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The absolute cross section for the reaction D(p,a)3 He from 400 Kev to 100 Kev Helmer, Richard Lloyd 1969-12-31

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THE ABSOLUTE CROSS SECTION FOR THE REACTION D(p,tf) He FROM 400 KeV TO 1100 KeV 3  by RICHARD LLOYD HELMER B . A . S c , University of B r i t i s h Columbia, 1 9 6 6  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of PHYSICS  We accept t h i s thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA April, 1 9 6 9  In presenting t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements  f o r an  advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study.  I further  agree t h a t permission f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s representatives.  I t i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r  f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission.  Department of Physics The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada  Date:  April,  1969  ABSTRACT 3  The absolute cross section of the reaction D(p,^) He has been measured i n the energy range from 400 Kev to 1100 Kev i n the laboratory system.  A target of deuterated polyethylene was used to measure the  r e l a t i v e y i e l d of the reaction over t h i s range, and the r e s u l t s were normali z e d to an absolute measurement made with a deuterium gas t a r g e t . The reaction i s of interest because i t enables some information to be obtained about the forces binding three nucleons together.  It  also has  some significance i n a number of astrophysical processes. In order to determine the cross section, the i n t r i n s i c  efficiency  of a 5 inch by 4 inch sodium iodide c r y s t a l s c i n t i l l a t i o n counter was measured by simultaneous alpha p a r t i c l e and gamma ray counting on the 340 Kev resonance of the reaction "^F(p,<*#)^0.  The i n t r i n s i c e f f i c i e n c y of the de-  tector was found to be .679 - .03 for the 6.14 Mev gamma rays from t h i s r e a c t i o n , with the p a r t i c u l a r geometry used. The absolute cross section for the reaction D(p,^T)^He was found by the gas target measurement to be 2.33 - .07 microbarns f o r an incident proton energy of 643 kev.  TABLE OF CONTENTS ABSTRACT  ii  TABLE OF CONTENTS  iii  LIST OF TABLES  •'  LIST OF FIGURES  .«  vi  ACKNOWLEDGEMENTS . . CHAPTER I  CHAPTER II  CHAPTER IV  CHAPTER V  ±  1  INTRODUCTION 1.1.  General Introduction  1  1.2.  Previous Work  3  The Angular D i s t r i b u t i o n  6  THEORY 2.1.  CHAPTER III  v  EXPERIMENTAL APPARATUS 3.1.  Target Chamber  II  3.2.  Targets  13  3.3.  Detectors, Collimators, and Shielding  14  3*4*  Electronics  16  3.5.  Data Analysis  3.6.  Proton Beam  ,  16 17  RELATIVE CROSS SECTION MEASUREMENTS 4.1.  Experimental Apparatus  •  •  19  4.2.  Procedure  22  4.3.  Data Analysis and Results  22  EFFICIENCY MEASUREMENTS 5.1.  Introduction  5.2.  Apparatus (a)  •  30 31  Target Chamber"i..... iii  ••  31  iv  5.3.  (b) F l u o r i n e Targets  33  (c) Alpha Detector E l e c t r o n i c s  35  (d) Gamma Detector E l e c t r o n i c s ...............  39  S o l i d Angle C a l c u l a t i o n s  39  (a) Alpha Detector  5.4. CHAPTER VI  39  (b) Gamma Detector  42  Results  46  GAS TARGET AND ABSOLUTE CROSS SECTION 6.1.  Introduction  48  6.2.  The Gas Target  49  6.3.  Current I n t e g r a t i o n  51  6.4.  Experimental Procedure  6.5.  Other C o r r e c t i o n Factors  55  6.6.  Results •  57  BIBLIOGRAPHY APPENDIX  •••••  •  •  54  6l COMPUTER PROGRAMS  62  LIST OF TABLES II-l  Ratios of c o e f f i c i e n t s from the angular d i s t r i b u t i o n measurements  II- 2  Smoothing factors  III- l  8 10  Dimensions of the D-detector assembly  •  •••••  16  III-2  L i s t of the electronic units used i n t h i s experiment  18  V-l  Properties of the alpha detector  31  V-2  Alpha detector s o l i d angle  39  V-3  Uncollimated gamma detector geometry  46  V-4  Crystal e f f i c i e n c i e s  •  47  VI- 1  Current integrator c a l i b r a t i o n  54  VI-2  Absolute cross section measurements •  •  ••  58  LIST GF FIGURES II-  l  Ratios of c o e f f i c i e n t s from the angular d i s t r i b u t i o n measurements  ••  •  9  III-  1  The r o t a t i n g target assembly  12  III-  2  A schematic diagram of the detector assembly  15  IV - 1 IV - 2 IV - 3  Detector-target configuration f o r the r e l a t i v e cross section runs  20  cross section runs  21  Block diagram of the electronic arrangement for the r e l a t i v e Typical spectrum a f t e r analysis by the NAILS computer  program  •*  24  IV - 4  Target decay from the 800 kev runs  25  IV - 5  Relative y i e l d curve obtained f o r each detector  27  3 IV - 6  Relative y i e l d f o r the reaction  V - 1  Fluorine - 19 target chamber  32  V  Alpha p a r t i c l e window  34  - 2  D(p,tf) He  28  19 V  - 3  V  - 4  V V  - 5 - 6  E x c i t a t i o n function for  measurements  7  F target used for the e f f i c i e n c y  36  Block diagram of the electronic arrangement for the c r y s t a l  e f f i c i e n c y measurements  37  5.13 Mev  38  239  Pu alpha p a r t i c l e spectrum  Typical alpha spectrum from  19  16  F(p,°00 0  V  - 7  Typical gamma spectrum from ^ F ( p , * X ) ^ 0  V  - 8  Relation of absolute e f f i c i e n c y to distance  V  - 9  Uncollimated gamma detector geometry  40 •  ••  41 44  •  45  VI - 1  The gas target assembly  52  VI - 2  The absolute cross section for the reaction D(p,tf) H e . . . . . . . vi  59  ACKNOWLEDGEMENTS  I wish t o express my g r a t i t u d e t o a l l the members o f the Van de Graaff group f o r t h e i r help during the course o f t h i s work.  P a r t i c u l a r thanks go t o  Dr. G. M. B a i l e y f o r h i s supervision o f the experimental p a r t , and t o Dr. G. M. G r i f f i t h s f o r h i s assistance and very h e l p f u l suggestions during the w r i t i n g of t h i s t h e s i s .  vii  CHAPTER I INTRODUCTION  1.1  General Introduction One key t o understanding the p r o p e r t i e s of n u c l e i would be t o d i s -  cover the c h a r a c t e r i s t i c s of the internucleon f o r c e .  A correlation exists  between various parts of the nuclear force and the d e t a i l e d character of nuclear bound state wave f u n c t i o n s .  Since many t h e o r e t i c a l studies have  been made t o r e l a t e d e t a i l s o f the force system i n a q u a n t i t a t i v e way t o the properties of few nucleon systems, i t i s important t o obtain as much e x p e r i mental information as p o s s i b l e about the bound states of n u c l e i , and p a r t i c u l a r l y l i g h t n u c l e i , where the many body aspects of the problem do not obscure the s p e c i f i c r e l a t i o n s between nuclear structure and c h a r a c t e r i s t i c s of the internucleon f o r c e . D i r e c t r a d i a t i v e capture reactions provide a r e l a t i v e l y simple way of determining  some of the p r o p e r t i e s of nuclear bound states and assessing  nuclear models through comparing t h e o r e t i c a l l y predicted and experimentally measured cross s e c t i o n s .  The s i m p l i c i t y i n comparison t o other reactions  a r i s e s because the t r a n s i t i o n which proceeds d i r e c t l y from a free nucleon state t o a bound state i s produced by a r e l a t i v e l y weak coupling t o the electromagn e t i c r a d i a t i o n f i e l d which does not produce a large perturbation on the system. Other d i r e c t reactions might be used t o study the bound s t a t e s , f o r example, the s t r i p p i n g r e a c t i o n , i n which one nucleon from an incoming complex p a r t i c l e i s s t r i p p e d o f f the complex and moves d i r e c t l y t o a f i n a l bound s t a t e without forming an intermediate compound s t a t e .  In t h i s case the i n t e r a c t i o n between  p a r t i c l e s occurs through the medium of another p a r t i c l e and involves strong 1.  "  2  nuclear f o r c e s .  This makes i t much more d i f f i c u l t t o extract information  about the nuclear forces since a knowledge o f the nuclear forces i s r e q u i r e d to understand t h e nature o f the t r a n s i t i o n from one nuclear s t a t e t o another. For the above reason and f o r f u r t h e r reasons noted below, a study 3 of the d i r e c t r a d i a t i v e capture of protons by deuterium t o form He should prove u s e f u l i n understanding the 3 nucleon system. F i r s t , t h i s r e a c t i o n r e 3 s u i t s i n the formation o f He, which i s more t i g h t l y bound than the deuteron, 3 the only bound two body nucleus. Also He has both s i n g l e t and t r i p l e t twonucleon spin configurations while the deuteron has only the t r i p l e t c o n f i g u r a 3 tion.  Thus the s t r u c t u r e o f He should be more s e n s i t i v e t o the short range  components o f the nuclear f o r c e as w e l l as t o the components which depend on the s i n g l e t spin c o n f i g u r a t i o n .  Therefore a study of three body n u c l e i should  provide more information about the i n t e r n u c l e o n force than can be obtained from the deuteron. Another reason why t h i s r e a c t i o n i s o f i n t e r e s t i s r e l a t e d t o a s t r o 3 physics.  The r e a c t i o n D(p,#) He i s the second step i n the chain o f r e a c t i o n s  which supplies most o f the energy i n the hydrogen-burning stage of the smaller main-sequence s t a r s .  This chain i s as f o l l o w s : p + p —  D + /3*+ T> 3 p + D — He + Y 3 3 4 He + ^He —- He + 2p Now although the r a t e o f energy release of a main sequence s t a r i s c o n t r o l l e d by the f i r s t r e a c t i o n since i t occurs by means of the very weak /3i n t e r a c t i o n , i t i s l i k e l y t h a t the r e a c t i o n D(p,2f) He i s the f i r s t t o supply nuclear energy as the s t a r contracts, and i t may consequently have considerable e f f e c t on the r a t e at which the s t a r condenses t o the main sequence, at l e a s t i f there i s as high a deuterium t o hydrogen r a t i o i n the i n t e r s t e l l a r gas as i s found i n the e a r t h . 3 In the e a r l y stages o f s t e l l a r condensation, the r e a c t i o n D(p,<5") He  competes w i t h the r e a c t i o n D(d,n)^He which has a much l a r g e r cross s e c t i o n , but a smaller p r o b a b i l i t y of occurring since the concentration of hydrogen i s much greater than the concentration of deuterium.  