t h e beam p a s s e s t h r o u g h t h e a p e r t u r e b u t a s m a l l p o r t i o n s t r i k e s t h e d e t e c t o r . T h i s s m a l l p o r t i o n o f beam c u r r e n t p a s s e s t h r o u g h d i o d e (See F i g u r e 2) s i n c e d i o d e D^ i s back b i a s e d i n t h e q u i e s c e n t s t a t e . The c u r -r e n t t h e n p a s s e s t h r o u g h t h e r e s i s t a n c e , s e l e c t e d by s w i t c h S, t o g r o u n d . T h i s g e n e r a t e s a v o l t a g e a t g r i d g^ o f the d o u b l e t r i o d e and, as p r e v i o u s l y d i s c u s s e d , c a u s e s t o r i s e . V q w i l l c o n t i n u e t o r i s e u n t i l ' a v o y a g e a p p e a r s a t g r i d g_, c a u s e d by t h e beam s t r i k i n g t h e u p p e r " S n i f f e r " . T h i s , t h e n , a c t i v a t e s t h e s e c o n d 12AX7 w h i c h l o w e r s t h e v o l t a g e a t p o i n t p^ below g r o u n d . T h i s f o r w a r d b i a s e s d i o d e d^ and t u r n s o f f t h e d e t e c t o r s i g n a l t o g^. The p l a t e v o l t a g e i s t h e n h e l d a t t h e c o r r e c t s e t t i n g by t h e s e r v o s y s t e m , - 10 -S h o u l d some sudden f l u c t u a t i o n i n t h e beam o c c u r and c a u s e t h e s e r v o s y s t e m t o l o s e c o n t r o l , w o u l d d r o p and t h e beam d e t e c -t o r w o u l d once a g a i n o p e r a t e . T h i s w o u l d a l l o w t h e s e r v o s y s t e m t o once more g a i n c o n t r o l . I t was f o u n d t h a t i f , f o r some r e a s o n , V r o s e t o o h i g h and t h e s e r v o s y s t e m l o s t c o n t r o l , t h e beam w o u l d s t r i k e t h e n e g a t i v e d e f l e c t i o n p l a t e . T h i s w o u l d c a u s e a h i g h (up t o 500 micro-ampsQ' s e c o n d a r y e l e c t r o n e m i s s i o n c u r r e n t w h i c h w o u l d l o a d t h e power s u p p l y h e a v i l y . As a r e s u l t o f t h e l o a d i n g , t h e o u t p u t v o l t a g e V q w o u l d d r o p and t h e s e r v o s y s t e m w o u l d g a i n c o n t r o l . No l a r g e s e c o n d a r y e l e c t r o n e m i s s i o n c u r r e n t r e s u l t s when t h e beam s t r i k e s t h e p o s i t i v e p l a t e b e c a u s e t h e h i g h e l -e c t r i c f i e l d i s b i a s e d t o r e s t r i c t e l e c t r o n e m i s s i o n . S a f e t y P r e c a u s i o n s ; The d e f l e c t i o n s y s t e m i s c o m p l e t e l y e n c a s e d i n a l u c i t e box w i t h t h e c o n t r o l s f o r the e l e c t r o n i c s mounted on t h e o u t s i d e . T h i s m i n i m i z e s t h e p r o b a b i l i t y o f b o d i l y c o n t a c t w i t h t h e h i g h v o l t a g e s u p p l y . To p r e v e n t t h e d e f l e c t i o n p l a t e v o l t a g e f r o m r i s i n g t o o h i g h and c a u s i n g breakdown t h r o u g h t h e l u c i t e s p a c e r s , a s a f e t y d e v i c e was a t t a c h e d t o t h e h i g h v o l t a g e o u t p u t . FIGURE 4 T h i s c o n s i s t s o f two s t e e l b a l l s mounted on a l u c i t e s t a n d f o r m -i n g a s p a r k gap. One b a l l i s c o n n e c t e d t o t h e h i g h v o l t a g e s i d e and t h e o t h e r t o t h e l o w . The d i s t a n c e between t h e b a l l s was a d j u s t e d so t h a t a s p a r k w o u l d be p r o d u c e d when t h e v o l t a g e d i f f e r e n c e was g r e a t e r t h a n 15 K.V. • The T w o - d i m e n s i o n a l M a g n e t i c S e r v o 5 y s t e m To make m i n o r c o r r e c t i o n s f o r f l u c t u a t i o n s i n t h e beam d i r e c t i o n a f t e r i t l e a v e s t h e 17° e l e c t r o s t a t i c d e f l e c -t i o n s y s t e m , two s e p a r a t e e l e c t r o m a g n e t s w i t h f i e l d s o r i e n t e d a t r i g h t a n g l e s t o t h e beam and a t r i g h t a n g l e s t o e a c h o t h e r a r e e m p l o y e d . These a r e d e s i g n e d t o r e s p e c t i v e l y d e f l e c t a 3 Mev(He ) beam one d e g r e e i n t h e h o r i z o n t a l and v e r t i c a l d i r e c t i o n s and i n c o m b i n a t i o n t o s e r v o on a p o i n t , i n much t h e same way as t h e e l e c t r o - s t a t i c d e f l e c t o r s e r v o s on a l i n e . The p o l e f a c e s o f t h e two e l e c t r o - m a g n e t s a r e 4" s q u a r e (See F i g u r e 4 ) . T h i s e n s u r e s a r e a s o n a b l y homogeneous m a g n e t i c f i e l d i n t h e m i d d l e o f t h e p o l e f a c e s . The m a t e r i a l c h o s e n f o r t h e magnets was AHMCD INGOT IRON b e c a u s e o f i t s low r e s i d u a l f i e l d . The beam t r a v e l s 4" t h r o u g h t h e m a g n e t i c f i e l d a n d, o 4 + t o p r o d u c e t h e 1 d e f l e c t i o n o f a 3 Mev(He ), a 500 g a u s s m a g n e t i c f i e l d i s needed. (See A p p e n d i x D ) . The c o i l u sed t o p r o d u c e t h e f i e l d has 200 t u r n s o f 13 guage e n a m e l l e d magnet w i r e , and i n d u c t a n t s o f 0 . 0 1 7 h e n r y and a d.c. r e s i s t a n c e o f in HAMMOND 1155 AX IIO V 14 V -#-35 V THYRECTOR -el—1 3000/xF 2N278 •400f2 FIGURE 5. —fr 5 R A N RECTIFIERS 6V Ju-ZENNER 2N30I lOOO^tF - 12 -0.4ohms. T h i s c o r r e s p o n d s t o a t i m e c o n s t a n t o f 0.04 s e c o n d s . The c u r r e n t needed t o p r o d u c e a 500 g a u s s f i e l d i s 5 amps w h i c h c o r r e s p o n d s t o a power d i s s i p a t i o n o f 10 -watts i n t h e c o i l . Two c o i l s a r e needed p e r magnet so t h a t e a c h power s u p p l y must d r i v e 0.034 h e n r y and 0.8 ohms. S e r v o C i r c u i t : f I n F i g u r e 5 a d i a g r a m o f t h e m a g n e t i c s e r v o s y s t e m and 6 v o l t power s u p p l y i s shown. The s e r v o c i r c u i t o p e r a t e s i n much t h e same way as t h e p r e v i o u s l y d e s c r i b e d c i r c u i t f o r t h e e l e c t r o s t a t i c d e f l e c t o r . The 12AX7 i s u s e d as a d i f f e r e n c e am-p l i f i e r . The v o l t a g e d i f f e r e n c e i s a m p l i f i e d by t h e t r a n s i s t o r c i r c u i t and a p p l i e d t o t h e base o f t h e 2N278 power t r a n s i s t o r , w h i c h i s o p e r a t i n g w i t h t h e c o i l as t h e e m i t t e r l o a d . The d.c. c u r r e n t c o n d i t i o n s a r e s e t by a d j u s t m e n t o f t h e 1 00 K p o t u n t i l t h e beam i s p a s s i n g a p p r o x i m a t e l y between t h e two " S n i f f e r s " . The s e r v o s y s t e m t h e n r e g u l a t e s t h e c u r r e n t t h r o u g h t h e magnet t o keep a p p r o x i m a t e l y t h e same amount o f c u r r e n t f a l l i n g on e a c h " S n i f f e r " . The 6 v o l t power s u p p l y i s needed t o d r i v e t h e t r a n s -i s t o r s and t h e c o i l c u r r e n t . The " S n i f f e r s * a r e a r r a n g e d i n p a i r s a d j a c e n t t o one a n o t h e r and s e p a r a t e d by a b o u t ar". Two p a i r s a r e needed and t h e y a r e p l a c e d a t r i g h t a n g l e s t o e a c h o t h e r . I f t h e beam moves i n any d i r e c t i o n , e i t h e r h o r i z o n t a l l y o r v e r t i c a l l y , i t s t r i k e s one o f t h e " 5 n i f f e r s " . T h i s s i g n a l i s f e d back t o t h e a p p r o p r i -a t e d i f f e r e n c e a m p l i f i e r and t h e c u r r e n t i n t h e magnet c o i l i s - 1 3 -c h a n g e d t o move t h e beam back i n t o t h e c e n t e r o f t h e s q u a r e f o r m e d by t h e f o u r " S n i f f e r s " . Two o f t h e s e g r o u p s o f f o u r " S n i f f e r s " a r e i n s t a l l e d i n t h e s y s t e m ; one a b o u t 5 f e e t f r o m t h e s e r v o magnets and t h e o t h e r 20 f e e t f r o m thern, i m m e d i a t e l y a d j a c e n t t o t h e t a r g e t a s s e m b l y . The c l o s e g r o u p s e r v e s t o d e f i n e t h e a p p r o x i m a t e d i r e c t i o n o f t h e beam and t h e f a r g r o u p d e f i n e s t h e e x a c t p l a c e m e n t . The f i r s t g r o u p a l s o s e r v e s t o keep t h e beam on t h e s e c o n d . Any l a r g e f l u c t u a t i o n i n t h e beam c o u l d p o s s i b l y c a u s e t h e g r o u p f u r t h e s t away t o l o s e c o n -t r o l w h e r e a s t h e f i r s t g r o u p o f " 5 n i f f e r s " s u b t e n d s a l a r g e r a n g l e and, as a r e s u l t , i s l e s s l i k e l y t o l o s e c o n t r o l . The 6 V o l t S u p p l y ; The c i r c u i t d r a w i n g o f t h e 6 v o l t s u p p l y f o r t h e magnets a p p e a r s i n F i g u r e 5, The s u p p l y has. been d e s i g n e d t o d e l i v e r 5 amps a t 6 v o l t s i