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The D (p,[gamma])He³ reaction at low energies Larson, Ernest Andrew Gustav 1957-12-31

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THE  D(p,3')H©  i  REACTION AT LOW ENERGIES by  Ernest Andrew Gustav  Larson  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS i n the Department of PHYSICS  accept t h i s thesis as conforming t o the standard required from candidates f o r the degree of MASTER OF ARTS  Members of the Department of Physios THE  UNIVERSITY  OF  October,  BRITISH 1957  COLUMBIA  ABSTRACT  A detailed study has been made of the D(p , V)He energies of 300 kev,  600 kev,  reaction at proton  and 1.0 l e v .  In order t o measure the absolute cross section f o r t h i s reaction the e f f i c i e n c y of a 2.5 inch by 3.5 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 measure-  19 ments on the 340 kev resonance of F  16 (p,c<,lQ0  .  The e f f i c i e n c y of the  counter f o r the 6.14 Mev gamma r a d i a t i o n from t h i s resonance has a measured value of 0.612 t 0.009. The angular d i s t r i b u t i o n of the gamma r a d i a t i o n from the D(p T)He 2 9  reaction has been found t o have the form 0.0795 ± 0.010, 600 kev and 1.0  0.032 ± 0.004  A ( s i n © +-b) where b equals  and Qp24± 0.003 a t proton energies of 300 kev,  Jfev respectively.  The absolute cross section of t h i s reaction has been measured a t proton energies of 300 kev and 1.0 Mev using the above calibrated s c i n t i l l a t i o n —30 counter. The cross section has been found t o be (0.8981:0.097) X 10 —30 square centimeters a t a proton energy of 300 kev and (3.24 t 0.35)X 10 square centimeters at a proton energy of 1.0 Mev.  In p r e s e n t i n g the  t h i s thesis i n p a r t i a l fulfilment of  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 t h a t it  freely available  agree that  the L i b r a r y  f o r r e f e r e n c e and study.  s h a l l make I further  p e r m i s s i o n f o r e x t e n s i v e copying o f 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 o f my Department o r by h i s r e p r e s e n t a t i v e .  I t i s understood  that  copying o r p u b l i c a t i o n o f 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  Department o f  P'U. y si c _s  The U n i v e r s i t y o f B r i t i s h Vancouver 8, Canada. Date  O /tXcK^W  a (5*5-7  Columbia,  permission.  ACKNOWLEDGEMENTS  The author wishes to thank Dr. G.M.  G r i f f i t h s f o r his generous  assistance with and attentive supervision of the work described i n t h i s thesis. I would l i k e to thank Mr. L.P. Robertson f o r his kind assistance during the experimental work.  Thanks are also due to Mr. P.J. R i l e y f o r  operation the Van de Graaff during the f i n a l part of the work and Mr. P h i l l i p s and Dr. B.L. White f o r many h e l p f u l discussions and  G.J.  suggestions.  F i n a l l y , I wish to thank the National Research Council and the Shell O i l Company of Canada f o r scholarships which have enabled me to carry out t h i s work.  TABLE  OF CONTENTS  Chapter I II  Title INTRODUCTION  3. 4. 5.  1  Q  1  6  3. 4.  Results  ••  •• ••  THE D(p,7T)He  3  3.  BIBLIOGRAPHY  Introduction Apparatus (a) The F (p,<**)0 Target Chamber (b) Fluorine Targets • • (c) Counters ( i ) Gamma Ray Counter ....................... ( i i ) The Alpha P a r t i c l e Counter ................ (d) Electronic Counting System Experiments Calculations Results •  Introduction Apparatus ..................... (a) Target Chamber (b) DgO Dispenser (c) S c i n t i l l a t i o n Counter Experiment  1. 2.  APPENDIX  1  3 4 4 5 6 6 7 8 9 11 13  DgO TARGET THICKNESS MEASUREMENTS. 1. 2.  17  .  GAMMA - RAY COUNTER EFFICIENCY MEASUREMENT 1. 2.  HI  Page  17 17 18 19 20 21  REACTION  Introduction ......................... 3 The Angular D i s t r i b u t i o n of the D(p,,2r)He Gamma Rays • (a) Apparatus • .. (b) Electronics • •• (c) Measurements ................................... (d) Results 3 ...... Absolute Cross Section Measurement of D(p,^)He ...... (a) Apparatus (b) Measurements ••••••••••••.••••••••••••••••••••» (c) Calculations •»•••..•.••..•••••••••••...•..»