The l a t t e r r e a c t i o n supplies  neutrons t o the i n t e r s t e l l a r gas which are then captured by the heavy elements and thus there may be s i g n i f i c a n t changes i n some isotope r a t i o s from the p r i mordial r a t i o s depending on the number o f neutrons supplied.  C l e a r l y the num-  ber of neutrons a v a i l a b l e f o r t h i s process i s dependent upon the i n i t i a l conc e n t r a t i o n o f deuterium and the amount of i t t h a t survives long enough t o produce neutrons.  Thus the isotope r a t i o s among the heavy elements could be  a f f e c t e d by the r e a c t i o n D(p, ZO^He, since much of the deuterium which would otherwise be a v a i l a b l e f o r the release o f neutrons i s removed by t h i s r e a c t i o n . 1.2  Previous Work Previous work on the r e a c t i o n by Fowler, L a u r i t s e n and T o l l e s t r u p  (FO 49) i n d i c a t e d that the angular d i s t r i b u t i o n was o f the form where the i s o t r o p i c part a was small but not zero.  a + b s i n -e2  The presence o f the s i n -©•  component i n the angular d i s t r i b u t i o n l e d these workers t o advance the hypothe s i s that the capture was mainly the r e s u l t of an e l e c t r i c dipole t r a n s i t i o n 3 of a p-wave proton t o the ground S - state of He. Their i n v e s t i g a t i o n of the y i e l d at 90^ f o r various bombarding energies showed t h a t the r e a c t i o n was nonresonant i n character, i n d i c a t i v e o f a d i r e c t capture  process.  In an ingenious experiment, Wilkinson (WI 52) showed that the gamma r a d i a t i o n a t 90° was plane p o l a r i z e d w i t h the e l e c t r i c dipole i n the r e a c t i o n plane.  This confirmed the hypothesis o f Fowler e t . a l . that the capture was  the r e s u l t of_an EL t r a n s i t i o n .  Wilkinson a l s o suggested that the small i s o -  t r o p i c component could a r i s e from a small amount o f s p i n - o r b i t coupling.  How-  ever, G r i f f i t h s and Warren (GR 55) found that the energy dependence o f the y i e l d was d i f f e r e n t at 90° from what i t was at 0°, and t h i s r a i s e d the possibi l i t y that the i s o t r o p i c component might a r i s e from S-wave capture of the  Verde (VE 50)  incoming protons.  had shown that magnetic dipole t r a n s i t i o n s  could occur between S-states of the continuum and the bound three nucleon Sstate as a r e s u l t of small non-central  components i n the nuclear  force.  Further measurement by G r i f f i t h s e t . a l . (GR 63) i n the energy range from 25 Kev to 45 Kev confirmed the hypothesis that the y i e l d at 0° followed an  en-  ergy dependence c h a r a c t e r i s t i c of incoming S-waves. The ground state of ^He i s known t o have  =  and thus can con-  55):  t a i n the components (SA  2  2  2  However, Derrick (De 60)  has shown that the amplitudes of the  P  4  P components are n e g l i g i b l e . The continuum states a r i s i n g from the  and  un-  bound p + D system contains the f o l l o w i n g components which can give r i s e t o electromagnetic 4  t r a n s i t i o n s to the bound state components:  s  2  > P  \  4  ^ 2  7 Thus the E l r a d i a t i o n i s the r e s u l t of t r a n s i t i o n s from p  P to  Si  states which gives r i s e to the main s i n •&• part of the angular d i s t r i b u t i o n . The i s o t r o p i c part a r i s e s mainly from Ml r a d i a t i o n , which r e s u l t s from t r a n s 4  i t i o n s from  2  S to  S^ s t a t e s .  Other t r a n s i t i o n s which could be of some s i g n i f -  icance are the f o l l o w i n g : E2 ( D - S ) , 2  4  E2( S -  2  E1( P 4  - S>),  E L ( F - ^D) 4  and  4  D).  There are also some i n t e r f e r e n c e terms.  The most important of  these i s the E l ( P - S ) / E 2 ( D - S ) i n t e r f e r e n c e . 2  2  2  2  Donnelly (DO 68) has i n v e s t i g a t e d the e f f e c t s of these t r a n s i t i o n s and t h e i r interferences t h e o r e t i c a l l y .  His r e s u l t s are based mainly on a two  body model d e s c r i b i n g the i n t e r a c t i o n between a proton and deuteron but i n c o r porating some three body parameters i n an e m p i r i c a l way.  I t i s important that  h i s f i n d i n g s be checked experimentally t o determine whether t h i s i s a u s e f u l  5. model f o r the r e a c t i o n , and i f so, t o t r y t o e x t r a c t some t h e o r e t i c a l l y s i g n i f i c a n t parameters from the data.  I t i s of p a r t i c u l a r importance t o i n v e s t i -  gate the cross sections predicted by t h i s semi-empirical theory, since i f these do not compare favorably w i t h experiment, i t i s u n l i k e l y that any of the other parameters w i l l be p a r t i c u l a r l y s i g n i f i c a n t .  Other work has been done r e c e n t l y  i n t h i s l a b o r a t o r y t o measure the angular d i s t r i b u t i o n of the emitted  radiation,  however the main object of the present work was t o measure the absolute cross s e c t i o n of the r e a c t i o n as accurately as p o s s i b l e .  CHAPTER I I THEORY A b r i e f d e s c r i p t i o n of the parameters required f o r the determination of the cross section i s given i n t h i s chapter. 2.1  The Angular D i s t r i b u t i o n  3 The measured angular d i s t r i b u t i o n o f the r e a c t i o n D(p,y) He can be described as a s e r i e s of Legendre polynomials i n the form  W(  )=J B Q  where  -©-'  1  P  (cos  A  (2.1-1)  i s measured i n the center of mass system.  Before the experimental angular d i s t r i b u t i o n can be compared w i t h the theory, i t must be corrected f o r the f i n i t e s o l i d angle o f the detector. I t has been shown by Rose (RO 53) that f o r an angular d i s t r i b u t i o n of the form (2.1 - l ) , these c o r r e c t i o n s are p a r t i c u l a r l y simple.  The corrected angular  d i s t r i b u t i o n i s given by W  * £ A Pn (cos  (•&')  (2.1 - 2)  £  where  - B /Qi • x  The s o - c a l l e d smoothing f a c t o r s , Q  A  take i n t o account the smearing  of the angular d i s t r i b u t i o n which r e s u l t s from the f i n i t e s o l i d angle o f the detector.  They are given by  / J , where c  i s obtained from the f o l l o w i n g  integral. "  f  K&s  $)[l- - ]M^U$ MXa)  t  (2.1 - 3)  o where  A  i s the h a l f angle of the detector  jU  i s the l i n e a r attenuation c o e f f i c i e n t  X$  i s t h e distance t r a v e r s e d by r a d i a t i o n i n c i d e n t on the c r y s t a l at an angle  and  ^ t o the a x i s  P. are the Legendre polynomials of order H.  Now the angular d i s t r i b u t i o n given by (2.1 - 2) i s e s s e n t i a l l y the d i f f e r e n t i a l cross s e c t i o n  , and from t h i s one can determine the expec-  t e d gamma r a y y i e l d , Ny (-«•), a t a p a r t i c u l a r angle the s o l i d angle  subtended by the detector at the source.  by i n t e g r a t i n g over The expression ob-  t a i n e d from t h i s i n t e g r a t i o n i s N, W  * NpA/ £ j i 0  where A/p =  [ i t k ?,Q, + £ PQ, + £ p ^ j  (2.1 - 4)  2  number of t a r g e t atoms per square centimeter  £ = f e t  0  number o f i n c i d e n t protons  No -  Jl  A  0 i t  e f f i c i e n c y o f the detector  =  s o l i d angle subtended by the detector at the source.  Terms f o r angular momentum 1  greater than three have not been i n -  cluded since i t has been shown (DO 67) t h a t the cross s e c t i o n f o r the Jl = 4  2  2  term, which would a r i s e from an E2 ( D -  /2 pared t o the main E l ( p -  2  S)  t r a n s i t i o n i s very small com-  x  S) t r a n s i t i o n .  The form of the angular d i s t r i b u t i o n given i n Chapter I i m p l i e s t h a t the maximum y i e l d i s obtained a t a l a b o r a t o r y angle of 90° t o the i n c i d e n t proton beam, and hence from the p o i n t o f view of the s t a t i s t i c a l s i g n i f i c a n c e of the number of counts obtained, i t i s best t o measure the gamma r a y y i e l d a t t h i s angle. Now the t o t a l cross s e c t i o n i s obtained from an i n t e g r a t i o n over a l l angles o f (2.1 - 2), and the r e s u l t i s 0~  where  A  0  r  =  (2.1 - 5)  i s given by (2.1 - 4)»  Thus the t o t a l cross s e c t i o n f o r a given energy by combining the l a s t two equations t o obtain  E , 0~ (i) i s computed T  8.  CT (E) T  »  N where  D  £ A  A/ C^^» y  :  given energy E evaluated f o r  D  E  [l + th. p,  F  Q,  +  4j p  z ( ? 2  +  ^  P j Q  (2.1 - 6)  l  i s the gamma ray y i e l d obtained at and the Legendre polynomials  •& = 90° f o r a  , P2 and P^ are  = 90°.  The other parameters are as previously described. The expression (2.1 - 6) shows that before the t o t a l cross section can be determined i t i s necessary to measure the angular d i s t r i b u t i o n i n order to obtain the r a t i o of the c o e f f i c i e n t s energy  E  (j-^j ,  and ^ ~ j  at which the cross section i s to be measured.  for a given  The measurements of  the angular d i s t r i b u t i o n has been made at laboratory proton energies of 500 Kev 650 Kev and 800 Kev (BA 69).  From a least squares f i t of these angular d i s t r i b -  ution measurements, the r a t i o s of the c o e f f i c i e n t s were determined. are l i s t e d i n Table II  - 1. and are shown i n Figure II  - 1.  The r e s u l t s  The other results  shown i n t h i s figure are from data obtained by previous workers. Table II  - 1 :  Ratios of Coefficients from the Angular D i s t r i b u t i o n Measurements.  Ep (lab)  A /A  455 kev  .072  -  .012  -.940 - .012  595 kev  .115  -  .013  -.965 - .013  760 kev  .127  -  .016  -.958 - .013  1  Q  = -A /A 3  Q  A /A 2  Q  The values of the smoothing factors f o r the detector geometry used i n t h i s experiment are l i s t e d i n Table II  - 2.  These were obtained from the com-  puter program DEWF, which was written previously (LE 64) to evaluate numerically the i n t e g r a l given i n (2.1 - 3)  9  X PRESENT WORK OLIVO (OL 68) T WOLFLI et. al l(WO 67) GRIFFITHS et. al. (GR 61)  T  0.4 0.8 1.2 1.6 LABORATORY PROTON ENERGY (Mev)  2.0  F i g . I I - l : Ratio of the c o e f f i c i e n t s from angular d i s t r i b u t i o n measurements.  10 Table I I - 2:  Smoothing Factors.  T. .9884  2 .9655  ^3 .9317  Thus the cross section can now be determined, i n p r i n c i p l e , i f the gamma ray y i e l d i s measured at 90° to the i n c i d e n t proton beam i n an accurately known geometry.  