n t o an i n d u c t a n c e o f 0.034 h e n r y w i t h a r i p p l e c u r r e n t o f l e s s t h a n 1 p a r t i n 2000. T h i s l o w r i p p l e i s needed t o a t t a i n t h e n e c e s s a r y s t a b i l i t y i n t h e beam d i r e c t i o n o f 1 p a r t i n 2000. To a c h i e v e t h e above d e s i g n , a s e r i e s t r a n s i s t o r r e g u l a t o r was u s e d i n c o n j u n c t i o n w i t h a 6.5 v o l t z e n e r d i o d e . The h i g h (3000 m i c r o f a r e d ) o u t p u t c a p a c i t y f o r the b r i d g e r e -c t i f i e r i s n e c e s s a r y t o m a i n t a i n t h e d.c. v o l t a g e above 7.5 v o l t s , when t h e l o a d i s d r a w i n g 5 amps. A l s o , by p u t t i n g 1000 m i c r o f a r a d s on t h e base o f t h e 2N301, t h e c a p a c i t y i s e f f e c t i v e l y m u l t i p l i e d by t h e g a i n o f t h e 21M301 t i m e s t h e g a i n - 14 -o f t h e 2N278. T h i s g i v e s a v e r y l a r g e e f f e c t i v e c a p a c i t y on t h e o u t p u t . A 1 ohm r e s i s t a n c e was c o n n e c t e d t o t h e e m i t t e r o f t h e 2N278 t o d e c r e a s e i t s power d i s s i p a t i o n . A l l power t r a n s i s t o r s and r e c t i f i e r s had;^to be mounted on c o p p e r h e a t - s i n k s and b l o w e r s used t o keep t h e h e a t -s i n k s c o o l . As a s a f e t y p r e c a u t i o n , a 35 v o l t t h y r e c t o r was p l a c e d a c r o s s t h e o u t p u t o f t h e t r a n s f o r m e r t o remove a l l t r a n s i e n t s w h i c h m i g h t blow o u t t h e r e c t i f i e r s i n t h e b r i d g e . t - 15 -CHAPTER I_H SURVEY UF THE 60° DOUBLE FOCUSING MAGNETIC SPECTROMETER A p r e l i m i n e r y i n v e s t i g a t i o n o f t h e p h y s i c a l d i m e n -s i o n s o f t h e s p e c t r o m e t e r had t o be c a r r i e d o u t i n o r d e r t o d e t e r m i n e t h e o b j e c t and image p o i n t s as w e l l as t h e two a c c e p t a n c e a n g l e s oF t h e s p e c t r o m e t e r * T h i s was a c c o m p l i s h e d by e m p l o y i n g a W i l d T-2 T h e o d o l i t e and a c a t h e t o m e t e r . When t h e s u r v e y was c o m p l e t e , a m o n o e n e r g e t i c s o u r c e o f p r o t o n s was p r o d u c e d by s c a t t e r i n g a p r o t o n beam f r o m t h e Van de G r a a f f o f f a t h i n aluminum f o i l . A r a d i o a c t i v e s o u r c e o f p a r t i c l e s was n o t us e d i n t h e t r a j e c t o r y s u r v e y s , s i n c e s o u r c e s w i t h s u f f i c i e n t l y h i g h s p e c i f i c a c t i v i t y t o g i v e t h e same s o u r c e s i z e e n e r g y r e s o l u t i o n and i n t e n s i t y as t h e s c a t t e r -ed p r o t o n s a r e i m p o s s i b l e t o . o b t a i n . A t h r e e - d i m e n s i o n a l s u r v e y o f t h e f o c a l p r o p e r t i e s o f t h e image o f t h e s p e c t r o -m e t e r was t h e n c a r r i e d o u t . The f o c u s o f t h e s p e c t r o m e t e r was d e t e r m i n e d t h e o r e t i c a l l y u s i n g a r a n g e o f v a l u e s f o r one a d j -u s t a b l e p a r a m e t e r . - i n t h e s p e c t r o m e t e r f i e l d s p e c i f i c a t i o n s ( t h e e x t e n t o f t h e f r i n g i n g f i e l d on t h e o u t p u t s i d e o f t h e m a g n e t ) , and compared w i t h t h e e x p e r i m e n t a l r e s u l t s t o d e t -e r m i n e t h e optimum v a l u e f o r t h i s p a r a m e t e r . W i t h t h e s e r e s -u l t s , i t was p o s s i b l e t o c a l c u l a t e t h e optimum d e t e c t o r 6 g e o m e t r y f o r d e t e c t i n g t h e n o n - m o n o e n e r g e t i c beam o f r e c o i l a l p h a s w h i c h r e s u l t f r o m t h e D(d,Jf)He 4 r e a c t i o n . A See r e a c t i o n , k i n e m a t i c s i n A p p e n d i x . - 16 -The Physical Dimensions of the Spectrometer: The relevant angles of the spectrometer as measured using a cathetometer are recorded in Figure 6. These compared very favorably with the angles given in the s p e c i f i c a t i o n . AA It w i l l be assumed in a l l the following theore t i ca l ca lcu lat ions that the angles in the spec i f i ca t ions are correc t ly determined. Also, the acceptance angle of the spectrometer in the v e r t i c a l d i r e c t i o n i n Figure 7, may be assumed to be the angle between the horizontal plane and the v e r t i c a l to the flange at the entrance to the spectrometer. The mean angle ( i . e . , the angle of the centra l ray) was then adjusted to 1 0 ° . Since the spectrometer accepts par t i c l e s over a 10° range, centered about , the minimum angle of acceptance is 5° and the maximum 1 5 ° . The spectrometer has a fixed scale which determines the angular rotat ion d> of the spectrometer in the horizontal plane (refer to Figure 7). The zero of this scale was determined by s ighting along the incident beam d i r e c t i o n , using a t r a n s i t , into the spectrometer. The spectrometer was then rotated in the horizontal plane u n t i l the plane of the pole faces was p a r a l l e l to the l ine of s ight . The reading on the spectrometer angle scale (£) was recorded to be 3 3 9 ° . This , then, i s the zero of the spectrometer. AA "The Developement of a Double Focusing Spectrometer". A . J . Stewart-Smith, M.A. Thesis , U . B . C . 1961. FIGURE 7. To e n s u r e t h e p r o p e r r e a d i n g on t h e s p e c t r o m e t e r s c a l e t h e beam must a l w a y s be i n c i d e n t i n t h e same d i r e c t i o n . F o r t h i s p u r p o s e s e v e r a l p o i n t s have been marked on the f l o o r w i t h t h e s y m b o l (2) . The beam must p a s s v e r t i c a l l y o v e r t h e s e p o i n t s and i n t h e h o r i z o n t a l p l a n e . Method o f F o c u s S u r v e y ; The f o c u s i n g p r o p e r t i e s o f t h e s p e c t r o m e t e r were measured u s i n g a m o n o e n e r g e t i c s o u r c e o f p a r t i c l e s a t t h e o b j e c t p o s i t i o n . T h i s m o n o e n e r g e t i c beam was p r o d u c e d by s c a t t e r i n g a 1 Mev p r o t o n beam f r o m t h e Van de G r a a f f o f a v e r y t h i n e v a p o r a t e d aluminum t a r g e t . The t a r g e t was p r e p a r e d by e v a p o r a t i n g aluminum o n t o a v e r y t h i n f i l m o f c o l o d i o n . The a c c e p t a n c e a n g l e s o f t h e s p e c t r o m e t e r had been p r e v i o u s l y a d j u s t e d t o be =10°. =0°, W i t h t h i s s e t t i n g t h e s p e c t r o -m e t e r a c c e p t s p a r t i c l e s a t a n g l e s = 5 ° t o H C ^ - 1 5 0 * ^ n ^ n ^ s r a n g e o f a n g l e s t h e e l a s t i c a l l y s c a t t e r e d p r o t o n s f r o m t h e t a r g e t a r e m o n o e n e r g e t i c t o b e t t e r t h a n 1%. To e n s u r e t h a t t h e t a r g e t was a t t h e o b j e c t p o s i t i o n t h e c a t h e t o m e t e r was l o c k e d i n p o s i t i o n w i t h t h e c r o s s h a i r s f o c u s e d on t h e o b j e c t p o i n t o f t h e s p e c t r o m e t e r . The o b j e c t p o i n t o f t h e s p e c t r o m e t e r i s shown i n t h e s p e c i f i c a t i o n s t o be p e r p e n d i c u l a r l y f r o m t h e geomet- • r i c a l c e n t e r o f t h e f r o n t o f t h e e n t r a n c e f l a n g e . To d e t e r m i n e t h i s p o i n t i n t h e l a b o r a t o r y a b r a s s p l a t e was made w h i c h f i t t e d t h e e n t r a n c e f l a n g e and a p o i n t e d b r a s s r o d was s o l d e r e d p e r p e n d i c u l a r t o t h e p l a t e a t i t s c e n t r e . When b o l t e d o n t o t h e - 18 -e n t r a n c e f l a n g e t h e p o i n t o f t h e r o d e x t e n d e d 6-5-" v e r t i c a l l y f r o m t h e f l a n g e . A s e c o n d p o i n t e d r o d was p l a c e d v e r t i c a l l y upward f r o m t h e a x i s o f r o t a t i o n o f t h e s p e c t r o m e t e r w i t h t h e p o i n t o f t h e r o d a t a h e i g h t o f 444~" f r o m t h e f l o o r , w h i c h i s t h e h e i g h t a t w h i c h t h e beam emerges f r o m t h e Van de G r a a f f . The s p e c t r o m e t e r l e v e l i n g s c r e w s were t h e n a d j u s t e d so t h a t t h e p o i n t s o f t h e two f i x e d r o d s c o i n c i d e d .TTh'is p 6 i h t _ d f c o i n c i d e n c e s h a l l be r e f e r r e d t o as t h e o b j e c t p o s i t i o n . W i t h t h e c a t h e t o m e t e r l o c k e d i n p o s i t i o n w i t h t h e c r o s s - h a i r s f o c u s e d on t h e o b j e c t p o i n t , t h e t a r g e t was p l a c e d , t o c o i n c i d e w i t h t h e c r o s s - h a i r s . The c