«••  24 24 25 26 29 35 36 36 41  LIST  Number  OF  ILLUSTRATIONS  Subject  Facing Page  Plates I  The D(p,?T)He  3  Apparatus  24  Figures 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.  19 Fl Target Pot Beam Tube • Photo M u l t i p l i e r Head Amplifier Alpha P a r t i c l e Counter ................................ Alpha Spectrum from F Block Diagram of Alpha Counting Apparatus Gamma - ray Spectra - 6.14 Mev. from F ., - 2.62 Mev. from RdTh l / r Plot f o r Sodium Iodide Crystal DgO Dispenser C a l i b r a t i o n Graph ....................... D 0 Ice Target thickness c a l i b r a t i o n ..... (a) Ice Target Positions (b) Gamma - ray Counter Geometry (c) Geometry f o r S o l i d Angle Corrections Gamma Spectra of D ( p , r ) H e , E = 300 kev Gamma Spectra of D(p,r)He , E l =. 1.0 Mev Angular D i s t r i b u t i o n of the D(p,V)He radiation 1 9  1 9  2  2  3  3  3  4 5 7 8 8 7 9 12 21 22 26 27 28 35  Tables I II III T? .7  E f f i c i e n c i e s of Nal Crystal Calculation of the D(p,tf)He Angular D i s t r i b u t i o n Angular D i s t r i b u t i o n Results Typical Cross Section Calculation E f f i c i e n c y of Small Nal Crystal  14 30 35 39 42  -  1  -  CHAPTER I  INTRODUCTION  A d e t a i l e d study of the three body systems He better understanding  3  and T should lead t o a  of the fundamental internuolear forces than i s possible  from a study of the simpler two body system, the deuteron, sinoe He and T 3  have approximately  2.5 Mev binding energy per p a r t i c l e i n f e r r i n g that the  p a r t i c l e s are oloser together than i n the deuteron where the binding energy i s only about 1 Mev per p a r t i c l e .  Also a comparison of the three body  nuclei with the deuteron should, i n p r i n c i p l e , allow one t o determine whether there are many body forces holding the nuoleons together i n a d d i t i o n t o two body forces which are the. only ones that oan play a r o l e i n the deuteron. At the moment such a comparison i s not possible because the problem i s complicated by r e l a t i v i s t i c effects of unknown amounts and due t o the existence of uncertain non-central components i n the binding f o r c e s .  A theoretical inter-  pretation of the r e s u l t s of the present experiments should give some underg standing of the symmetry c h a r a c t e r i s t i c s of the forces binding the He  nucleus  together. 3  The D(p  )He r e a c t i o n i s also of i n t e r e s t t o astrophysics since i t  constitutes an important  l i n k i n the conversion of hydrogen into helium i n the  lower temperature main sequence stars by the s o - c a l l e d proton-proton  chain.  In the lower temperature stars t h i s process predominates over the carbonnitrogen cycle sinoe the coulomb b a r r i e r s involved are smaller. Weak capture r a d i a t i o n from t h i s reaotion was f i r s t reported by Curran and Strothers (1939).  Fowler, Lauritsen and Tollestrup (1949) measured the  angular d i s t r i b u t i o n f ron a thiok i c e target a t a bombarding energy of 1.4 Mev and found that i t had the form A ( s i n ^ 0 + b v  ) where b was small.  They  o also measured the t h i c k target y i e l d a t 90  i n the energy range 0.5 Msv t o  1.7 Mev giving the t o t a l cross section && <T 3 0*74 B^* ^ X  10*^ em^  7  with a probable error of about 15% i n the exponent and of about 50f* Ixi the coefficient* A d e t a i l e d study of the angular d i s t r i b u t i o n at proton energies of 1.0 Mev and 1.75 Mev was made previously i n t h i s laboratory ( G r i f f i t h s and Warren 1955).  The angular d i s t r i b u t i o n was of the form A(s>n 0 + b  )  2  where b was small and increased as the proton energy decreased from 1.75 t o 1*0 Mev and then decreased as the proton energy went below 1*0 Mev.  This  decrease i n b as the proton energy decreased was puzzling t h e o r e t i c a l l y and i t was f e l t that more accurate i n v e s t i g a t i o n a t lower energies would be of interest.  ^  None of the previous workers were able t o give an accurate value f o r the absolute cross section of the reaction.  The present work has attempted  to measure the absolute cross section a t 0.3 Mev and 1.0 Mev and t o make a detailed study of the angular d i s t r i b u t i o n c o e f f i c i e n t b i n this energy -  range.  