But before the d e s c r i p t i o n o f t h i s measurement, a t t e n t i o n w i l l  f i r s t be focussed on the apparatus used i n the experiment, followed by a d i s cussion o f the measurement o f a s e r i e s of r e l a t i v e c r o s s - s e c t i o n s , and f i n a l l y the determination  o f the gamma detector e f f i c i e n c y , which i s required f o r the  computation of the absolute cross s e c t i o n .  CHAPTER I I I EXPERIMENTAL APPARATUS 3.1  Target Chamber The t a r g e t chamber used f o r most of the angular d i s t r i b u t i o n runs and  f o r the measurement o f the r e l a t i v e cross sections was developed i n t h i s l a b o r a t o r y by the author i n conjunction w i t h G.M. B a i l e y and M.A. O l i v o .  The t a r g e t  consisted o f a r o t a t i n g copper disk covered by a t h i n l a y e r o f deuterated* ethylene, ( C D^) » 2  n  poly-  The polyethylene was obtained i n powdered form from Merck,  Sharp and Dohme o f Canada Limited, Montreal, Canada. The chamber was made of brass and the dimensions were approximately eight inches high by s i x inches i n diameter.  In order t o reduce the gamma r a y absorption through the w a l l s of the  chamber, the l / 8 i n c h w a l l thickness was machined t o a thickness o f .040  inch  i n the region over which gamma rays from the r e a c t i o n could enter the detector. The target chamber was mounted on an angular d i s t r i b u t i o n t a b l e .  A  l u c i t e i n s u l a t i n g d i s k was attached t o the bottom of the chamber, so t h a t the chamber would be i s o l a t e d e l e c t r i c a l l y from the t a b l e .  Figure I I I - 1. shows  the chamber and the means of l o c a t i n g i t on the t a b l e .  The nut on the concentric  rod attached t o the bottom o f the chamber enabled the chamber t o be r a i s e d or lowered. A l u c i t e i n s u l a t i n g r i n g was placed on the top o f the chamber, and the assembly containing the target d i s k and the motor which rotated i t was placed on top o f the l u c i t e . gassing.  P r o v i s i o n was made t o water c o o l the d i s k t o reduce out-  The top part could be r o t a t e d t o place the plane o f the disk at any  desired angle t o the incoming beam. The gas t a r g e t which was used f o r the measurement o f the absolute cross s e c t i o n w i l l be described i n a l a t e r s e c t i o n .  11.  12  F i g . I I I - l : The r o t a t i n g t a r g e t chamber.  3.2  Targets The method of making the t a r g e t s was as f o l l o w s .  F i r s t the deuterated  polyethylene was d i s s o l v e d i n xylene by b o i l i n g the mixture gently f o r approximately three minutes.  The r e s u l t a n t s o l u t i o n was then poured onto the disk  and was prevented from running over the edge by an 0-ring which was clamped t o the edge of the disk w i t h a metal r i n g .  A smaller 0-ring surrounding the cen-  t r a l p a r t of the disk l i m i t e d the deposit t o a band about 3 cm. wide.  The  xylene was then allowed t o evaporate slowly at room temperature i n a dust f r e e atmosphere, l e a v i n g behind a f a i r l y uniform l a y e r of polyethylene. Note: A superior method of making the t a r g e t s has since been found and a b r i e f d e s c r i p t i o n of t h i s technique f o l l o w s .  The t a r -  get i s machined out of l/U i n c h t h i c k brass l e a v i n g two r i n g s of brass t o contain the xylene i n s t e a d o f using G-rings f o r t h i s purpose.  The target thickness a f t e r machining was ap-  proximately 0.066 inches. The disk i s then preheated t o a temperature at which xylene w i l l b o i l and the mixture of xylene and polyethylene i s then poured i n t o the container and i s allowed t o b o i l u n t i l a l l the xylene has evaporated.  The disk  i s f i n a l l y removed from the heat and i s allowed t o c o o l . This method o f preparing the t a r g e t has three d i s t i n c t advantages.  F i r s t , the deposited l a y e r of polyethylene i s smoother  and hence more uniform than was obtained before.  Second, there  are no l o s s e s of the xylene s o l u t i o n through spaces which forme r l y occurred between the 0 - r i n g and the d i s k , and t h i s method reduces the time taken t o make a target from twenty hours t o approximately one h a l f hour. To reduce the background from the copper backing which could be expect e d at proton energies above approximately 1 Mev, a .001 i n c h t h i c k platinum  14. f o i l was attached, to the target base with a high thermal conductivity epoxy (Delta Bond 152, obtained from Wakefield Engineering Inc., Wakefield, Massachusetts) before depositing the polyethylene.  The deuterated polyethylene  target was rotated while a run was i n progress i n order to reduce the rate of deterioration. 3.3  Detectors. Collimators, and Shielding. Two i d e n t i c a l 5 inch diameter by 4 inch deep Nal (Tl)  gamma ray  detectors (HARSHAW type 20 MBS 16/B) mounted on 3 inch photomultipliers (RCA 8054) were used i n t h i s experiment. In order to reduce the background and to keep to a minimum the number of gamma rays scattered i n t o the detectors, they were shielded i n the following manner.  One, c a l l e d the D detector during the angular d i s t r i b u t i o n  runs, was placed inside a heavy lead s h i e l d i n g , the dimensions of which are shown i n Figure III  - 2 . , and l i s t e d i n Table III  - 1.  This detector was also  shielded by an 8 inch diameter lead c o l l a r with a 1 5/8 inch t h i c k wall which f i t t e d over the photomultiplier.  Mounted i n front of the detector was a lead  collimator which l i m i t e d the acceptance angle for gamma rays coming from the source.  This collimator was not used during the r e l a t i v e cross section runs,  however; instead a l/8 inch thick f l a t lead sheet was placed i n front of the detector to reduce the i n t e n s i t y of low energy gamma rays. The other c r y s t a l c a l l e d the M detector, was placed inside a c y l i n d r i c a l c o l l a r with a l/4 inch thick w a l l , and was shielded i n front by a l / l 6 inch thick lead sheet.  The back of t h i s detector was shielded by a l/8  inch t h i c k lead covering which extended over and hence gave further protection to the sides of the c r y s t a l .  F i g . I I I - 3 : A schematic diagram of the detector assembly.  The dimensions are given i n Table I I I - l .  16  Table I I I - 1. Dimensions of the D-dector assembly Collimator Half-angle  e  12.0 - 0.2  Source t o C r y s t a l Face  R  19.52  Source t o Collimator Face  p  12.46  Collimator Thickness  S  6.54  C r y s t a l Diameter  D  12.70  C r y s t a l Thickness  L  10.16  Collimator Face Inner Diameter  I  5.30  Collimator Face Outer Diameter  0  11.6  Thickness o f Lead S h i e l d i n g  T  4.0  3.4  + + + + + + +  degrees  0.05 cm 0.05 cm 0.05 cm 0.02 cm 0.02 cm 0.05 cm 0.1  cm cm  Electronics The e l e c t r o n i c equipment used i n the experiment i s discussed i n some  d e t a i l i n the section t o which a p a r t i c u l a r c o n f i g u r a t i o n i s r e l e v a n t .  Cir-  c u i t diagrams o f the p h o t o m u l t i p l i e r s and p r e a m p l i f i e r s f o r the detectors have p r e v i o u s l y been presented (0L 68). A complete l i s t of the e l e c t r o n i c s used during the experiment i s given i n Table I I I - 2. The numbers i n parentheses i n the block diagrams r e f e r t o the numeral order i n Table I I I - 2.  3*5 Data Analysis Several computer programs were w r i t t e n f o r the U.B.C. IBM 7044 computer t o a s s i s t i n the a n a l y s i s o f the data.  The rather complex analysis pro-  cedure was required i n order t o separate from the gamma r a y spectra background r a d i a t i o n s f a l l i n g i n the same energy range as the D(p,y)-%e gamma rays. The main c o n t r i b u t i o n s t o t h i s background were 6 and 7 Mev gamma rays from the r e a c t i o n "^F(p,<xtf)^0  , and 8 Mev gamma rays from the r e a c t i o n " "^C(p,y)'^N J  A l i s t o f the computer programs, w i t h a b r i e f d e s c r i p t i o n o f each, i s given i n the Appendix.  17.  3.6  Proton Beam The proton beam was obtained from the U.B.C. Van de Graaff a c c e l e r a t o r .  This machine i s capable of d e l i v e r i n g a beam of approximately 20 microamps on t a r g e t f o r the energy range covered during t h i s experiment.  18.  TABLE I H - 2 :  L i s t of the electronic units used i n t h i s experiment  1.  FLUKE Model 412-B High Voltage Power Supply  2.  HARSHAW Type 20MBS16/B 3 inch photomultiplier  3.  U. B. C. Power Supply  4.  U. B. C. Preamplifier  5.  U. B. C. Pulse generator  6.  NUCLEAR DATA ND-160 Dual Parameter Analyzer  7.  NUCLEAR DATA ND-120 Pulse Height Analyzer  8.  NUCLEAR DATA ND-500 Dual Amplifier and Single Channel Analyzer  9.  ORTEC Model 430 Scaler  5"^x 4" Nal(TL) c r y s t a l coupled to an RCA 8054  10. -  ORTEC Model 210 Detector Control Unit  11.  RCA Type C-3-75-0.2 Diffused Junction Detector  12.  ORTEC Model 101 Low Noise Preamplifier  13.  ORTEC Model 201 Biased Amplifier  14.  CANBERRA INDUSTRIES Model 1410 Linear Amplifier  15.  FLUKE Model 881A DC D i f f e r e n t i a l Voltmeter  16.  ELECTRO SCIENTIFIC INDUSTRIES Model 250 DE Impedance Bridge  17.  ELECTRO SCIENTIFIC INDUSTRIES Model 300 Potentiometric Voltmeter-Bridge  18.  ELDORADO ELECTRONICS Model CI-110 Current Integrator  CHAPTER I V RELATIVE CROSS SECTION MEASUREMENTS 4.1  Experimental Apparatus The absolute cross s e c t i o n measurement was made w i t h a gas t a r g e t  which could only take a small amount o f beam and therefore required a long run.  To measure cross sections at a l l energies w i t h t h i s ' t a r g e t would have  required a very long time.  Thus i t was decided t o determine the r e l a t i v e  y i e l d of the r e a c t i o n at s e v e r a l energies from 400 kev t o 1100 kev w i t h the deuterated polyethylene t a r g e t , and then t o measure the absolute cross s e c t i o n at only one energy, thereby e f f e c t i v e l y determining the absolute cross s e c t i o n over the e n t i r e energy range explored.  The target was prepared as discussed  i n the previous chapter, and i t s thickness was estimated t o be approximately 2 50 micrograms per cm cident protons.  