o i n c i d e n c e o f t h e t a r g e t p o s i t i o n and o b j e c t p o s i t i o n was c h e c k e d r e p e a t e d l y t h r o u g h o u t t h e s u r v e y . A beam c o l l i m a t i n g s y s t e m was s e t up i n f r o n t o f t h e t a r g e t t o e n s u r e t h a t t h e beam p a s s e d d i r e c t l y t h r o u g h t h e o b j e c t p o i n t . The d e t e c t o r u s e d f o r t h e s u r v e y was an RCA 5 I L I C 0 N JUNCTION ALPHA PARTICLE DETECTOR - TYPE A-4 75 VOLTS. The a c t i v e s u r f a c e o f t h i s c o u n t e r was 2 mm i n d i a m e t e r . W i t h t h i s s m a l l a c t i v e s u r f a c e i t was p o s s i b l e t o d e t e c t c h a n g e s i n t h e f l u x o f a n a l y s e d p a r t i c l e s i n t h e image p l a n e , i . e . i n t h e shape o f t h e image, o v e r 1/10" i n t e r v a l s . A low i n t e n s i t y p r o t o n beam, o f t h e o r d e r o f 0.0003 microamp, was o b t a i n e d by c o l l i m a t i n g a v e r y s m a l l amount o f a low f l u x beam f r o m t h e Van de G r a a f f . T h i s beam was d i r e c t e d o n t o t h e t a r g e t . The c u r r e n t t h r o u g h t h e s p e c t r o m e t e r f i e l d - 19 -c o i l s was a d j u s t e d t o g i v e t h e maximum c o u n t r a t e , on t h e e l a s t i c a l l y s c a t t e r e d p eak, f r o m t h e s o l i d s t a t e c o u n t e r p l a c e d i n t h e a p p r o x i m a t e r e g i o n o f t h e f o c u s . The c u r r e n t p a s s i n g t h r o u g h t h e aluminum t a r g e t was measured by means o f a beam c a t c h e r p l a c e d d i r e c t l y b e h i n d t h e t a r g e t and f a r enough away n o t t o i n t e r f e r e w i t h t h e beam s c a t t e r e d a t an a n g l e g r e a t e r t h a n 5°. The t o t a l number o f c o u n t s f o r a p r e s e t i n t e g r a t e d beam c u r r e n t was r e c o r d e d . R e f e r r i n g t o F i g u r e 7, t h e c e n t r a l r a y , as d e s c r i b e d i n t h e m a n u f a c t u r e r s s p e c i f i c a t i o n s , was t h e n o r m a l t o t h e p l a n e o f s u r v e y and s h a l l be r e f e r r e d t o as t h e Z a x i s . The p l a n e o f t h e s u r v e y i s t h e X,Y p l a n e , t h e X a x i s b e i n g p a r a l l e l t o t h e p o l e f a c e s o f t h e s p e c t r o m e t -e r and t h e Y a x i s b e i n g n o r m a l t o t h e p l a n e o f t h e p o l e f a c e s . The o r i g i n o f t h e c o o r d i n a t e s y s t e m i s as shown i n F i g u r e 8. W i t h t h e s p e c t r o m e t e r c u r r e n t h e l d c o n s t a n t t h e s o l i d - , . s t a t e c o u n t e r was moved i n t h e Y d i r e c t i o n a t 1/10" i n t e r v a l s w i t h f i x e d X, Z c o o r d i n a t e s , t h e number o f c o u n t s f o r t h e same i n t e g r a t e d beam c u r r e n t was r e c o r d e d a t e a c h i n t e r v a l . When t h e s u r v e y was c o m p l e t e d on t h i s l i n e t h e c o u n -t e r was moved 1/10" i n t h e X d i r e c t i o n . The c u r r e n t i n t h e s p e c t r o m e t e r was once a g a i n a d j u s t e d t o g i v e t h e maximum c o u n t r a t e a t t h i s p o i n t . W i t h t h i s c u r r e n t s e t t i n g t h e s u r v e y i n t h e Y d i r e c t i o n was r e p e a t e d . The above d e s c r i b e d method was c o n t i n u e d u n t i l one c o m p l e t e p l a n e had been s u r v e y e d . - 20 -The c o u n t e r was t h e n moved i n t h e Z d i r e c t i o n and a new p l a n e was s u r v e y e d i n t h e same f a s h i o n as t h e p r e v i o u s one. The s u r v e y was c o m p l e t e d o v e r a number o f p l a n e s u n t i l t h e p o i n t o f maximum c o u n t s , f o r t h e same i n t e g r a t e d beam c u r r e n t , had been e s t a b l i s h e d . The c o u n t s l\l r e c o r d e d by t h e s o l i d s t a t e c o u n t -e r a r e due t o t h e e l a s t i c a l l y s c a t t e r e d p r o t o n s . T h a t i s Where N- N<X.Y.Z.I s p B c - e , 4> / b e a m ' ^ « E ) X , Y , Z = c o u n t e r c o o r d i n a t e s I = c u r r e n t i n s p e c t r o m e t e r f i e l d c o i l s s p e c O '(]) = s p e c t r o m e t e r a c c e p t a n c e a n g l e s I, = beam c u r r e n t beam ^ = f u n c t i o n d e s c r i b i n g t a r g e t p r o p e r t i e s E = beam e n e r g y D u r i n g t h e s u r v e y t h e beam e n e r g y and c u r r e n t and t a r g e t p r o p e r t i e s r e m a i n e d c o n s t a n t . The t o t a l number o f c o u n t s may be r e w r i t t e n as an i n t e g r a l o v e r t h e t i m e o f e a c h r u n and o v e r t h e s u r f a c e o f t h e c o u n t e r . T h a t i s N = K I b e a m ^ C T ( e , 0> ) S ( X , Y , Z , I ^  ^ ) where K= a c o n s t a n t CV ( •© » ty ) = n u c l e a r c o u l o m b c r o s s e c t i o n 5 (X , Y , Z , I g p e c . ) - F u n c t i o n d e s c r i b i n g t h e f o c a l p r o p e r t i e s o f t h e s p e c t r o m e t e r . X IN INCHES F I G U R E . 9. 10 2.80 2.05 1.0 TT .\J . t_ \S - i • i (X) D I S T A N C E IN I N C H E S / T O P O L E F A C E FIGURE 10 NORMALIZED COUNT RATE (XlO~ 4) ( X ) D I S T A N C E / T O P O L E F A C E FIGURE \z.. - 21 -The survey i s d i r e c t e d at determining the func-t i o n S, so that, throughout the survey, i t waa important to hold a l l other f u n c t i o n s constant. This i s p a r t i c u l a r l y true forQ"(^,^)) which i s the coulomb c r o s s e c t i o n and which f o r -4 small acceptance angles-© v a r i e s as •©• . Therefor the angles of the spectrometer had to be f i x e d s e c u r e l y throughout the survey. It was found that the c l o s e s t quadrupole lens could not be used s i n c e t h i s a f f e c t e d the angle of i n c i d e n c e of the beam on the t a r g e t by making the beam convergent, r a t h e r than p a r a l l e l , and had a s i g n i f i c a n t e f f e c t on the count rate again through t h e © , dependance of Cf", The normalized r e s u l t s of the survey are summar-i z e d i n Figures 8-12. Figure 8 d i s p l a y s the count rate as a f u n c t i o n of Y f o r a constant X,Z and spectrometer c u r r e n t and f o r d i f f e r e n t X c o o r d i n a t e s . Figure 9 d i s p l a y s the primary f o c u s i n g q u a l i t y , that i s , the'count rate as a f u n c t i o n of X f o r a constant Y,Z coordin a t e s and constant spectrometer c u r -rent, The maximum count r a t e s f o r each survey i n the Y d i r e c -t i o n , with constant X,Z over the whole plane, are shown f o r f i v e s u r f a c e s surveyed i n Figure 10. F i n a l l y , the maximum count r a t e p o s i t i o n s i n each of the planes surveyed i s r e -corded i n Figures 11-12. Figure 11 shows the shape of the 2nd order focus at each p o i n t . Figure 12 shows t h e i r p o s i t i o n s i n the X,Z plane and maximum count r a t e . Primary Focusing Q u a l i t y ; Over the whole volume surveyed i t was found that the s i z e (width at h a l f maximum of the coulomb peak) of the primary focus of the spectrometer, that i s , the focus i n the X d i r e c t i o n , was of the order of, or l e s s than, the s i z e of the counter diameter. Figure 9 shows a. t y p i c a l survey of the f i r s t order f o c u s i n g . This peak width did not change n o t i c e -ably over the whole volume surveyed. The width of the peak i s c o n s i s t e n t with the s i z e of the t a r g e t spot and the m a g n i f i -c a t i o n of the spectrometer. The s i z e of the source was d e t e r -mined by the beam entrance aperture which was 3/32". W.G. 2 Cross gives the t h e o r e t i c a l value f o r the m a g n i f i c a t i o n i n terms of the parameters of the s e c t o r magnet. On s u b s t i t u t i o n of the -values corresponding to the U.B.C. 60° double f o c u s i n g magnetic spectrometer , a value of 0.77 i s found f o r the mag-n i f i c a t i o n . Therefor, the s i z e of the image could be about 1/10", which i s of the order of the s i z e of the a c t i v e region of the counter. It may a l s o be noted that, as the c u r r e n t of the spectrometer f i e l d c o i l s i s decreased, the primary focus moves i n the X,Z plane toward the more p o s i t i v e Z and Negative X. (5ee Figure 12), The t h e o r e t i c a l curve shown as a dark l i n e i s d erived using a f r i n g i n g f i e l d extension at the e x i t of 0.56" as i n Figure , Agreement between the t h e o r e t i c a l l y c a l c u l a t e d p a r t i c l e o r b i t s and primary f o c a l p o i n t s f o r a p a r t i c u l a r spectrometer c u r r e n t and the e x p e r i m e n t a l l y observed f o c a l p o i n t s could not be e s t a b l i s h e d with the spectrometer char-2.W.G.CrDss R e v . S c i . I n s t r . 