In order t o do t h i s an accurate measurement of the e f f i c i e n c y of the gamma ray counter and an accurate measurement of the D target thickness was necessary, Measurements were complicated by the D(d,n)He  reaction since when protons  bombard the D target some of the deuterons i n the target were e l a s t i c a l l y scattered and c o l l i d e d with other deuterons producing neutrons by the 3 D(d,n)He  reaction.  The neutrons from t h i s secondary reaction affeot the  gamma detector and so i t was necessary t o investigate t h i s e f f e c t and t o correct f o r i t .  - 3 -  CHAPTER I I  1.  GAMMA COUNTER EFFICIENCY MEASUREMENT  INTRODUCTION  In order t o have a s c i n t i l l a t i o n oounter of known e f f i c i e n c y f o r 3 absolute oross seotion measurements of the D(p  }  Y )He  reaction the e f f i c i e n c y  of a 2*5 inches by 3.5 inches sodium iodide c r y s t a l f o r 6.14 Mev gamma r a d i a t i o n has been  measured by simultaneous counting of the alpha and gamma rays from  the F ( p , o c , r ) 0 19  1 6  reaotion.  The alpha p a r t i c l e s which are i s o t r o p i e a l l y emitted are counted i n an accurately known geometry*  Therefore one oan calculate the t o t a l number of  alphas emitted i n the reaotion. For each alpha emitted there i s a 6.14 Mev gamma ray and therefore one has a gamma source of known i n t e n s i t y which oan be used t o determine the 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 c r y s t a l as suggested by Van A l l e n and Smith (1941). The resonant capture of protons by F  1  9  forms N e  i n a highly excited  2 0  16 state. (  This state decays by alpha emission forming 0  o c ) or i n one of the excited states a t 6.06 Mev 0  6.91 Mev ( o c ) and 7.12 Mev ( o c ) 2  g  #  i n the ground state ( cc  r  ) , 6.14 Mev ( oC^)  t  (Ajzenberg and Lauritsen, 1955). The  6.14, 6.91* and 7*12 Mev states decay by ground state gamma ray emission. Freeman (1950) has measured the i n t e n s i t y r a t i o s of the short range alphas, ( cx ^ , (K g  }  CKg) f o r proton energies between 300 kev and 950 kev  obtaining a value of 0.024 f o r the r a t i o  ^  2  * ^  3  •  Chao e t al(l950)  found that a t the 340 kev resonance the ground state group group t o the pair emitting state  OC  0  and the  ^ T T , were not experimentally observable.  They also noted that the t o t a l number of alpha p a r t i c l e s was olosely equal t o the t o t a l number of gamma rays a t the resonances measured.  The experimental  Fig.I , F  1 9  TARGET  POT  results of Devon and Hlne (1949) and the spin assignments of Chao (1950) show that the alpha p a r t i c l e s and gamma rays are i s o t r o p i c a l l y distributed a t the 340 kev resonance* H. Dosso (1957) i n t h i s laboratory has measured the r e l a t i v e  intensities  of the 6.14 Mev gamma ray and the sum of the y i e l d s of the 6*91 and 7.12 Mev gamma rays with a four c r y s t a l spectrometer.  He gives 2,3% *  r a t i o of 6.91 Mev plus 7.12 Mev t o the 6.14 Mev gamma rays.  0,2% as the  This r e s u l t i s  i n very good agreement with the value of 2.4$ as found by Freeman from r e l a t i v e alpha p a r t i c l e i n t e n s i t y measurements* Van A l l e n and Smith (1941) used a v a r i a b l e pressure absorption c e l l ionization chamber as an alpha counter and a thin-ended geiger counter f o r the gamma rays.  In the present work the alpha p a r t i c l e s were counted by a  gas proportional counter sensitive only t o the 6.14 Mev state alpha p a r t i c l e s . From the known s o l i d angle the t o t a l number of alpha emitted by the source could be calculated and t h i s corresponds t o the t o t a l number of 6.14 Mev gamma rays emitted by the source.  The t o t a l number of gamma rays was assumed  to be equal to the t o t a l number of 6.14 Mev gamma rays plus 2JSt% t o allow f o r the 6.91 and 7.12 Mev gamma rays f o r which the alpha p a r t i c l e s had i n s u f f i c i e n t energy t o enter the proportional counter.  The d e t a i l s of the  counters are described below.  2.  (a)  APPARATUS  The F  19  16 (p,<*-,T)0  Target Chamber  The target chamber used i n t h i s experiment i s shown i n F i g . 