corresponding t o an energy l o s s o f 14 kev f o r 800 kev i n -  The r o t a t i n g d i s k was set a t an angle o f 45° t o the incoming  beam as shown i n Figure I V - 1. Also shown i n t h i s f i g u r e are the two detectors placed at 90° t o the incoming beam, which were shielded i n the manner discussed i n the l a s t chapter.  The distance from the target centre t o the c r y s t a l face  was 4g inches. The r o t a t i n g d i s k was e l e c t r i c a l l y connected t o the r e s t o f the t a r get chamber so that electrons which were ejected from the target by secondary emission caused by the incoming protons would not cause an e r r o r i n the measurement o f the current, since these emitted electrons would eventually reach the chamber w a l l s .  There would also be some protons scattered o f f the target t o the  w a l l s and t h i s e l e c t r i c a l t i e u p insured that these protons would also be measured.  The current was i n t e g r a t e d by an Eldorado E l e c t r o n i c s Current I n t e g r a t o r ,  Model CI-110, which was checked f o r leakage current at the completion o f the run. A block diagram of the e l e c t r o n i c s used i s shown i n Figure IV - 2. 19.  F i g . TV-1  : Detector target c o n f i g u r a t i o n f o r the r e l a t i v e cross s e c t i o n runs.  21.  H. V. P O W E R (0  SUPPLY  SOURCE DETECTOR'W  DETECTOR"M"  (2)  (2)  PULSE  (5)  GENERATOR  PRE(4) AMPLIFIER  MAIN  POWER SUPPLY  (3)  (4) P R E AMPLI FIER  (14)  KICKSORTER  AMPLIFIER  (7)  KICKSORTER  AMPLIFIER-A  (6)  (8) A M P L I F" I E R - B  U3)  S. C . A . - A S.  (8)  C.A.-B  (8)  SCALER  (9)  SCALER  (9)  F i g . IV-2 : Block diagram of the electronic arrangement for the r e l a t i v e cross section runs.  22.  The pulse generator was used t o check the l i n e a r i t y of the k i c k s o r t e r and f o r s e t t i n g the windows on the s i n g l e channel analyzers. The s c a l e r s were used t o monitor the d e t e r i o r a t i o n r a t e of the t a r g e t , but were not used at a l l i n the a n a l y s i s of the data.  4.2  Procedure I t was known that the t a r g e t would decay appreciably during the runs  so i t was necessary t o c o n s t a n t l y remeasure the y i e l d at one p a r t i c u l a r energy so t h a t the y i e l d at other energies could be normalized t o t h i s .  These norm-  a l i z a t i o n measurements were taken at a proton l a b o r a t o r y energy of 800 kev, and the other measurements were taken at proton energies of 400 kev, 470 kev, 520 kev, 620 kev, 700 kev, 1000 kev, and 1100 kev. i n t e g r a t e d charge of from 6000 t o 22,500  A l l the runs were taken f o r an  microcoulombs.  The data was analyzed by the method discussed i n the next s e c t i o n .  4.3  Data A n a l y s i s and Results Rather than add together the data c o l l e c t e d by the two detectors and  determine the r e l a t i v e y i e l d from t h i s , i t was decided t o analyze the r e s u l t s separately, thereby determining a r e l a t i v e y i e l d curve f o r each detector. These two y i e l d curves were then blended together to obtain the r e l a t i v e y i e l d at the various energies.  The two sets of data are r e f e r r e d t o as the M c r y s t a l and  D crystal results. The spectra were f i r s t g a i n - s h i f t e d t o a standard gain and zero by the computer program TREAT.  This program was a l s o used t o subtract a time  dependent room background from the data.  The modified data was then processed  by NAILS, a complex a n a l y s i s program, which analyzed the data i n t o a s p e c i f i e d set  of  components.  From t h i s ,  one could determine  the  number  of gamma  23.  •  3  rays i n the spectrum which o r i g i n a t e d from the D(p,tf) He r e a c t i o n .  A typical  output o f the NAILS program i s shown i n Figure IV - 3, which gives the r a t i o of the number o f counts i n a preselected range of the spectrum introduced by various components as l i s t e d 19  F(p,°a) 0,  1 3  15 M4.439 gives  (M5.224 gives D(p,tf) He component^, F19MHI gives  C135M gives C ( p , t f ) N ,  l6  1 4  NBGSM gives neutron background, and  12 N(p,°0Q  C  ). The curve shows the t o t a l spectrum f i t t e d t o the  data. The spectrum represented i n t h i s f i g u r e i s f o r a proton bombarding energy o f 1100 kev.  From the r e l a t i v e i n t e n s i t i e s l i s t e d , i t i s c l e a r that a  considerable amount of the spectrum arose from gamma rays o r i g i n a t i n g from the other r e a c t i o n s , and from the neutron background which arose p a r t l y from D on D knock-on r e a c t i o n s i n the t a r g e t and p a r t l y from D on D reactions i n the magnet box. 3 The number o f gamma rays from the D(p,2f) He r e a c t i o n was corrected f o r dead time l o s s e s i n the k i c k s o r t e r , and f o r absorption o f gamma rays by the target backing, t h i s l a t t e r c o r r e c t i o n being applied only i n the case o f the D crystal results. Now i t was necessary t o normalize a l l the r e s u l t s t o a given target thickness since the target was decaying while the runs were i n progress. I n order t o monitor t h i s decay, several r e p e t i t i o n runs were made a t a proton energy o f 800 kev.  The r e s u l t s o f these runs are shown i n Figure IV - 4. The  y i e l d s shown were those obtained from the a n a l y s i s as described so f a r .  The  e r r o r bars i n d i c a t e the s t a t i s t i c a l uncertainty r e s u l t i n g from the number o f counts.  A small c o r r e c t i o n was added t o allow f o r e r r o r s i n the computer •pro-  gram NAILS (part o f the output of t h i s program was an estimate of the e r r o r ) . The f o u r t h run was omitted as being i n c o n s i s t e n t w i t h the r e s t .  Probably the  beam spot s h i f t e d during t h i s run. I t i s seen t h a t the M c r y s t a l y i e l d i s about 20 percent higher than  F i g , IV-3 : T y p i c a l spectrum a f t e r a n a l y s i s by the NAILS computer program.  25.  I800-J UJ _l  < o OT  >-  1600-  5  <t rr CD  rr  <  T + 1400H 1  UJ CD  rr < x U  1200-  z  i T +•  ZD  1  rr UJ  o- 1000o _i UJ  UJ  >  H <t _J UJ  800-  f  rr  600  ~1 30  "~1 60  ACCUMULATED  T 90 CHARGE  120 CxlOOO  150  MICROCOULOMBS)  F i g . IV-4 : Target decay from the 800 kev runs. The c i r c l e s r e f e r t o the M c r y s t a l . The crosses r e f e r t o the D c r y s t a l .  180  26.  the D c r y s t a l y i e l d .  This i s the r e s u l t of the more scanty shielding of the M  c r y s t a l , and of the absorption of gamma rays by the target backing which a f f e c ted only the D c r y s t a l . The r e s u l t s of the normalization runs were fed into the computer p r o gram POLY-D, which f i t t e d each curve separately as the sum of two exponentials. The y i e l d per unit charge f o r each of the r e l a t i v e cross section runs was then determined and the counts obtained for each run were m u l t i p l i e d by the approp r i a t e amount to allow for the target decay.  A small correction was also applied  to allow f o r the e f f i c i e n c y change of the detectors with the changing energy of the gamma ray. The r e s u l t of t h i s normalization procedure was to obtain r e l a t i v e cross section curves, one for the D c r y s t a l and one f o r the M c r y s t a l .  These  curves are shown i n Figure IV - 5» The error bars indicate p a r t l y the s t a t i s t i c a l error r e s u l t i n g from the number of counts.  This was t y p i c a l l y of the order of 3 percent.  Again, a  small amount was added to t h i s to allow for errors i n the computer program NAILS.  The rest of the error results from an uncertainty of about 3 percent i n  the target decay.  The root mean square sum of these errors was approximately 5  percent. The two r e s u l t s were then blended together i n the following way. F i r s t , each set of r e s u l t s was f i t t e d with a cubic least squares curve.  The D  curve was then m u l t i p l i e d by a constant factor to give the best f i t with the M curve.  This analysis was done with the computer program CSFIT.  A small correc-  t i o n was then applied to allow for the change of the angular d i s t r i b u t i o n with energy.  The resultant r e l a t i v e cross section curve i s shown i n Figure IV - 6. The errors arise from two sources.  F i r s t , there i s the error out-  l i n e d above f o r the r e s u l t s from each c r y s t a l . error f o r the blending procedure done by CSFIT.  Added to t h i s i s a 1 percent The t o t a l error then i s  •  27.  240CH  1  o  M CRYSTAL  CO  > 2000-  cc  <E  T  +D CRYSTAL  K  CD GC  1  1  UJ CD Ct  <r x o  I i  1600-  Z  i  CC UJ  Q.  Q _1  ^ I200-  T T + 1  1  UJ  > t< _J  UJ  cc 800  —I—  0.4  —I  0.5  — r —  0.6  0.7  I  0.8  0.9  1.0  LABORATORY PROTON ENERGY (Mev)  F i g . IV-5 : Relative y i e l d curve obtained f o r each detector.  I.I  28.  2400-  UJ _J  <  O CO  >-  c<tc cc  2IOO-  H  CD CC <  $ 1800CC  I  o  1500CC UJ Cu  Q  ui >-  I  £ 1200P  _j UJ CC  900 0.4  X  0.5  0.6  0.7  0.8  LABORATORY PROTON ENERGY  F i g . IV-6  T  0.9  ~I—  l.O  (Mev)  : R e l a t i v e y i e l d f o r the r e a c t i o n D(p,tf) He.  29.  approximately 6 percent. With t h i s section of t h e work completed, i t now remained only t o f i x the l o c a t i o n of the curve by measuring the absolute cross s e c t i o n .  Before t h i s  could be done, however, i t was necessary t o determine the c r y s t a l e f f i c i e n c y , which i s the subject of the next chapter.  CHAPTER V  EFFICIENCY MEASUREMENTS 5.1  Introduction I t was necessary t o determine an accurate detection e f f i c i e n c y of  the s c i n t i l l a t i o n counters f o r gamma rays before the absolute cross s e c t i o n could be obtained.  The r e a c t i o n "^F(p,«y)"^0 was u t i l i z e d f o r t h i s purpose. 19  In t h i s r e a c t i o n the protons can be captured by  F at s e v e r a l resonances t o  20  form e x c i t e d states of  Ne, which subsequently decay by alpha emission t o the  ground state o f "^0 (°<»)* or t o one o f the e x c i t e d states o f t h i s nucleus. These l a t t e r states are the 6.06 Mev s t a t e (<Xrr)> which decays by e l e c t r o n p a i r emission t o the ground s t a t e , the 6.14 Mev state ( ° 0  t h e 6.91 Mev state  and the 7«12 Mev state (<*j) which a l l decay by gamma ray emission t o the ground state.  I t has been shown (FR 50) that f o r the 340 kev resonance where the  present measurements were made, t h e r a t i o o f  i s 0.024.  