2 2 , 717 (1951) (X) DISTANCE / / T O FIGURE: 13 P 0 L E F A C E - 23 -a c t e r i s t i c s s u p p l i e d by the manufacturer. The value of the magnetic f i e l d i p s i d e the spectrometer was measured using a proton resonance head, so the only remaining q u a l i t y of the spectrometer not predetermined i s the extent of the f r i n g -ing f i e l d at the entrance and e x i t of the spectrometer. In the s p e c i f i c a t i o n s f o r the spectrometer, the f r i n g i n g f i e l d i s taken i n t o account by extending the spectrometer f i e l d by about one gap width (3/4") out from the edges of the pole faces of the spectrometer. It was found that, by decreasing the extent of the f r i n g i n g f i e l d to 0.56" past the e x i t of the spectrometer and l e a v i n g the entrance f i e l d as s p e c i f i e d , agreement could be e s t a b l i s h e d between p r e d i c t e d and e x p e r i -mentally determined primary f o c a l p o i n t s . ( R e f e r ti> Figure 13). The f r i n g i n g f i e l d was changed only at the e x i t aperture f o r convenience. It i s reasonable that the f i e l d should extend the same d i s t a n c e from both entrance and e x i t a p ertures. However, i n the c o n s t r u c t i o n to f i n d the distance the f r i n g i n g f i e l d should extend from the edge of the gap, i t was found e a s i e r to vary only the e x i t f r i n g i n g f i e l d . When r e s u l t s c o n s i s t e n t with the experiment were found by vary-ing only the e x i t f i e l d , i t was assumed that t h i s would be s u f f i c i e n t to c a l c u l a t e the f o c a l p o i n t of the alphas from the D(d,IT)He4 r e a c t i o n . Counter P o s i t i o n and B a f f l i n g : With t h i s value of extent of f r i n g i n g f i e l d i t —jf~ T A R G E T INCIDENT B E A M SOLID S T A T E COUNTER E d = 2.5 M E V . R = 1 4 INCHES FOR I O ° R A Y B — 5 3 0 0 G A U S S in tc o - 24 -i,s: now possible to predict t h e . t r a j e c t o r i e s of the ;part i c l e s in the spectrometer with some degree of c er ta in ty . In par-t i c u l a r , the t ra jec tor ie s of the r e c o i l alphas from the D(d,y)He^ react ion can be predicted. The kinematics of t h i s , reaction are calculated in Appendix^,, The alphas w i l l emerge from the target inside a cone of 1 5 ° half angle with respect to the beam and the spectrometer, with »1 0 ° , <j) =0° , w i l l accept those par t i c l e s which emerge at an a n g l e b e t w e e n 5° an d 15 . At any p a r t i c u l a r angle-O- there w i l l be two energy groups of alphas.(Refer to Appendix A ). The experiment w i l l be directed at detecting only the higher energy group. These par t i c l e s w i l l hav/e an energy speed of about 500 Kev for a 3 Mev beam of incident deuterons, the alphas at 5° having an energy of 2.21 Mev and at 15° having an energy of 1.41 Hev. The predicted t ra jec tor i e s of these alphas are shown in Figure 14. Since they are not monoenergetic, they do not have a common focal point in the usual sense. However,a large portion of the t ra jec tor i e s converge in the region shown in Figure 14, which may be ca l l ed a pseudo focus. The pseudo focus occurs because, at a p a r t i c u l a r beam energy, there i s a unique re la t ion between the energy of a p a r t i c l e entering the spectrometer, and the p a r t i c u l a r trajectory i t fol lows. With a large counter i t i s possible to intercept most of these t r a j e c t o r i e s . The size of the counter used was l imited by the reso lut ion desired, since the resolut ion de-creases proportionately to the area of the s o l i d state counter. - 2 5 -A counter of length 14 ram was s e l e c t e d , the width to be det-ermined by the second order f o c u s i n g . This counter allows the i n t e r c e p t i o n of alphas that emerge between = 5 ° and - 1 2 ° which i s an energy range of from 2 . 2 1 Mev to 1 , 6 5 Mev. Also shown i n Figure 14 i s the b a f f l i n g system designed to i n t e r c e p t p a r t i c l e s which may otherwise, by m u l t i p l e s c a t t e r i n g , reach the counter. These b a f f l e s a l s o serve to de-f i n e the t r a j e c t o r i e s of the alpha p a r t i c l e s i n the s p e c t r o -meter. L u c i t e p l a t e ( 1 / 8 " thick), was chosen as the m a t e r i a l from which to f a b r i c a t e the b a f f l e s , p r i m a r i l y because of i t s low average nucleonic charge and r e s u l t i n g low coulomb s c a t t e r i n g c r o s s e c t i o n and, secondly because of i t s ease of f a b r i c a t i o n . 5econd Order Focusing! Second order f o c u s i n g i s the term used to des-c r i b e the e f f e c t t o n p a r t i c l e t r a j e c t o r i e s i n the d i r e c t i o n p e r p e n d i c u l a r to the pole faces of the f r i n g i n g magnetic f i e l d s . The t h e o r e t i c a l c a l c u l a t i o n of t h i s / e f f e c t has been 3 2 t r e a t e d e x t e n s i v e l y by W.E.Stephens and W.E.Cross . The curvature of these f r i n g i n g f i e l d s has the e f f e c t of e x e r t -ing a f o r c e towards the centre of the gap on any p a r t i c l e i n c i d e n t at an angle to the edge of the pole f a c e s . The net r e s u l t i s that, f o r a proper geometrical arrangement, the p a r t i c l e s are focused i n the Y 9Z plane. This focus and the - 26 -primary focus, which in general do not co-incide, have been made to co-incide in the 60° double focusing spectrometer for a par t i c u l a r set of p a r t i c l e t r a j e c t o r i e s correspond-ing to a particular set of angles between trajectory and f i e l d at entrance and exit to the f i e l d . As can be seen from Figure 13 , the primary focus can be moved about at w i l l by changing the magnet current. Without the second order focusing the count rate at each primary focal point would be the same. However, the second order focusing chang-es with spectrometer current in a manner different from that of the f i r s t order focusing. As a result, the count rate at each primary focal point w i l l be d i f f e r e n t . The v primary focal point with the-maximum count rate i s referred to as the focal point of the spectrometer. At this paint the primary and secondary focal points co-incide. Second order focusing i s c l e a r l y evident in Figure B where a sharp count rate peak can be seen in the centre of the d i s t r i b u t i o n . The zero point on the Y axis corresponds to the centre of the gap. The focus i s d i s -placed 1/10" to one side because the centre of the target spot was displaced a l i t t l e less than 1/10" to the other side of the object point. The position of maximum count 3. W.E.Stephens Phys.Rev. 4J5, 51 3, ( 1 934) - 27 -rate, that i s the focal point, was found to be displaced s l i g h t l y from the focus described by the spectrometer spec-i f i c a t i o n s and previous discussion of fringing f i e l d e f f e c t s . (See Figure 13.) The width of the counter needed to intercept the large majority of the beam may now be determined from Figure .11. A width of 7 mm was chosen and, as can be seen, this i s s u f f i c i e n t to cover most of the second order focus width„ - 28 -CHAPTER IV COUNTER CHARACTERISTICS As p o i n t e d o u t i n t h e i n t r o d u c t i o n , i t i s i m p o r t a n t t h a t t h e c o u n t e r be a b l e t o d i f f e r e n t i a t e be-tween p r o t o n s and a l p h a s o f t h e same e n e r g y . F o r t h i s r e a s o n t h e ORTEC SILICON SURFACE BARRIER DETECTOR was c h o s e n . T h i s d e t e c t o r i s a l a r g e a r e a p-n j u n c t i o n d i o d e , w i t h an e x t r e m e l y t h i n p - t y p e l a y e r , on t h e s e n s i t i v e s i d e o f t h e d e t e c t o r . The p - t y p e l a y e r i s p r o d u c e d by t h e m e t a l t o s e m i c o n d u c t o r j u n c t i o n . The e l e c t r i c a l c o n t a c t s t o t h e d i o d e .are made on t h e p - t y p e r e g i o n t h r o u g h a v e r y 2 t h i n (50-100 m i c r o g r a m s / c m ) g o l d f i l m and on t h e n - t y p e s i d e t h r o u g h a n o b m i c c o n t a c t . At e l e c t r i c a l e q u i l i b r i u m , when a r e v e r s e biass. ' i s a p p l i e d t o t h e d i o d e , a s t r o n g e l e c t r i c f i e l d r e g i o n ( c h a r g e d e p l e t e d r e g i o n ) i s f o r m e d a r o u n d t h e p-n j u n c t i o n . The r e g i o n e x t e n d s i n t o t h e n-t y p e m a t e r i a l a d i s t a n c e D. T h i s d