1. The alpha p a r t i c l e oounter was attached t o the middle of the three brass tubes of the chamber. prevent small angle alpha  This tube had a brass stop located so as t o  scattering.  V a n d e G r a a f fj  Beam  F i g. 2  STOP  Beam  Tube  The target chamber was aligned using the viewing tube with the glass window In the following manner. The target was rotated so that the polished back was a t an angle of 45° t o the beam tube.  A l i g h t shining into the beam  tube could be seen through the beam stops r e f l e o t e d on the target backing. The target chamber was then adjusted by moveable bellows u n t i l i t was conc e n t r i c with a stop i n the main Van de Graaff beam tube.  Any f u r t h e r a l i g n -  ment was done so as t o maximize the current on the target and t o minimize that soattered i n the beam tube. The target plate was bolted onto a copper frame which was e l e o t r i o a l l y insulated by l u c i t e spacers from the outer chamber. f o r replacement of targets.  The frame could be rotated  The experiments were done with the target a t 45°  to the beam so that the alpha p a r t i c l e s came through a minimum thickness of calcium f l u o r i d e .  The gamma ray oounter "looked" at the back of the t a r g e t .  The absorption of the gamma rays by the 0.029 inch t h i c k aluminium window was about 0,5% and by the 0.015 inch thiok copper target backing was about 0,9%. The gamma ray y i e l d was corrected f o r t h i s  absorption.  A l i q u i d nitrogen vapour trap was used i n f r o n t of the target chamber to prevent carbon from the o i l d i f f u s i o n pumps of the main vacuum system being l a i d down on the target.  See F i g . 2. Molybdenum and gold stops were  used i n the beam tube as shown as those materials produce very l i t t l e background. A magnetically controlled quartz beam stop was used t o cut the beam from the target except when runs were being made. (b)  Fluorine Targets The targets were prepared from powdered calcium f l u o r i d e evaporated i n  a b e l l j a r under vacuum on t o t h i n copper p l a t e s .  The calcium f l u o r i d e was  weighed before evaporation and the distances between the boat and the copper sheets measured so that targets could be reproduced. t i c u l a r evaporation 0.031  For example, i n one par-  gm of oalcium f l u o r i d e produced on a sheet of copper  25 cm above the boat a target of three kev thickness f o r 340 kev protons.  The  target thickness was approximately inversely proportional to the square of the distance from the boat. The targets were inspected v i s u a l l y f o r uniformity and any non-.uniform ones were discarded.  The shape of the e x c i t a t i o n ourve was also noted during  the experiments and any nonuniform!ty of the targets was shown by the asymmetry of the ourve.  Some targets, e s p e c i a l l y those used f o r the high beam  current t r i a l s , showed b l i s t e r i n g from the heating effeot of the beam. Targets were changed frequently during the experiment t o prevent t h e i r deterioration.  (o) Counters ( i ) Gamma Ray Counter The s c i n t i l l a t i o n c r y s t a l which was c a l i b r a t e d i s a Harshaw Thallium activated sodium iodide s r y 3 t a l .  I t s dimensions, as supplied by Harshaw, are  2.500 - 0.005 inches diameter by 3.500 - 0.005 inohes long.  The c r y s t a l was  mounted by Harshaw i n an aluminum can with magnesium oxide r e f l e c t o r . The photomultiplier tube was a Dumont No. 6363 with a 2-5/8 photooathode surface.  inoh diameter  The o r y s t a l was held on to the photomultiplier tube by  a vulcanized rubber band.  Dow Corning 200,000 oentistoke S i l i c o n e o i l was  used to ensure good o p t i c a l coupling between the c r y s t a l and the photomultiplier tube. The c r y s t a l and photomultiplier together with the preamplifier were a l l mounted inside a 3-3/8  inch brass tube approximately f i f t e e n inches long.  The  +300V  Ti  330KS  J_  470  K  , 600  Ml'  3 KV IOOK <  470 3  ,  V  JEsf Si MEGQTN'  I 4 7 O X 3 KV -1 4 7 0  I  I  J-L—l  _J_3KV  Anode' O O p f  10. i »0p4: T pf  M-*  6J6  } V470<  K  OOI  33 D yhodes  IN34 »|  5 K  025 — I I — 3  330K  HI OUT  -11—£) LO •5 K  4 7 0 K <, P h o t o c o t h o d e Fig.3  PHOTOM ULTIPLIER  =3.  