I t has also  been found t h a t at 340 kev bombarding energy, the alpha decay t o the ground s t a t e ( <*<>) and t o the p a i r emitting s t a t e (^cV) were not experimentally  observ-  able (CH 50). This same experiment showed that the number o f alpha p a r t i c l e s emitted was i n close agreement w i t h the number o f gamma r a y s , and that the angular d i s t r i b u t i o n o f both r e a c t i o n products was i s o t r o p i c . Devons and Hiney (DE 49) had p r e v i o u s l y shown that t h e gamma rays were i s o t r o p i c . The foregoing discussion i m p l i e s that t o determine t h e e f f i c i e n c y o f a gamma ray detector o f a s p e c i f i e d geometry one has only t o measure the number of alphas emitted i n t o a known geometry.  One can then get the e f f i c i e n c y as  the r a t i o o f t h e number o f gamma rays detected t o the number o f alphas detected, a f t e r s u i t a b l y c o r r e c t i n g f o r the d i f f e r e n t geometries o f the two detectors. 30.  »  31  That i s to say, the e f f i c i e n c y i s  I -  -~-—-  where S i s the i n t r i n s i c e f f i c i e n c y and Ny  i s the number of gamma rays detected  N a i s the number of alphas detected w<* i s the s o l i d angle subtended at the source by the alpha counter oJy  i s the s o l i d angle subtended at the source by the gamma detector.  5.2 Apparatus (a)  Target Chamber The target chamber used f o r the e f f i c i e n c y measurements (Figure V-l)  has been used previously i n t h i s laboratory (LE 64) for the same purpose.  The  o r i g i n a l alpha detector had been destroyed, however, and so t h i s was replaced by one of similar dimensions.  The c h a r a c t e r i s t i c s of the alpha detector (RCA  diffused junction detector type C-3-75-0.2) are l i s t e d i n Table V-1.  TABLE V-1:  Properties of the alpha detector  Material  Phosphorus diffused into n-type s i l i c o n  Resistivity  1000 ohm-cm  Diffusion Depth  0.2 microns  Sensitive Area  ™ 20 mm  Operating Voltage  20 v o l t s  Leakage Current (measured)  0.43 microamps  Resolution (5»13 Mev alphas)  107 kev  2  i  to  33  A 25 micro-inch sheet o f Grade C (pinhole f r e e ) n i c k e l f o i l obtained from the Chromium Corporation o f America was placed i n front o f the alpha det e c t o r i n order t o reduce the scattered proton f l u x which would otherwise enter the detector a t a s i m i l a r energy t o the alphas.  This n i c k e l window a l s o r e -  duced the energy o f the °(z and 0/3 p a r t i c l e s , so t h a t these now appeared i n the same region as the s c a t t e r e d protons.  The entrance window t o the alpha detector  i s shown i n d e t a i l i n Figure V- 2. The t a r g e t chamber was a l i g n e d making use of the angular d i s t r i b u t i o n t a b l e on which i t r e s t e d , and the gamma detector c o l l i m a t o r , which had cross wires mounted on the f r o n t and back.  These cross-wires were placed i n such a  way as t o a c c u r a t e l y define the centre of the c o l l i m a t o r .  One then a l i g n e d  the centre of the beam entrance c o l l i m a t o r w i t h the p r e v i o u s l y mentioned c r o s s wires; then the angular d i s t r i b u t i o n t a b l e was r o t a t e d t o check t h a t the l i n e j o i n i n g the centre of the entrance window t o the alpha counter was i n l i n e w i t h the cross-wires.  This ensured that the a x i s of both detectors passed  through  the centre o f the beam spot on the t a r g e t .  (b) F l u o r i n e Targets The requirements f o r a s a t i s f a c t o r y t a r g e t i s t h a t i t must be t h i n enough t o allow the alphas t o escape and the protons t o pass through without too much degradation o f energy, and t h i c k enough t o get a reasonable y i e l d . For 340 kev bombarding protons, t h i s means t h a t a thickness o f approximately 5 t o 10 kev would be s u f f i c i e n t . Following the procedure used by Larson (LA 57) i n t h i s l a b o r a t o r y , the targets were made by evaporating powdered calcium f l u o r i d e onto t h i n copper plates.  The method i s t o put the CaF i n a tantalum boat and pass through t h i s -5  a l a r g e current while the apparatus i s under vacuum (approximately 10 mmHg). The vapour then deposits on the copper p l a t e s which are placed above the boat.  2-56  16 25/u.in JNICKEL 8  4.  INCHES  \  /  5 8 27" 32  11  \  /  F i g . V-2 : Alpha p a r t i c l e window.  35.  The stand holding the plates was arranged so that two targets could be made at one time, each at a d i f f e r e n t distance above the boat.  Three p a i r s of targets  were made i n t h i s fashion, varying each time the amount of C&F^ placed i n the boat.  Six targets of d i f f e r e n t thicknesses were thus obtained. The targets were then mounted i n the chamber, one at a time, to de-  termine t h e i r thicknesses to 340 kev protons.  To ensure that the target was  at an angle of 45° to the beam d i r e c t i o n a micrometer depth gauge was clamped onto the back of the chamber, and the feeler rod was screwed i n u n t i l i t touched the back of the target.  just  The target was then rotated u n t i l the rod and  i t s r e f l e c t i o n i n the target formed a straight l i n e .  Since the back of the  chamber was 45° to the beam d i r e c t i o n , the target then was also oriented t h i s way.  The excitation function i s shown i n Figure V-3 for the target selected.  The thickness at h a l f maximum was approximately 7 kev.  (c) Alpha Detector Electronics Pulses from the alpha detector were fed into an Ortec Model 101-201 Low Noise Preamplifier-Amplifier combination, and from there into 512 channels of a Nuclear Data Type 160 1024-channel k i c k s o r t e r .  The alpha p a r t i c l e pulses  were also fed to a single channel analyzer and scaler i n order to monitor the number of alphas during the run. A block diagram of the electronics (including the gamma detection c i r c u i t ) i s given i n Figure V-4. Chapter  A description of each unit appears i n  III. 239 The kicksorter was calibrated with 5.13 Mev alphas from a  which was inserted into the target chamber for t h i s purpose. obtained i s shown i n Figure V-5.  Pu source  The spectrum thus  Since the energy of the alphas from the r e a c -  t i o n i s only 1.73 Mev i n the laboratory system, the gain of the main amplifier was halved after c a l i b r a t i n g the k i c k s o r t e r , so that the alpha spectrum from the  36.  F i g . V-3 : Excitation function f o r F target used f o r the e f f i c i e n c y measurements  37.  BIAS (JO) SUPPLY ALPHA (||) DETECTOR PRE- (12) AMPLIFIER  H.Y  SOURCE  POWER  SUPPLY  (0  GAMM A  (2)  D E T E C :TOR  PULSE  (5)  GENERATOR  PRE-  (4)  POWER  KICKSORTER  MAIN (13) AMPLIFIER  (7) AMPLIFIER-AJ  KICKSORTER (6)  (8)  CxMPLIFIER-B (e0 S. C. A - A  (8)  S, C. A.-B (8)  SCALER (9)  (3)  SUPPLY  AMPLIFIER  SCALER  (9)  F i g . V-4 : Block diagram o f the e l e c t r o n i c arrangement f o r the c r y s t a l e f f i c i e n c y measurements.  38  500-1  400-  30 oH \-  z o o  tj.FWHM 2 . 2 %  200H  V (107 Kev)  lOOH  O 370  ~1  390  1  410  430  CHANNEL NUMBER  F i g . V-5 : 5.13 Mev  Pu alpha p a r t i c l e spectrum,  450  39. reaction would, be more nearly i n the centre of the range.  F i n a l l y the l i n e a r -  i t y was checked using the p u l s e r , and t h i s was found t o be excellent over the 19 , entire range.  A t y p i c a l alpha spectrum from the  X  16  F(p,«^)  0 reaction i s  shown i n Figure V - 6. (d) Gamma Detector Electronics The pulses from the gamma detector were fed i n t o a preamplifier and then d i r e c t l y i n t o the ND 120 k i c k s o r t e r .  A single channel analyzer and  scaler were also used so that a continuous check could be made on the number of gamma rays being detected and hence on the deterioration of the t a r g e t .  A  t y p i c a l gamma spectrum from the reaction i s shown i n Figure V - 7«  5.3  S o l i d Angle Calculations (a) Alpha Detector The alpha detector i s mounted so that i t detects p a r t i c l e s at 135° to  the incident proton beam and 90° to the target face.  The relevant geometry  f o r the c a l c u l a t i o n of the s o l i d angle i s displayed i n Figures V - 1  and V - 2,  and the dimensions shown there are l i s t e d i n Table V - 2.  Table V - 2:  Alpha detector s o l i d angle Method of Measurement  Distance Measured Window diameter  (2r)  Distance A Distance B Target backing  t  3.196 - .001 mm  T r a v e l l i n g microscope over 15 diameters  3.9836 - .001 i n  Precision depth gauge  .7225 - .0001 i n  Precision depth gauge  .0115 - .0001 i n  Micrometer  Detector Window t o Target Face R = A-B-t  3.2496 - .0002 i n  S o l i d Angle (calculated)  (1.18  -3  - .01) x 10  steradians  5.62 Mev  6.13 Mev  1.46 Mev 40 K  \  3492 Mev  6.48 M.ev  \  i  \  J  \  0  30  60 F i g . V-7  1 90 120 CHANNEL NUMBER  n  150  T y p i c a l gamma spectrum from ^E(p,«2f)"^"^0.  \ \i  180  210  42  The e r r o r s quoted are standard deviations taken over s e v e r a l measurements.  (b) Gamma Detector The main purpose f o r the measurement of the c r y s t a l e f f i c i e n c i e s was 3  so t h a t t h e cross s e c t i o n f o r the r e a c t i o n D (p, K ) He could be determined. I t was decided t h a t c r y s t a l D would be used f o r t h i s purpose, f u l l y c o l l i m a t e d as shown i n Figure I I I - 2 .  A summary o f the dimensions a p p l i c a b l e t o the  c a l c u l a t i o n o f the s o l i d angle has been given i n Table I I I - 1. An e r r o r occurred here, however, since an unreported change had been made t o the c o l l i m a t o r .  Approximately 1.1 cm. had been shaved o f f the f r o n t  end, and t h i s was not known a t the time t h a t the measurements were made. Hence the gamma detector was a c t u a l l y set 1.1 cm. c l o s e r t o the t a r g e t than i t should have been. Since the cross s e c t i o n measurements were made a t the proper distance, i t was necessary t o extrapolate the measured c r y s t a l e f f i c i e n c y t o what i t would have been at the proper distance by using a computed change o f e f f i c i e n c y w i t h distance.  