i s t a n c e i s d e p e n d a n t on t h e r e v e r s e b i a s a p p l i e d and t h e r e s i s t i v i t y o f t h e m a t e r i a l . When a c h a r g e d p a r t i c l e e n t e r s t h e s e n s i t i v e s i d e o f t h e c o u n t e r i t l o s e s a s m a l l amount o f e n e r g y i n t h e "window", t h a t i s , t h e g o l d f i l m c o n t a c t , and t h a n e x t e n d s i t s r e m a i n i n g e n e r g y i n t h e n - t y p e r e g i o n . The e n e r g y l o s t i n t h e s e n s i t i v e r e g i o n goes i n t o c r e a t i n g e l e c t r o n - h o l e p a i r s . These a r e swept o u t o f t h e s e n s i t i v e r e g i o n by t h e e l e c t r i c f i e l d . The c h a r g e a r i s i n g f r o m t h i s - 2 9 -i s f e d o n t o a c a p a c i t o r . The v o l t a g e p u l s e a r i s i n g has a h e i g h t p r o p o r t i o n a l t o t h e e n e r g y t h e p a r t i c l e l o s t i n t h e s e n s i t i v e r e g i o n . As m e n t i o n e d p r e v i o u s l y , i t i s i m p o r t a n t t o be a b l e t o d i f f e r e n t i a t e between p r o t o n s and a l p h a s o f t h e same e n e r g y . One method o f d i f f e r e n t i a t i o n w o u l d be t o make t h e a c t i v e r e g i o n j u s t deep enough t o s t o p a l p h a s . A p r o t o n o f t h e same e n e r g y w o u l d t h e n p a s s t h r o u g h t h e a c t i v e r e g i o n and expend o n l y a p o r t i o n o f i t s e n e r g y t h e r e . The r e s u l t w o u l d be t h a t t h e p u l s e h e i g h t f o r t h e a l p h a p a r t -i c l e w o u l d be much h i g h e r t h a n f o r a p r o t o n . A l p h a s o f e n e r g i e s up t o 2 Mev a r e t o be d e t e c t e d f r o m t h e r e a c t i o n , so t h a t f r o m i n s p e c t i o n o f F i g u r e 15, t h e nomograph, a l o w r e s i s t i v i t y c o u n t e r i s needed. A l s o , s i n c e r e s o l u t i o n o f t h e a l p h a and p r o t o n p e a k s i s ne e d e d , a h i g h r e s o l u t i o n c o u n t e r i s n e c e s s a r y . The s i z e o f t h e c o u n t e r was d e t e r m i n e d i n C h a p t e r IV t o b e s t s u i t t h e f o c u s o f t h e s p e c t r o m e t e r . The d e t e c t o r w h i c h s u i t e d a l l o f t h e above c h a r a c t e r i s t i c s was an ORTEC SURFACE BARRIER DETECTOR. I t has a r e s i s t i v i t y o f 300 ohm—cm +_ 2 5 % , an a c t i v e s u r f a c e 7 X 1 4 mm and a 2 window t h i c k n e s s o f 50-100 m i c r o g r a m s / cm . T h i s window t h i c k n e s s amounts t o 20-40 Kev f o r a 1.6 Mev a l p h a . The r e l a t i v e r e s p o n s e o f t h e d e t e c t o r t o a l p h a s and p r o t o n s was d e t e r m i n e d by d e t e c t i n g a l p h a s and p r o t o n s o f t h e same e n e r g y and r e c o r d i n g t h e p u l s e h e i g h t as a f u n c t i o n o f t h e a p p l i e d b i a s v o l t a g e . - 30 -Counter T e s t i n g Experimental Arrangements; The obvious way to produce p a r t i c l e s to t e s t the response of the counter to alphas and protons i n the energy range 1,5 to 2.0 Mev i s to use the Van de Graaff beam. However, i t i s not p o s s i b l e simply to run the beam d i r e c t l y onto the counter since t h i s high p a r t i c l e f l u x would destroy i t . To overcome t h i s d i f f i c u l t y , a much lower i n t e n s i t y source was made by coulomb s c a t t e r i n g the beam o f f a t h i n homogeneous aluminum f o i l . The f o i l was prepared the same way as the f o i l i n Chapter I I I . ^ s p r e p a r a t i o n c o n s i s t e d of mixing approximately equal amounts of Cdlodion and Amyl-acetate. Acetone was then added to t h i s mixture as a t h i n n e r . A c y l i n d r i c a l l y - s h a p e d c o n t a i n e r , of c r o s s e c t i o n a l area a l i t t l e l a r g e r than the t i r g e t des-i r e d , was f i l l e d with d i s t i l l e d water and a few drops of the thinned mixture placed on the water s u r f a c e . When the f i l m formed on the surface had d r i e d , i t was removed by means of a wire bent to form a r i n g with r a d i u s equal to the de-s i r e d f i l m r a d i u s . The t h i c k n e s s of the f i l m was v a r i B d by changing the amount of mixture added and the CQRsis.tency c o n t r o l l e d by the t h i n n e r . Aluminum was then evaporated onto the face of the f i l m and the r e s u l t i n g f o i l used as the t a r -get . The a p p r o p r i a t e energy of the s c a t t e r e d beam was then r e s o l v e d out by the 60° double f o c u s i n g s p e c t r o -meter which had been preset with = 10° and <jj> • 0° which SPECTROMETER CURRENT IN AMPS FIGURE i 6 . - 31 -i s a spread i n - ^ - o f from 5 ° to 15°. The energy l o s s by the s c a t t e r e d p a r t i c l e to the r e c o i l nucleus i n nuclear coulomb s c a t t e r i n g i s n e g l i g i b l e at these angles. Therefore, the energy of the p a r t i c l e s s c a t t e r e d from the t h i n aluminum f o i l i s the same as the i n c i d e n t beam energy minus the energy l o s s due to the t a r g e t t h i c k n e s s . The same c o l l i m -a t i o n system as o u t l i n e d i n Chapter III was used to ensure the beam was d i r e c t e d onto the t a r g e t at the object poin t of the spectrometer. With a small beam of known energy from the Van de Graaff f a l l i n g on the s c a t t e r i n g f o i l the s p e c t r o -meter c u r r e n t was v a r i e d . For c u r r e n t p r o f i l e s see Figure 16 0 R e f e r r i n g to t h i s diagram, when the cpunt rate reaches a peak, the spectrometer c u r r e n t has been adjusted so that the counter i s reading the e l a s t i c a l y s c a t t e r e d beam from the f o i l . The low count background i s due to small angle s c a t t e r i n g of the beam from c o l l i m a t o r s along the beam path and to s c a t t e r i n g i n s i d e the spectrometer. In the case of the alpha beam, i t i s expected that the c u r r e n t p r o f i l e 4 would have two peaks, one due to s i n g l y i o n i z e d He and the other due to the doubly i o n i z e d . (See Figure 15). At a beam energy of 1.5 Mev. NUCLEAR DATA TABLES 1961 Pg.79 gives an expected r a t i o ( H e 4 ) + / ( H e 4 ) + + of 1 to 12. It can be seen that t h i s r a t i o compares fa v o u r a b l y with the value shown i n Figure 15. - 32 -.The procedure was to run a beam from the Van de Graaff onto the scattering f o i l and adjust the current in the spectrometer so that the 'counter was reading the e l a s t i c a l y scattered peak. The pulse height of the peak was then recorded as a function of the bias applied to the s o l i d state counter. This procedure was repeated at d i f f e r -ent energies for both alphas and protons. The results of this survey are shown in F i g -ures 17-19. In these graphs a correction for the aluminum f o i l thickness has been made. The thickness was c a l c u l a t -ed by noting the difference in spectrometer current for the same incident alpha and proton energies. The difference in spectrometer current corresponds to a difference in magnetic f i e l d in the spectrometer which, in turn, corres-ponds to a difference in momentum between alphas and protons emerging from the scattering f o i l . Knowing the incident energy of the alphas and protons, i t i s easy to calculate the target thickness necessary to produce this energy d i f -ference. The calculation of the Aluminum f o i l thickness can be found in Appendix D. The target thickness was found 2 + to be equivalent to 130 micrograms / cm of Aluminum - 2 0 $ . The uncertainty in target thickness arises from the uncer-tainty in the difference of magnet currents plus the uncer-tainty in theoretical values of the stopping crossection for Aluminum. This target thickness for protons of 2 Mev. energy corresponds to 14.5 KBV.SO that, the uncertainty in 3 5 0 3 0 0 — 2 5 0 h 2 0 0 .985 M.EV. 1.87 M.E.V-1.4 8 M£.V 1.36 MEV 97 5 M.E.V 8 6 M.E.V . 67 5 M.E.V. 100 .4 7 M.E.V. . 37 M.E.V. PROTONS a PARTICLES F IGURE 17 , 315 4 0 B I A S V O L T S 50 O Q O O Q O O m o ^ o m o 10 ro ho co CJ ~ — d3aiAinN "13NNVHO E N E R G Y IN M . E . V . FIGURE 19. - 33 -proton energy i s only of the order of 3 Kev. and i s n e g l i -g i b l e compared to the proton energy. jndow • Thickness; The energy i n t e r c e p t s of Figures 18, 1 9 , i n d i c -ate the window thickness of the s o l i d s t a t e counter. This can be seen from the curves to be l e s s than 3D Kev. f o r Alpha p a r t i c l e s of energy greater than 0.5 Mev, This checks favourably with the rated t h i c k n e s s of 20-40 Kev., f o r a 1.6 Mev.alpha. * L i n e a r i t y : It i s expected from i n s p e c t i o n of the nomograph Figure 15, that a l l alphas i n the energy range 0.5 - 2 Mev., w i l l be stopped i n the a c t i v e region of the s o l i d s t a t e counter f o r an a p p l i e d bias of 1 V o l t or g r e a t e r . There-fore the p l o t of pulse height against c o r r e c t e d energy should be l i n e a r f o r a l l a p p l i e d • b i a s e s . This i s v a r i f i e d i n Figures 18, 19. The response of the counter to protons should be l i n e a r u n t i l the protons s t a r t p e n e t r a t i n g p i s t the a c t i v e region of the counter. The proton curve then should &%p§rt*-from l i n e a r i t y , and the pulse height of alphas, of the same energy, should be higher than that of the protons. The point of departure of the counter from l i n e a r response to protons can be c a l c u l a t e d from Figure 20. For example, with an a p p l i e d BARRIER DEPTH IN M.E.V _ _ _ _ _ _ _ ro ro cn CD b ro o> co b bias voltage of 2 V o l t s the counter bias w i l l be 2.6 v o l t s (Add 0.6 v o l t s f o r contact p o t e n t i a l ) . At t h i s b i a s , the b a r r i e r depth D i s 14 microns, A proton of energy 0),9 Mev. w i l l penetrate to the edge of the a c t i v e r e g i o n , so that f o r higher energy, the proton w i l l expend some energy i n the i n a c t i v e r e g i o n . As a r e s u l t , above t h i s energy the r e -sponse of the counter w i l l be n o n - l i n e a r . Figure 20 i s a p l o t of energy at which the response of the counter goes no n - l i n e a r against bias v o l t a g e . The dark l i n e i s the theor-e t i c a l curve and the point s marked are the experimentally determined poi n t s from Figures 18,19. As can be seen, the experimental p o i n t s l i e on the t h e o r e t i c a l curve, w i t h i n experimental accuracy. The v a r i a t i o n i n slope of the l i n e s i n Figures 18, 19, i s due to the v a r i a t i o n i n counter c a p a c i t y with bias v o l t a g e . Figure 15 shows that, as the bias voltage i n c r e a s e s , the c a p a c i t y of the counter decreases,, The head a m p l i f i e r used i s a cascode with a grounded cathode fed back by a 4.4 pf., condenser. This a m p l i f i e r was working with a gain of approximately 400. Therefore the c a p a c i t y to ground, l o o k i n g i n t o the a m p l i f i e r , was about 1700 pf. The c u r r e n t pulse generated when a p a r t i c l e i s i n c i d e n t on the counter i s shared between the counter c a p a c i t y and the 1700 pf., head a m p l i f i e r c a p a c i t y . As the counter c a p a c i t y changes so does the amount of cur r e n t fed onto the head - 35 -a m p l i f i e r c a p a c i t y and, as a r e s u l t , the pulse height changes. For example, at a 6 v o l t b i a s , the counter cap-a c i t y i s about 500 pf., and at 40 v o l t s the c a p a c i t y i s 200 pf. (See Figure 15). The r a t i o of the pulse height f o r these two d i f f e r e n t biases should be i n v e r s e l y pro-p o r t i o n a l to the r a t i o of the sums of the c a p a c i t i e s be-for e and a f t e r . That i s : & ^ 1 * *"amp. + ^*counter(2) 2 amp. counter 11 ) PH^=Pulse height f o r counter c a p a c i t y .counter(1) 2=Pulse height f o r counter c a p a c i t y counter(2) PH At 1 Mev. the pulse heights are: PH 1 =145 f o r 6 v o l t s bias PH2=19B f o r 40 v o l t s b i a s . counter! 1 )' = 500 pf. j ; ' 'counter(2) = 200 pf. amp. =1700 pf. Camp. + C c o u n t e r ( 2 ) m 1700 + 200 t 0.8 Camp."!" C c o u n t e r ( 1 ) 1700.+ 500 ^ 1 ts 145 <\/ n _ ^amp.+ ^counter(2) PHL 198 " U , t ) 8 C C , /. x 2 amp.+ counter(1; It i s evident, then, that the v a r i a t i o n i n slopes of the curves i s c o n s i s t e n t with the v a r i a t i o n i n counter c a p a c i t y . - 36 -CHAPTER V. EXPERIMENTAL, D(d,tf)He 4 REACTION In t r o d u c t i o n ; A p r e l i m i n a r y experiment i n the measurement of the D(d,2f)He 4 r e a c t i o n c r o s s e c t i o n was performed. The r e -s u l t s of t h i s p r e l i m i n a r y experiment are not d i r e c t l y use-f u l i n the determination of the c r o s s e c t i o n of t h i s r e a c t i o n . The reason f o r t h i s appears to l i e i n the c o l l i m a t i n g of the bombarding beaip. The c o l l i m a t i o n i s s u f f i c i e n t l y i n -accurate to s c a t t e r a l a r g e number of p a r t i c l e s from the beam d i r e c t l y i n t o the spectrometer. The r e s u l t i n g count r a t e i n the system i s many orders of magnitude greater than what could reasonably be expected from Q(d,"^)He . Hence a measurement of the c r o s s e c t i o n could not be made. During t h i s experiment, s e v e r a l measurements of relevance to the ult i m a t e measurement of t h i s c r o s s e c t i o n by t h i s method were made. They are discussed i n the remain-der of t h i s chapter; they concern 1 ) the s t a b i l i t y of D^D trans m i s s i o n t a r g e t s and 2) the time dependant background i n the r e l e v a n t energy r e g i o n of the s o l i d s t a t e s p e c t r o -meter. A d e s c r i p t i o n of the p r e l i m i n a r y experiment mention-ed above i s a l s o i n c l u d e d , s i n c e i t w i l l be u s e f u l f o r the a n a l y s i s of the f a u l t s i n the present system. - 37 -Time Dependent Counter Background: Because of the d e t e r i o r a t i o n of the performance 2 of the counter described i n Chapter IV, an R.C.A. 20 mm counter was used. Its window thickness was determined to be 500 Kev,, energy l o s s f o r 5.3 Mev., alpha p a r t i c l e s by means of the d i f f e r e n t i a l range/energy r e l a t i o n s h i p s f o r alpha p a r t i c l e s i n a i r . The pulse amplitude versus energy l o s s i n the counter c a l i b r a t i o n was determined and was con-s i s t e n t with the known p r o p e r t i e s of the a m p l i f i e r system and the energy l o s s per e l e c t r o n - h o l e pairV^P^raf-'the?ra.--^ a c t i o n kinematics,the energy spectrum of the alphas r e -s u l t i n g from the D(d,tf)He 4 which would s t r i k e the counter, was c a l c u l a t e d , taking i n t o account the a v a i l a b l e Van de G r a a f f v o l t a g e , the stopping power of the t a r g e t and the or b i t / e n e r g y r e l a t i o n s h i p s discussed i n Appendix A. The "Time Dependent" background i n t h i s region of the pulse spectrum was then measured. The Van de Graaff was oper-ated at 2.2 Mev., during t h i s period so that the "Time Dependent" background i n c l u d e d counts from Van de Graaff sparks and other Van de Graaff-induced events (apart,from d i r e c t beam on-target produced e v e n t s ) . The r e s u l t s were i n the pulse amplitude region corresponding to energy l o s s e s i n the counter l y i n g between 1.5 and 1.6 Mev,, which i s the energy region s p e c i f i e d above. The "Time Dependent" background was 0.2 counts/min. This count r a t e i m p l i e s an upper l i m i t to the smallest, measureable c r o s s -- 38 -e c t i o n f o r the r e a c t i o n . Assuming an experimental run would 2 l a s t not longer than approximately 3 x 1 0 min., the "Time Dependent" background would be 60 Counts. This background can, of course, be c o r r e c t e d f o r , but only to an accur-acy of — \/"N" where N i s the number of counts. Hence, the i r -r e d u c i b l e l i m i t to the count rate due to background i s app-roximately 8 counts i n 300 min. The c r o s s e c t i o n 0~" i s r e l a t e d to the number of counts i n the c o r r e c t energy region by :-Q = the charge i n the beam s t r i k i n g the 4 t a r g e t « 2 x 10 microcoulombs f o r a 2 1 microamp beam f o r 3 x 1 0 min. e = e l e c t r o n i c charge. N^ * t a r g e t n u c l e i d e n s i t y i n number of D 2 18 nuclei/cm which = 3 x 10 f o r a 30 Kev. t h i c k n e s s f o r a 2 Mev.deutron. ^O. = e f f e c t i v e d e t e c t o r s o l i d angle = 47Tx 10 s t e r a d i a n s . ( e f f e c t i v e means that t r a n s -formation from centre of mass to l a b o r -atory co-ordinates has been allowed f o r . This gives an upper l i m i t to the c r o s s e c t i o n of N. = Q B Where: cm 2 SPECTROMETER ENTRANCE APERTURE /COL LIM AT I ON/ ,SLIT LIQUID N 2 TRAP • L 3 B E A M CATCHEF B E L L O W S MOVEABLE D£ DISPENSER INCIDENT BEAM DIRECTION B E A M IOCOLLIMATORS BELLOWS FIGURE 21 THE TARGET ASSEMBLY - 39 -Heavy Water Transmission Target S t a b i l i t y : A target of D2O was l a i d down on a. 23 x 1fJ~^in. aluminum f o i l , cooled to / l i q u i d