This c o r r e c t i o n was made by r e d e f i n i n g the e f f i c i e n c y t o be A = S^K  where A i s the absolute e f f i c i e n c y defined as the p r o b a b i l i t y o f a gamma ray emitted i s o t r o p i c a l l y from the source being absorbed by the c r y s t a l . The computer program DEWF which c a l c u l a t e s the absolute e f f i c i e n c y of c o l l i m a t e d gamma ray detectors, was used t o obtain the t h e o r e t i c a l absolute e f f i c i e n c y o f the detector a t the two source t o c r y s t a l distances o f i n t e r e s t . The c o r r e c t i o n was then a p p l i e d i n the f o l l o w i n g way.  F i r s t the absolute  e f f i c i e n c y was c a l c u l a t e d using the data from the experimental runs.  Then the  expected experimental value f o r the proper source t o c r y s t a l distance was pred i c t e d making use of the computer r e s u l t s r e f e r r e d t o above.  This was done  43.  as a d i r e c t r a t i o between the experimental and computed absolute e f f i c i e n c i e s at the two distances.  F i n a l l y , the i n t r i n s i c e f f i c i e n c y f o r the proper distance  was obtained by d i v i d i n g the absolute e f f i c i e n c y by the s o l i d angle subtended by the detector at the source.  The s o l i d angle i s defined as shown i n  Figure I I I - 2. In order t o check that a l a r g e e r r o r was not being introduced by t h i s method due t o the e f f i c i e n c y not varying smoothly w i t h d i s t a n c e , the t h e o r e t i c a l absolute e f f i c i e n c y f o r several source t o c r y s t a l distances was computed and p l o t t e d . The r e s u l t s are shown i n Figure 7 - S.  I t i s seen t h a t the absolute  e f f i c i e n c y follows an approximate inverse square behaviour as the distance between the source and c r y s t a l i s v a r i e d .  This i s the f a m i l i a r r e s u l t f o r u n c o l -  limated detectors and i t i s of i n t e r e s t t o note that the presence of the c o l l i mator does not cause a r a d i c a l departure from t h i s behaviour. Arrow "A" shows the source t o c r y s t a l distance used f o r the e f f i c i e n c y measurements; arrow "B" shows the proper source t o c r y s t a l d i s t a n c e , taken from Table I I I - 1 (R = 19.52  cm.).  I t was a n t i c i p a t e d t h a t the e f f i c i e n c y f o r c r y s t a l M might a l s o be required at some time i n the f u t u r e , and a l s o f o r both c r y s t a l s uncollimated at the f r o n t face.  These measurements were also taken.  For the purpose of g e t t i n g the e f f i c i e n c y w i t h the c r y s t a l s uncollimated, the r e l e v a n t geometry i s shown i n Figure V - 9, w i t h the symbols and t h e i r dimensions l i s t e d i n Table V - 3«  44.  16-1  14-  12H  ID-  CM o  z  w o  S'  LL LL  UJ HI h-  3 _J O  6-J  CO CO  <  4H  DISTANCE FROM SOURCE TO CRYSTAL FACE (cm) o  0  10  15  20  1  1  25  28  F i g . V-8 : Relation o f absolute e f f i c i e n c y t o distance.  F i g . V-9  : Uncollimated gamma detector geometry.  46  Table V - 3s Uncollimated gamma detector geometry Symbol  Distance  R  6.5 i n .  L  2.5 i n .  $  21° 63»  The s o l i d angle was taken from the source t o the middle of the det e c t o r , and was c a l c u l a t e d t o be 0.571 steradians.  5-4*  Results A f t e r c a r e f u l l y checking the alignment o f the target-detector system,  an e x c i t a t i o n f u n c t i o n was again run on the t a r g e t t o l o c a t e the 340 kev resonance, and then a l l the e f f i c i e n c y runs were made at an energy 2 kev higher. The i n i t i a l y i e l d was approximately 4000 gamma counts per minute w i t h from oneh a l f t o one microampere current on the t a r g e t .  The target was s h i f t e d whenever  the number o f gamma counts f e l l t o 2000 counts per minute.  I t was necessary t o  run a t the low beam current i n order to maintain the dead time o f the k i c k s o r t ers  below 2%,  The time o f the runs was determined by the time required t o get  approximately 6000 alpha counts, and was t y p i c a l l y around three hours. The number o f alpha counts was summed from the minimum i n the spectrum t o the upper edge o f the alpha counts (approximately channel 250), and was then corrected f o r dead time l o s s e s i n the k i c k s o r t e r .  No c o r r e c t i o n was neces-  sary f o r the <*x and <*j counts since the energy o f these alphas a f t e r passing through the n i c k e l window was considerably l e s s than the lowest energy p a r t i c l e s t h a t were counted.  The gamma counts were analyzed by the TREAT com-  puter program, which g a i n - s h i f t e d a l l the r e s u l t s t o the same s e t t i n g s as were used i n the absolute cross-section a n a l y s i s . counts from 3«492 Mev t o 6.48 Mev —  This program then summed the  the same l i m i t s as used f o r the  47  c r o s s - s e c t i o n measurements — dependent  room background.  and subtracted the appropriate amount o f time These r e s u l t s were f i n a l l y corrected f o r dead-time  l o s s e s i n the k i c k s o r t e r and f o r absorption l o s s e s i n the aluminum window and t a r g e t backing.  A small c o r r e c t i o n , based on the shape o f the spectrum, was  a l s o a p p l i e d t o a l l o w f o r the °<z and <j gamma rays which were i n the energy region o f i n t e r e s t .  No beam dependent background was subtracted since a run  on a clean t a r g e t backing showed that the c o r r e c t i o n would be l e s s than 0.3 percent. The absolute e f f i c i e n c i e s were f i n a l l y c a l c u l a t e d as A = N K  and  w ?  the i n t r i n s i c e f f i c i e n c i e s as £ = A/W  . The i n t r i n s i c e f f i c i e n c y f o r the  proper c o l l i m a t e d distance was determined i n the way discussed p r e v i o u s l y . The i n t r i n s i c e f f i c i e n c y f o r the uncollimated c r y s t a l s was c a l c u l a t e d using the s o l i d angle shown i n Figure V - 9« The r e s u l t s o f the four measurements are l i s t e d i n Table V - 4* The c a l c u l a t e d e r r o r i s l e s s than 3 percent on a l l the measurements.  Table V - 4:  Crystal efficiencies  Collimated c r y s t a l s : Intrinsic Efficiency  Absolute E f f i c i e n c y Detector  Experiment  Proper Distance  Experiment  Proper Distance  D  .00838  .00743  .704  .679  M  .00864  .00769  .730  .702  Uncollimated c r y s t a l s : Intrinsic Efficiency  Detector  Absolute E f f i c i e n c y  D  .0218  .482  M  .0218  .482  CHAPTER VI GAS TARGET AND ABSOLUTE CROSS SECTION 6.1  Introduction The main sources of u n c e r t a i n t y associated w i t h the measurement of an  absolute cross s e c t i o n are the l a c k of p r e c i s i o n i n the knowledge of the number of n u c l e i i n the t a r g e t and the number of p a r t i c l e s i n c i d e n t on the t a r g e t .  The  l a t t e r i s determined by i n t e g r a t i n g the charge c o l l e c t e d by the t a r g e t , and the former requires a knowledge of the t a r g e t thickness. I t was o r i g i n a l l y hoped t h a t the deuterated polyethylene  target  thickness could be found accurately by measuring the energy l o s s of alpha part i c l e s passing through i t .  These alphas were to o r i g i n a t e from a source depos-  i t e d onto the t a r g e t backing before the polyethylene was poured on.  However,  d r i f t s i n the e l e c t r o n i c s made i t impossible t o measure accurately enough the l o c a t i o n of the alpha peak (and hence the alpha energy) before and a f t e r p u t t i n g on the polyethylene l a y e r , so t h i s method was  discarded..  A second p o s s i b i l i t y f o r determining the t a r g e t thickness was  to  rt  measure the neutron y i e l d from the D(d,n) He r e a c t i o n .  However, t h i s method was  a l s o discarded since i t required knowing accurately the e f f i c i e n c y of the neutron counter, and i t was expected that a l a r g e c o r r e c t i o n would be required f o r the beam dependent background f o r t h i s e f f i c i e n c y measurement since the a c c e l e r a t o r had j u s t been used w i t h a deuterium beam f o r some time. F i n a l l y a d e c i s i o n was made t o use a gas t a r g e t , where the number of n u c l e i involved can be determined knowing the pressure of the gas and the length of the a c t i v e volume.  The f o l l o w i n g s e c t i o n describes the target used, and the  method of determining the required parameters. 48.  *  49  6.2  The Gas Target One of the problems encountered i n measuring the gas pressure i n v o l v e s  l o c a l heating e f f e c t s r e s u l t i n g from the passage o f the i n c i d e n t beam through the gas.  This heating causes the gas i n the a c t i v e volume t o expand s l i g h t l y ,  thus reducing the density i n the region of the beam.  To minimize t h e c o r r e c -  t i o n required f o r t h i s e f f e c t the brass backstop of the t a r g e t was made very l a r g e i n the hope t h a t the conduction would be great enough t o maintain a constant temperature throughout the c e l l .  The temperature of the backstop was  monitored w i t h a copper-constantin thermocouple which was i n s e r t e d i n t o a hole d r i l l e d i n t o the stop.  No appreciable d i f f e r e n c e could be detected between  the stop temperature and room temperature w i t h the beam on the t a r g e t . A f i r s t attempt t o measure the e f f e c t of l o c a l heating by passing beams through the gas; c e l l w i t h varying currents had a l s o f a i l e d because o f a slow carbon buildup on the f o i l while the runs were t a k i n g p l a c e .  This carbon  buildup produced an energy l o s s i n the i n c i d e n t beam w i t h an e r r o r l a r g e r than the e f f e c t being studied.  However, the e f f e c t has been measured p r e v i o u s l y i n  t h i s way (RO 6 l ) using deuterium gas but at a higher pressure.  A f t e r making the  appropriate allowances f o r the d i f f e r e n t pressure, i t was found t h a t , w i t h the beam current used f o r the cross s e c t i o n measurements, the gas i n the beam path was 0.8$ l e s s dense than t h a t i n the remainder o f t h e t a r g e t chamber, t h e pressure of which was measured w i t h a manometer. The entrance window t o the gas target was a 30 micro-inch n i c k e l f o i l obtained from the Chromium Corporation o f America.  This f o i l thickness was  chosen as a compromise among the f o l l o w i n g f a c t o r s : the strength required t o withstand the gas pressure, a minimum energy l o s s and s t r a g g l i n g of the beam i n passing through the f o i l , and a maximum allowable beam current.  