nitrogen temperature. The target was prepared by effusing D.,0 vapour through a d i f fus ing je t onto the cooled surface (See Figure 21). A beam of protons of energy i Mev., (corresponding to 2 Mev.,deuterons in energy l o s s in the target) was passed through the target . The b e a m w a s approximately 1 microamp and was spread uniformly over the surface of the target . The D-jQ target thickness was measured by magnetic ana l -ys i s of the scattered protons, the target thickness being equal to the difference in energy- between the protons scat -tered with and without B^O frozen on the aluminum. The target thickness remained constant under th is beam for more than 30 minutes. Beam Scattering into Spectrometer: In Figure 21, the co l l imat ing arrangements used at the present stage in the experiment i s shown. Col l imat ion of the incoming beam i s necessary to define the target spot, and to prevent beam from s t i k i n g other material than the target . Coll imators are necessary on the input to the spec-trometer to r e s t r i c t i t s f i e l d of view to the target spot. During the past measurement, beams werB passed - 5 into the chamber under three condit ions: §1) with 23 x 10 A l - 40 -f o i l i n the target mount and b) with f o i l removed and c) with the aluminum f o i l and the beam catcher removed. In a l l cases, the pulse amplitude spectrum from the s o l i d s t a t e counter was observed as a f u n c t i o n of magnet c u r -rent; that i s , the p a r t i c l e s being produced w i t h i n the spectrometer!s f i e l d of view were analysed f o r momentum and energy,In c o n d i t i o n a) the spectrum comprised a v e r y strong component a t t h e energy and momentum corresponding to e l a s t i c a l y s c a t t e r e d p a r t i c l e s ; at lower energies and momenta, a s l i g h t l y weaker, but s t i l l very intense f l u x was observed. C o n d i t i o n b) was then e s t a b l i s h e d i n order to determine the source of the lower energy p a r t i c l e s . With no aluminum f o i l i n the t a r g e t mount, there was no e l a s t -i c a l y s c a t t e r e d f l u x as i n case a) but the lower energy f l u x continued at about the same l e v e l . Since i t was con-s i d e r e d p o s s i b l e that these p a r t i c l e s were being degraded i n energy and s c a t t e r e d i n t o the spectrometer by the rim of the beam catcher, t h i s was removed and c o n d i t i o n c) e s t a b l i s h e d . This did not di m i n i s h the i n t e n s i t y of the low energy f l u x . It seems l i k e l y that t h i s f l u x i s pro-duced i n the c o l l i m a t i n g system. Further work on t h i s i s the r e f o r e necessary before the inherent c a p a b i l i t i e s of the r e s t of the experimental system can be r e a l i z e d . APPENDIX A D(d ,TpHe 4 REACTION KINEMATICS The reaction considered has as i t s i n i t i a l state an energetic deuteron incident on a stat ionery target deu-teron. Inthe centre of mass (C.M.) system, both deuterons 'd -ft are moving toward each other with equal ve loc i ty (v, ). i . e ; Let m^  =« deuteron mass L ^ = gamma energy. v o c 5 3 ve loc i ty of the resultant alpha in C . M . system Then V , = V j » V =» V d. cL cm d Where v = ve loc i ty of C.M. cm J v^ = ve loc i ty of incident deutrons in lab system. In the centre of mass system, conservation of energy and momemtum gives Where T .+ T , = 21 , a -Q + tL + Een. 1 ) d, dz d, * T » k inet ic energy in C.M.system Q = react ion Q value. E a energy in C .M.system. - 42 -A l s o U s i n g Then S u b s t i t u t i n g i n t o 1) 3) 2 S u b s t i t u t i n g 2) i n t o 3) So P* - P* P s= momentum i n C . M . s y s t e m . S q u a r i n g 2 2 m^c + (Q * E^) ^ ( ^ 2 ) + 2 v 2 ( Q + E d ) 4) R e a r r a n g i n g 4) ;  / 2 2 E^=n V <c 2 + Q+E d +||(matc2+ Q + E r f ) -{Q±E d) 2~ I 2~ 2~" From above i t i s e v i d e n t o n l y t h e minus s i g n i s a p p l i c a b l e , f o change t o t h e l a b o r a t o r y s y s t e m c o n c i -d e r t h e v e c t o r r e l a t i o n s h i p : *v ; •./ •: y - 43 -cm «. e* That i s -*2 2 2 _ 2 2 __ -*2 n 4 v. Multiply by nj^ 2 Squaring, after solving for ^  E c x = % E d C 0 8 ^ + ^ i J ( V d C 0 s 2 ^ C ) i : - ( % ( E : d ~ C ) ^ ' 6 ) 4 ^ ~ l 1 " ^ . ^7" Using equations 5) and 6) i t i s possible tb calculate the energy of the resultant alpha as a function of and Ej, ~ 44 -APPENDIX B. THE 17° ELECTROSTATIC DEFLECTION SYSTEM As described in Chapter II, the system con-s i s t s of a section of a cencentric c y l i n d r i c a l condenser with: When a pa r t i c l e of charge Ze, kinetic energy T, and mass m i s incident on the entrance aperture*tangent to the deflection plates, a voltage difference v must be applied between the plates to deflect the par t i c l e s 17°. The e l e c t r i c f i e l d E between the plates is assumed to be constant along the whole p a r t i c l e path be-tween the plates. (Refer to Chapter II for discussion.) When the pa r t i c l e s are passing correctly between the plates they w i l l describe a c i r c u l a r orbit with a radius of cur-vature equal to the average radius of curvature of the deflection plates. Radius of curvature r => 161" Plate separation dr - 0.375" Arc length s - 48 " That i s : mv ss ZeE r Where v=velocity of incident p a r t i c l e s . But E = V dr - 45 -•J-mv2 - T So; 2T . Zev 1 ) r d T Let the potential of the Van de Graaff be \ZQ,then: T - ZeV 2) o Substitute 2) into 1) 2ZeV o = ZeV r dr Or; 2V o = r v dr Therefore, the potential v necessary to cause the p a r t i c l e to move in an orbit of radius r i s independent of the type of pa r t i c l e being accelerated and d i r e c t l y pro-portional to the Van de Graaff voltage V . For example When V = 3.5 Mev. o v = 2drV 2(0.375) (3.5) = 16.3 Kev. o — _______ r 161 - 4 6 -APPENDIX C ELECTRO-MAGNET IC SERVO LOCK-ON MAGNETS. Each electro-magnet i s designed to d e f l e c t a 4 + 3 Mev. He up to 1 from i t s i n c i d e n t path. The d e f l e c t i o n takes place between the pole faces of the electro-magnet, which are 4 " square and separated by a 1 " gap. The f o l l o w i n g i s an approximate, although q u i t e 4 + accurate, estimate. The time,_t the He spends i n the f i e l d B i s : / _ t - d v d a 4 " v = v e l o c i t y of i n c i d e n t charged p a r t i c l e . The change i n momentum/_p i n the t i m e / _ t i s : _ _ P m F A t F - f o r c e exerted by the f i e l d B on the charged p a r t i c l e . -FsxqvB where q = charge on p a r t i c l e t h e r e f o r e _^p=qvBd = q B d ~ v i f f i e angular d e f l e c t i o n /_©for s m a l l ^ O i s /Cafifet t a n " ttSp/p) = ^ p - 4 7 -Therefore A Q ° q B d Using; 2mE E a energy of the i n c i d e n t p a r t i c l e . __-0 = 1 ° = 1 0 " radians m= 4 ( 1 . 6 6 x 1 0 ~ )gms q- 1.6 x 1 0 " 2 0 E* 3 ( 1 . 6 x 1 0 " 6 ) e r g s d « 1 0 cm. S u b s t i t u t i n g i n t o above expression f o r the max-imum B necessary: B ss 5 0 0 gauss It i s now p o s s i b l e to c a l c u l a t e the number of amp turns necessary to produce t h i s f i e l d i n the gap. Con-s i d e r an ord i n a r y C magnet with cu r r e n t i i n the c o i l and N t u r n s . Let B^  » f i e l d i n s i d e c o i l . B,, -J f i e l d i n gap. Amperes c i r c u i t a l laws H.dS = Ni Ni « H^ft + H 2 1 2 - B l V B2l2 - 48 -^ m p e r m e a b i l i t y l ^ = s path i n magnet 1 2 = gap width. Let B 2 »0*B 1 (X - leakage c o e f f i c i e n t - 0.6 This i s the usual assumption f o r a constant • c r o s s e c t i o n C magnet and should be an upper l i m i t f o r the magnet used i n the d e f l e c t i o n system. Also, s i n c e : Pi » Ml, B 1 1 2 Theref o r e Ni » o f B 1 l 2 The f i e l d i n the gap o<B^  =» 500 gauss = 500 x 10~ 4Webers/m 2 1 2= 2.54 cm = 0 . 0 2 5 4 m ^IX0= 4 x 10 henry/m 3 Ni_1 0 amp turns , A cu r r e n t of 5 amps was used which r e q u i r e d N ss 200 turns of magnet wire to produce the necessary f i e l d . T h i s number of turns was wound around a 10" diameter s p i n -dle to f i t the magnet shown i n Figure 4. This amounts to 167 ' of wire. The enamelled magnet wire used was 13 gauge,, - 49 -Then since S u b s t i t u t i n g the values given f o r above and using the f a c t that the area of the ga£ i s 8" sq„ L =0.017 henry - 50 -APPENDIX D TARGET THICKNESS CALCULATION In Chapter IV, a c o r r e c t i o n to the energy of the p a r t i c l e s emerging from the s c a t t e r i n g f o i l was found necessary. This c o r r e c t i o n must be a p p l i e d to the i n c i -dent beam energy to f i n d the energy of the p a r t i c l e s em-erging from the f o i l . The e f f e c t of the f o i l t h i ckness was observed by noting the d i f f e r e n c e i n energy between the alphas and protons emerging when both were i n c i d e n t at the same energy. This energy d i f f e r e n c e was detected by the 60°tlouble .focusing spectrometer and appeared as a d i f f e r e n c e i n f i e l d c o i l c u r r e n t necessary to s i t on the a l a s t i c a l y s c a t t e r e d peak f o r each p a r t i c l e beam. The equations of motion of the p a r t i c l e s i n the spectrometer are governed by the f o l l o w i n g : -p » ZBp 1 ) Where p <= momentum of the p a r t i c l e . Z = charge of the p a r t i c l e . B = magnetic f i e l d between pole faces of spectrometer. p a r a d i u s of curvature while i n mag-n e t i c f i e l d . 2 Also E = £ 2 a ) 2m E s p a r t i c l e energy, m = p a r t i c l e mass. - 51 -D i f f e r e n t i a t i n g : dE « 2dp 2b) E p D i f f e r e n t i a t i n g : ! ) dp = ZpdB ii : 3) S u b s t i t u t e 3) i n t o 2b) dE 2_>dB 4) E Since B = k l spec, k = constant. I =s spectrometer c u r r e n t , spec. ^ 4) then becomes dE 2 d i 5) —— 8 8 spec . E I spec. Considering 1) and 2a) Bp = p = (m{2E Z Z From t h i s i t can be seen that the r a t i o m/Z i s the same f o r protons and alphas, so that the o r b i t s f o r protons and alphas of the same energy are e q u i v a l e n t . Knowing t h i s , i t i s now evident that equation 5) holds f o r both alphas and protons at the same time. Therefore any small energy d i f f e r e n c e dE between alpha and proton w i l l appear as a small f i e l d c o i l c u r r e n t d i f f e r e n c e d i i n the manner p r e d i c t e d by equation 5). For example, f o r i n c i d e n t 2r;Mev., alphas and protons d i = I - I « 27.4 - 26.7 = 0.7 amps p alpha r I & I lpha e x P e r i m B n ^ a H y determined, - 52 -Therefore dE . 2(o.7)2 x 10 3Kev. = 102 Kev. 27.4 Knowing t h i s energy d i f f e r e n c e , i t i s now pos-s i b l e to c a l c u l a t e the t a r g e t t hickness necessary to give t h i s dE. From NUCLEAR DATA TABLES pg.79 » i i u K e v cn ^ dxl2 Mev proton dE | - 110 ev m /mg d E = 1000 Kev.cm^/mg. dxJ2 Mev.alpha Then, the energy d i f f e r e n c e between protons • and alphas emerging from the t a r g e t of thickness T i s : dE T T d E i - dE l l= L d x l r t d x j p j Using above val u e s : T 5 0 102 Kev. _p118 micrograms/cm 890 Kev.cm mg S i m i l a r c a l c u l a t i o n s were c a r r i e d out f o r d i f -f e r e n t beam energies and are l i s t e d below: Beam energy Exp.energy d i f f . C a l c u l a t e d T 0.5 125 152 1.0 137 129 1.5 139 145 2.0 102 118 2 T =131 micrograms/cm ave. 3 - 53 -The l a r g e s t d e v i a t i o n from the mean i s about 18% . With the accuracy quoted i n NUCLEAR DATA TADLE5 of dE/dx of 1%, the maximum expected e r r o r i n T i s about 19%, that i s : T -s 131 micrograms/cm 2 i 26 micrograms/cm 2. APPENDIX E . ESTIMATE OF D(d ,7 j)He 4 REACTION CR0S5ECTION The model of the i n t e r a c t i o n to take place i s the f o l l o w i n g . The deuteron i s i n c i d e n t on the t a r g e t deuteron i n an S wave c o n f i g u r a t i o n . The wave f u n c t i o n amplitude w i l l be attenuated due to the coulomb b a r r i e r and r e f l e c t i o n from the nuclear p o t e n t i a l . The p a r t i c l e w i l l then be considered to pass only once across the n uclear diameter and the electro-magnetic t r a n s i t i o n must take place during t h i s t r a n s i t time. The estimate of the t r a n s i t i o n p r o b a b i l i t y to be used i s the usual B l a t t ck Weiskoff t r a n s i t i o n p r o b a b i l i t y . The r e a c t i o n c r o s s e c t i o n may be w r i t t e n : Where coulomb tr a n s m i s s i o n c o e f f i c i e n t T nuclear t r a n s m i s s i o n c o e f f i c i e n t n s c a t t e r i n g c r e s s e c t i o n , which i s an estimate of the p r o b a b i l i t y of the two deutrons being c l o s e enough to i n t e r a c t . T ^ d ) x* magnetic d i p o l e t r a n s i t i o n p r o b a b i l i t y , t » length of i n t e r a c t i o n time or length of time i n which the i n t e r a c t i o n may occur. - 55 -Treating each term i n d i v i d u a l l y , f i r s t l e t us consider the coulomb transmission c o e f f i c i e n t . The el e c t r o -s t a t i c coulomb forces w i l l be considered to be effective up to the point where the nuclear forces are appreciable. That i s , the coulomb barrier B c i s the potential energy of the two deuterons separated by two deuteron interaction r a d i i , or: 2 2 B » Z e c r where Z a 1 for deuterons a = the electronic charge r = 2 deuterons r a d i i - 2(4.3 x 10" 1 3) cm. Substituting these values into the above: B c = 0.168 Mev. Since the energy in the centre of mass system of the bombarding deuterons i s 1,5 Mev., the coulomb barrier i s much less than the energy of the incident deuteron. In the f i r s t approximation then, the coulomb transmission c o e f f i c i e n t i s one. An estimate of the transmission c o e f f i c i e n t through a discontinuity in potential, due to the attrac-tive nuclear potential i s given in Dlatt &. Weiskoff Pg.627 as T = 4kK 0  n (kTi<T2 where k=wave number of the incident p a r t i c l e . - 56 -K - the wave number of the p a r t -i c l e i n s i d e the nucleus. In the compound nucleus model, the energy of the p a r t i c l e s i n the nucleus i s shared e q u a l l y and K q i s + 13 a constant equal to about 10 cms. Also M =s energy of the deuteron i n = mass of the deuteron the centre of mass system or about 1.5 Hev. S u b s t i t u t i n g these values i n t o the above expre-s s i o n : 1 2 k = 2 x 10 cms OR k = K o 5 Therefore; T a 2/3 n Also from B l a t t &. Weiskoff pg.627, an estimate of the magnetic d i p o l e t r a n s i t i o n p r o b a b i l i t y i s given as: In the t r a n s i t i o n to be considered, 1 = 1 and i s approximately a 25 Mev.gamma. The t r a n s i t i o n i s to take place i n s i d e the combined deuteron r a d i i or s 1 = 1 -fii<) = 25 Mev. R - 8.6 Fermi - 57 -S u b s t i t u t i n g these values i n t o T ^ d ) i t i s found T ( l ) equals 4 x 10^/second. The time of nuclear m i n t e r a c t i o n of the two deuterons i s assumed to be of the order of the t r a n s i t time of the i n c i d e n t deuteron across the nucleus. Since the deuteron i n s i d e the nuclear rad i u s i s i n a 25 Mev.excited s t a t e , t h i s i s assumed to be ap-proximately the k i n e t i c energy of the deuteron i n the nucleus. That i s , :• K.E.=-fMv2 = 25 Mev. V M and the t r a n s i t time i s : t » R . nucleus v where R , - nuclear radius which nucleus 0 , . n-T3 - 8.6 x 10 cms. v - v e l o c i t y of the deuteron i n the nucleus. t h e r f ore: t - R M = 2 x 1 0 sec. V 2 E The p r o b a b i l i t y of the alpha being formed with s p i n J - 1, may be c a l c u l a t e d with the assumption that no s p i n o r i e n t a t i o n i s p r e f e r r e d over any other. Then, the number of ways any t o t a l s p i n J can be formed i s j u s t 2J+1. Three d i f f e r e n t s p i n combinations can be formed by the two sp i n J = 1 deuterons. They are J « 0, 1 &. 2. The p r o b a b i l i t y of J = 1 being formed i s the t o t a l number of ways J = 1 can - 58 -be farmed d i v i d e d by the t o t a l number of ways a l l three spins can be formed. That i s : P.. « 2J + 1 ds . s = 1 i £ ( 2 J . '+ D = =1/3 F i n a l l y , an estimate of the s c a t t e r i n g c r o s s -e c t i o n i s needed, which i s an estimate of the p r o b a b i l i t y that the two deuterons w i l l come c l o s e enough to each other to i n t e r a c t . The usual estimate i s th a t : 12 k a 2 x 10 /cm C ^ c ^ T J x 10* 2 4cm 2 4 Using the above derived values, i t i s now p o s s i b l e to estimate the c r o s s e c t i o n . S u b s t i t u t i n g these values i n t o the previous equation i t i s found: CV ^ 1 0 ~ 2 9 c m 2  Factors reducing the estimated c r o s s e c t i o n ! 1 i) T r a n s i t i o n may be E2 2) T ,1) i s u s u a l l y found to be from 10 to m \ 100 times too b i g . - 59'-j BIBLIOGRAPHY Fowler, L a u r i t s o n , T o l l e s t r u p . Phys . Rev .76,, 1 767 ( 1949). W.G.Cross R e v . S c i . I n s t r . 22, 717 (1951). W.E.Stephens Phys.Rev. 45, 513 (1934) Nuclear Data Tables pg.79 (1 961.) A.J.Stewart Smith. The Developement of a Double f o c u s i n g Spectrometer. M.A. Thesis U.12.C. (1961 ) Blat t , J . M . and Weisskoff V.F. T h e o r e t i c a l Nuclear Physics New York, Wiley and Sons (1958) 

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