The energy  l o s s was measured by noting t h e s h i f t of the 992 kev resonance of the 27 AI  28  ( , P  rr  S i r e a c t i o n w i t h the f o i l i n place, and then c o r r e c t i n g f o r the  50  stopping cross section difference between t h i s energy and 780 kev and 800 kev, the energies at which the absolute cross section were measured*  The f o i l t h i c k -  ness was found i n t h i s way to be 127 kev at 780 kev incident proton energy. The maximum allowable beam current for 780 kev incident protons i s approximately 0.8 microampere according to curves published i n the I960 Nuclear Data Tables (Part 3, P« 124); the runs were made at a current of 0.5 microamperes. The length of the gas c e l l was determined by f i r s t measuring with a t r a v e l l i n g microscope the distance between the f o i l holder and the backstop. Now the gas i n the c e l l causes the f o i l to depress s l i g h t l y , and t h i s depression was measured by noting the d i f f e r e n t focussing locations of the t r a v e l l i n g microscope when focussed on the edge of the holder compared to when i t was focussed on the point where the beam passed through the f o i l .  The length was  determined to be 1.019 - .002 cm. The average energy of the proton beam i n the gas c e l l can be determined by subtracting from the incident beam energy the energy l o s s as the beam passes through the f o i l , and one-half the energy l o s s of the beam as i t passes through the gas.  This l a t t e r quantity was determined by the computer program ENL0TA,  which subdivides the gas c e l l length i n t o several elements of length, and then computes the energy l o s s i n each small sub-length.  In t h i s way, the v a r i a t i o n  i n the stopping cross section of the gas with energy i s allowed f o r .  For 800 kev  and 780 kev incident proton energies, the average energy i n the gas c e l l was found to be 663 kev and 643 kev r e s p e c t i v e l y . The gas pressure was measured with a U-tube manometer f i l l e d with mercury.  Provision was made to evacuate both arms of the tube and then, by closing  a glass tap, one of these could be i s o l a t e d from the main system p r i o r to f i l l i n g the gas c e l l .  This enabled the pressure i n the c e l l to be read d i r e c t l y as the  difference i n the l e v e l of mercury i n the two arms.  After f i l l i n g the c e l l , a  ;  51  glass tap on the other arm was also closed t o prevent any mercury contamination i n the system. Other features o f the target include an a l l - b r a s s construction except f o r a l u c i t e window on one side through which the beam could be viewed h i t t i n g the backstop, and an aluminum window on the other side through which the gamma rays passed on t h e i r way t o the detector. The c o l l i m a t o r s were made o f platinum w i t h a view t o reducing the contaminant background r a d i a t i o n , e s p e c i a l l y that a r i s i n g from ^F(p,<*0"^0, since previous t e s t s had i n d i c a t e d t h a t platinum had the l e a s t contaminating material.  For t h i s same purpose, a piece o f platinum was attached t o the face  of the backstop where the beam h i t i t . A diagram o f the target w i t h the n i c k e l f o i l holder, c o l l i m a t o r s and e l e c t r o n suppression assembly and gas f i l l i n g device i s shown i n Figure VI - 1.  6.3  Current I n t e g r a t i o n The other problem associated w i t h measuring the cross section was an  accurate determination of the charge d e l i v e r e d t o the gas t a r g e t by the beam. The f i r s t point o f concern here i s the e j e c t i o n of secondary electrons from the backstop, which would r e s u l t i n an e f f e c t i v e increase i n the p o s i t i v e charge measured.  To overcome t h i s d i f f i c u l t y , a p o s i t i v e b i a s was put on the backstop  to prevent t h e electrons from escaping.  This introduces a second problem,  however, which r e s u l t s from the i o n i z a t i o n of the gas as the beam passes through it.  I f t h e backstop i s p o s i t i v e l y biased and the r e s t of the target assembly,  i n c l u d i n g t h e n i c k e l f o i l , i s unbiased, then the negative ions w i l l d r i f t t o the backstop and the p o s i t i v e ions t o the f o i l and chamber w a l l s . i n a decrease i n the amount o f p o s i t i v e charge measured.  Hence the f o i l ,  t a r g e t chamber and backstop must a l l be at the same p o t e n t i a l . ment, +90 v o l t s was used.  This w i l l r e s u l t  In t h i s e x p e r i i  52.  TO  PUMP  Fig. VI-1 : The gas target assembly.  53. The p o s i t i v e b i a s on the n i c k e l f o i l has the added b e n e f i t that copious numbers of e l e c t r o n s , which would otherwise be ejected from the f o i l , are prevented from escaping. A problem d i d a r i s e from the f a c t that the f o i l and t h e f o i l holder were t i e d t o the backstop.  I t was necessary that no pro-  tons h i t the edges or sides of the holder; otherwise charge i s c o l l e c t e d which has not passed through the gas.  To prevent t h i s from happening, a c o l l i m a t o r  system was designed t o l i m i t the diameter of the beam t o l e s s than 0.1 i n c h , whereas the width of the f o i l which was exposed t o the i n c i d e n t beam was 0.3 inch.  A check was made t o ensure t h a t the beam was not diverging by i n s e r t i n g  a quartz backstop i n t o the t a r g e t chamber.  An end-on view of the proton beam  was thus a v a i l a b l e . F i n a l l y , any secondary electrons which might be emitted from t h e edges of the c o l l i m a t o r s must be prevented from reaching the f o i l assembly. To t h i s end, a suppressor w i t h a -300 v o l t b i a s was placed i n the beam l i n e between the c o l l i m a t o r s and the f o i l holder. The current measured i n the target chamber was f e d t o an Eldorado E l e c t r o n i c s Current Integrator, Model CI - 110, the same as used during the r e l a t i v e cross s e c t i o n measurements.  Very c a r e f u l c a l i b r a t i o n of the current i n t e -  grator was o f course required since any error a r i s i n g here would be transmitted d i r e c t l y t o the c r o s s - s e c t i o n . The c a l i b r a t i o n was c a r r i e d out using a Weston Standard C e l l and a Gambrell p r e c i s i o n r e s i s t o r .  The accuracy of the standard c e l l was checked  using two d i f f e r e n t r e s i s t a n c e bridges (Electro S c i e n t i f i c Industries Model 250DE Impedance Bridge and Model 300 Potentiometric Voltmeter-Bridge).  The d i f f e r e n c e  between the measured value and the quoted value f o r both the c e l l and the r e s i s t o r was found t o be l e s s than the e r r o r of the measuring instruments.  The error  of t h e combination of standard c e l l and p r e c i s i o n r e s i s t o r was taken t o be l e s s than two parts i n a thousand.  54  The method of c a l i b r a t i n g the current integrator was to feed i n a current on the current range used during the cross-section runs, and then to compare the charge integrated f o r t h i s known current and known time to the charge which was expected. shown i n Table Table V I - 1 .  A summary of the r e s u l t s of t h i s c a l i b r a t i o n i s  VI-1. Current integrator c a l i b r a t i o n  Known Current  1.0185  -  .001 uamps  + Known Time Known Charge (Known Current x Known Time)  Charge Setting on the Current Integrator  1138.5  -  1159.6  -  3.5 sec.  +  3.5 ucoul  1200 ucoul  This table shows that the actual integrated charge i s 96.6 i 0.4 percent of the charge indicated by the current integrator and t h i s correction was applied to the f i n a l r e s u l t s .  6.4  Experimental Procedure The collimated Nal  ( T i ) detector (D c r y s t a l ) was placed at 90° to  the incident beam i n order t o obtain the maximum y i e l d of gamma rays from the reaction.  The cross hairs on the collimator, previously described i n the sec-  t i o n on the c r y s t a l e f f i c i e n c y , were used to ensure that the detector was aimi n g at the centre of the t a r g e t .  The c r y s t a l was set at the proper collimated  distance from the centre of the target by measuring the distance from the front face of the c r y s t a l t o a mark i n the centre of the outside face of the backstop. The data c o l l e c t i o n from the detector was accomplished using the same electronic arrangement used f o r the measurement of the c r y s t a l e f f i c i e n c i e s , except that the ND 160 was used i n place of the ND 120.  A scaler was again  employed so that the number of counts obtained i n a given time i n t e r v a l could ' 1  55  be p e r i o d i c a l l y monitored t o ensure that a l l the equipment was performing s a t isfactorily. F i n a l l y , the measurement of the cross s e c t i o n was broken down i n t o f i v e separate runs i n order t o reduce the r i s k of l o s i n g a l l the data i f somet h i n g were t o go wrong, such as the f o i l breaking or l a r g e d r i f t s occurring i n the e l e c t r o n i c s , and t o average out any small background v a r i a t i o n s .  Each run  took approximately 4 hours and was f u r t h e r s p l i t up i n t o two p a r t s , one w i t h deuterium i n the gas c e l l , and the other w i t h hydrogen.  In t h i s way the beam  dependent background could be accounted f o r by s u b t r a c t i n g the hydrogen run d i r e c t l y from the deuterium.  This method proved p r a c t i c a l since no l a r g e  buildup o f background occurred during any one p a r t i c u l a r run.  A c o r r e c t i o n was  a l s o applied f o r the time dependent background, but t h i s was very small since i t was necessary t o take i n t o account only the time d i f f e r e n c e between a hydrogen run and a deuterium run.  The deuterium was obtained from the L i q u i d Car-  bonic D i v i s i o n of General Dynamics, and had a quoted p u r i t y o f 99.7 percent. In order t o change the gas i n the c e l l , the c e l l was f i r s t evacuated, then flushed w i t h the new gas and evacuated again before the f i n a l f i l l i n g took place.  The runs were made w i t h approximately 150 mm Hg gas pressure i n the c e l l ,  measured w i t h the manometer p r e v i o u s l y described. The t o t a l i n t e g r a t e d charge was 2400 microcoulombs per run f o r four of the runs and 3600 microcoulombs f o r the other. A c o r r e c t i o n was then applied t o the charge c o l l e c t e d t o a l l o w f o r the e r r o r i n the current i n t e g r a t o r , which has been described p r e v i o u s l y .  6.5  Other Corrections Factors Reference t o equation (2.1 -5 ) and the ensuing discussion shows that  the s o l i d angle subtended by the detector and the angular d i s t r i b u t i o n f a c t o r  56  4* i <?i + — ffi5, 4;, V, p  ft  must also be determined i n order to compute the  no  cross s e c t i o n .  A small correction must also be applied to the detector e f f i c -  iency, since t h i s was measured with 6.14 Mev gamma rays compared to the 5«92 3 Mev gamma rays obtained from the reaction D(p, y ) He at a proton bombarding energy of 643 kev, which was the average proton energy i n the gas c e l l . The s o l i d angle was calculated from the data l i s t e d i n Table III for Figure III  - 2.  - 1.  and was found to be 0.1376 - .0006 steradians.  To determine the angular d i s t r i b u t i o n f a c t o r , use i s made of the data l i s t e d i n Tables II  - 1. and II  - 2.  The Legendre polynomials were c a l -  culated f o r centre of mass angles, and i t i s found that an angle of 90° i n the laboratory frame corresponds to 90.71 degrees i n the centre of mass frame. Thus the angular d i s t r i b u t i o n factor was calculated to be 1.4624. In order to determine the e f f i c i e n c y change of the detector, use was made of the computer programs LFIT and SHAPE.  These programs used i n conjunc-  t i o n with each other produce from known gamma ray shapes at various energies interpolated gamma ray shapes f o r intermediate energies. shape f o r the 5»92 Mev gamma rays from the D(p, *)  Thus the standard  He reaction was found. 3  Consider two gamma rays, the 5*92 Mev D(p,y) He radiation and the 19  16  6.14 Mev  F(p,<><y)  0 radiation f o r which the absolute e f f i c i e n c y has been de-  termined.  Now i f each standard gamma ray spectrum has the same number of counts  i n the t o t a l spectrum and i s p l o t t e d f o r the same energy gain and zero, and we assume that the two gamma rays have approximately the same energy so that the shapes of the two spectra can be considered to be the same, then the r a t i o between the number of counts i n a given energy region of the two spectra w i l l give the r e l a t i v e e f f i c i e n c y of the detector f o r the two gamma rays, provided that the upper l i m i t of the energy region considered i s above the f u l l photopeak, and the lower l i m i t i s approximately one-half the f u l l energy, or lower. It was found that over the chosen energy region from 3*492 Mev to  57  6.48  Mev,  there were  991«4  counts of the 5*92 Mev r a d i a t i o n and 1 0 0 0 counts  of the 6 , 1 4 Mev r a d i a t i o n . Hence the e f f i c i e n c y f o r the D detector which was found as described i n the l a s t chapter was m u l t i p l i e d by . 9 9 1 4 t o allow f o r the change i n energy of the gamma ray. Two other c o r r e c t i o n s , both of which r e s u l t e d i n a m o d i f i c a t i o n t o the number o f detected gamma rays, were required.  The f i r s t o f these arose  from dead time l o s s e s i n the kicksorter,.and r e s u l t e d i n a f a c t o r o f 1 . 0 0 3 i n crease i n the number o f gamma rays detected.  The second arose from absorption  losses through the aluminum window, and required a f a c t o r o f 1 . 0 0 6 increase. F i n a l l y , the pressure i n the gas c e l l was corrected f o r the density change o f mercury w i t h temperature, since the measurements were not made a t the standard temperature and pressure.  6.6  Results The spectra, which were obtained from the f i v e r u n s — e a c h c o n s i s t i n g  of one hydrogen and one deuterium p a r t — w e r e g a i n - s h i f t e d t o the same gain and zero by the computer program TREAT, and then were summed over the energy region  3«492  Mev t o  6.48  Mev.  The appropriate corrections which have j u s t been  described were then applied t o these r e s u l t s , and the absolute cross s e c t i o n was c a l c u l a t e d f o r each run.  The r e s u l t s o f these c a l c u l a t i o n s are l i s t e d i n  Table VI - 2 . The e r r o r quoted w i t h each r e s u l t i s the root mean square e r r o r of the q u a n t i t i e s which contribute t o the cross s e c t i o n .  58. Table VI - 2:  Absolute cross section measurement  Laboratory Proton Energy  Absolute Cross Section  663 kev  2.33 - .10 microbarns  663 kev  2.57 - .11  643 kev  2.35  643 kev  2.28 - .10  643 kev  2.42 - .11  ±  .10  The measurements made at 663 kev were converted to the equivalent 643 kev r e s u l t making use of an approximate expression for the cross section given i n the paper by Fowler et a l which has been discussed previously. This expression i s n = KE x where  —20 2 10 cm  (6.6 - 1)  K = 0.74 - 50% n - 0.72 - 15%  and It  E i s the laboratory energy i n Mev.  i s found that t h i s conversion gives the f i r s t run a r e s u l t of 2.28  microbarns and the second a r e s u l t of 2.51 microbarns. The r e s u l t of the second run seems inconsistent with the other four, and hence was discarded.  No reason for the discrepancy was r e a d i l y apparent.  The r e s u l t of averaging the other four runs gives the cross section as 2.33 - .07 microbarns, where the error i s the standard deviation of the four runs.  Thus the absolute cross section i s e f f e c t i v e l y determined for the entire  range of values over which the r e l a t i v e cross section was measured.  Figure  VI-2  shows these r e s u l t s , and the r e s u l t s of previous measurements made i n t h i s laboratory. The present work gives quite good agreement with the previous r e s u l t s ,  59.  60-i  5.0-  4.0-  I  3.0-  T + 1  T  2.0-  t  I.O-  I  T  0.3  0.6 LABORATORY  0.9 PROTON  1.2 ENERGY  1.5  (Mev)  F i g . VI-2 : The absolute cross section f o r the r e a c t i o n D(p,y) He. The c i r c l e s are the r e s u l t s of G r i f f i t h s e t . a l . (GR 6 l ) . The crosses are the present measurements.  1.8  60  although at higher energies the present r e s u l t s seem t o be s l i g h t l y lower. This i s p o s s i b l y due t o an incomplete subtraction of the f l u o r i n e contamination i n the e a r l i e r measurements.  BIBLIOGRAPHY » BA 69  G.M.Bailey,  to be published.  CH 50  C.Y.Chao, A . V . T o l l e s t r u p , W.A.Fowler and G.C.Lauritsen,  Phys.  Rev.,  22 (1950) 108 DE 49  S.Devons and M.G.N.Hine,  DE 60  G.Derrick,  DO 67 FO 49  T.W.Donnely, Ph.D. Thesis, University of B r i t i s h Columbia (1967). W.A.Fowler, C.C.Lauritsen and A . V . T o l l e s t r u p , Phys. Rev., 7j> (1949) 1767.  FR 50  J.M.Freeman,  GR 55  G.M.Griffiths and J.B.Warren,  GR 61  G . M . G r i f f i t h s , E.A.Larson, and L.P.Robertson, (1962) 402.  GR 63  G . M . G r i f f i t h s , M.Lai and C.D.Scarfe,  LA 57  E.A.S. Larson,  LE 64  J.L. Leigh,  M.Sc. Thesis, University of B r i t i s h Columbia (1964).  OL 68  M.A. O l i v o ,  Ph. D. Thesis, University of B r i t i s h Columbia (1968).  RO 53  M.E. Rose,  RO 61  L.P. Robertson, B.L.White and K.L. Erdman, 1405.  VE 50  M. Verde,  Proc. Roy. Soc. (London) 199A (1949) 56.  Nucl. Phys. 16 (i960) 405.  P h i l . Mag. 42 (1950) 1225. Proc. Phys. S o c , 68 (1955) 781. Can. J . Phys. 4J)  Can. J . Phys., 41 (1963) 724.  M.A. Thesis, University of B r i t i s h Columbia (1964).  Phys. Rev., 9_1 (1953) 610. Rev. S c i . I n s t . , 22 (I96l)  Helv. Phys., Acta 23, (1950) 453.  WI 52  D.H. Wilkinson,  P h i l . Mag., 42 (1952) 659.  WO 67  W.Wolfli, R. Bosch, J.Lang, R. Muller, and P. Marmier, Acta, 40 (1967) 946.  61  Helv. Phys.  APPENDIX COMPUTER PROGRAMS DEWF"  : This program c a l c u l a t e s the absolute detection e f f i c i e n c y o f s c i n t i l l a t i o n c r y s t a l s f o r gamma r a y s , and the weighting (Q) f a c t o r s that compensate f o r the f i n i t e s o l i d angle o f the  LFIT  counter,  : The input t o t h i s program i s a number o f standard gamma ray shapes o f various energies.  The f u l l peak o f each input spectrum appears i n the  same channel and has the same number o f counts as a l l the other spectra, and a l l spectra have the same gain.  The program then does a cubic f i t  of the counts versus energy r e l a t i o n f o r each channel o f the input spectra.  The output i s a matrix g i v i n g the four c o e f f i c i e n t s from the  cubic f i t f o r each channel. SHAPE  : The input t o t h i s program i s the output from LFIT.  The program then  determines the number o f counts i n each channel f o r a gamma ray o f a s p e c i f i e d energy.  Thus LFIT and SHAPE used i n conjunction i n t e r p o l a t e  the shape o f a s p e c i f i e d gamma ray from several given gamma r a y s . TREAT  ; This i s a general purpose program f o r the p r e l i m i n a r y treatment o f data p r i o r t o the d e t a i l e d a n a l y s i s done by NAILS.  The program can be used  t o smooth the data, g a i n - s h i f t i t , and sum the counts between two given energies.  Up t o eight spectra can be subtracted from or added t o the  spectrum being t r e a t e d . NAILS  : This program i s used t o determine by an i t e r a t i v e l e a s t squares procedure the r e l a t i v e amounts of various s p e c i f i e d components i n a given spectrum.  Included i n the output i s an estimate o f the accuracy of the  r e s u l t s based on the d i f f e r e n c e s o f the intermediate i t e r a t i o n s w i t h  63  the f i n a l r e s u l t s .  The input t o NAILS was u s u a l l y the output of  TREAT. POLY-D : This program c o r r e c t s f o r t h e d e t e r i o r a t i o n o f deuterated p o l y ethylene t a r g e t s by f i t t i n g the t a r g e t decay w i t h the sum o f two exponentials. CSFIT  : This program f i t s both o f the r e l a t i v e cross s e c t i o n r e s u l t s o f the two detectors w i t h a cubic l e a s t squares curve, and then m u l t i p l i e s one o f these curves by a constant f a c t o r t o give the best f i t w i t h the other.  ENLOTA  This program c a l c u l a t e s t h e energy l o s s o f a beam when passing through a gas t a r g e t .  Allowance i s made f o r the v a r i a t i o n o f the stopping  power of t h e gas w i t h energy.  

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