PREAMP  ^COUNTER  1^9  HEAD  AMPLIFIER  out  ECKO AMPLIFIER! 10 4 9 B  pos. out  Fig. BLOCK  ATOMIC 1NSTR. SINGLE neg. CHANNEL K.S. NO. 5IO  6 DIAGRAM  PCCOUNTING  OF APPARATUS  p o s . o ut OYNATRON SCALER MODEL lOO|  BERKLEY SCALER  counter i s shown i n Plate 1. The single c y c l i n d i c a l u n i t made preoise l e v e l l i n g and positioning of the counter as described l a t e r r e l a t i v e l y easy.  A mu metal  s h i e l d was put around the photomultiplier tube t o s h i e l d i t from the f i e l d of the Van de Graaff's main magnet. The preamplifier, mounted inside the brass tube, was a 6J6 cathode follower.  The c i r c u i t diagram i s given i n P i g . 3.  This s c i n t i l l a t i o n counter has now operated w e l l f o r a year with no noticeable change i n i t s energy r e s o l u t i o n .  A r e s o l u t i o n of about seven per  cent f o r the photo-peak of the 2.62 Mev RdTh gamma ray has been obtained.  (ii)  The Alpha P a r t i c l e Counter The alpha counter was attached t o the target chamber as shown i n F i g . 1.  The proportional counter i s a stainless s t e e l tube 1.5 inches i n diameter and f i v e inches long.  I t i s f i l l e d with eleven cm of argon and one cm of a l c o h o l .  The counter size and gas pressure was chosen so that the alpha p a r t i c l e s associated with the 6.14 Mev gamma rays of the reaotion would stop i n the gas of the counter. The counter has a 6.1 mm a i r equivalent mica window cemented as shown i n F i g . 4.  This window thickness was chosen so as t o stop a l l scattered  protons from the target  and as a r e s u l t i t also stops the 6.91 and 7.12 Mev  state alpha partloles from entering the counter.  The 6.14 Mev state alpha  p a r t i c l e s with an i n i t i a l energy of 1.85 Mev pass through the window with an energy of about 0.7 Mev. The counter body i s o f f s e t from the center of the entrance aperture so that alpha p a r t i c l e s would not h i t the centre wire.  The centre wire i s  0.005 inches i n diameter made of a copper-nickel a l l o y and was diamond drawn t o ensure uniformity along i t s entire length.  For the precise  PROPORTIONAL  0-005CU-NI  COUNTER  WIRE BRASS  WO-18 •+ MICA"  '  6  3-5 mmi^  1 7  m  m  3  CEMENTED  02 mm  \ ^ 5 \  SCALE WINDOW Fig. 4  DETAIL  Alp no P o r t i l e C o u n t e r  X 5  CAP  - 8~  c a l i b r a t i o n of the Nal c r y s t a l i t was e s s e n t i a l that the s o l i d angle of the alpha counter be w e l l defined*  The entrance window i s shown i n F i g . 4. The  entranoe aperture dimensions and the counter t o target distances shown i n F i g . 1 were a l l accurately measured. A " f l a t " vacuum valve was between the counter and the target chamber arm.  This valve was opened only when the target tube had been evacuated.  t h i s way the mica window was protected from atmospheric  In  pressure when the  counter was not i n operation. The proportional counter centre wire was operated a t a p o t e n t i a l of 800 v o l t s which gave a gas m u l t i p l i c a t i o n f a c t o r of ten.  The guard rings  which define the sensitive volume of the counter were a t the same voltage as the centre wire. A t y p i c a l alpha p a r t i c l e spectrum i s shown i n F i g . 5. A r e s o l u t i o n of 12.5% was obtained f o r the alpha p a r t i c l e group associated with the 6.14 Mev gamma ray of the f l u o r i n e r e a c t i o n .  (d) Electronic Counting System A block diagram of the alpha p a r t i c l e counting system i s shown i n F i g . 6. Negative pulses from the alpha - counter were f e d v i a a 6AK5 cathode follower into an E.K. Cole Model 1049 B amplifier. were put into an Atomic Instruments Model 510.  Positive pulses from t h i s unit  Single Channel Pulse Height Analyzer  The single ohannel "kicksorter" window was set t o give out only  those pulses i n the 1.85 Mev alpha p a r t i c l e peak corresponding t o the 6.14 Mev gamma ray as shown i n F i g . 5. The positive output pulses from the window were f e d into a deoade scaler.  The negative output from the base l i n e discriminator was fed into a  Dynatron Model 100 s c a l e r .  In t h i s way a record was kept of a l l alpha pulses  5000H  F(P,a,y)0 E  , D  FR0M  p = 340  6 1 4 MeV  RAY  5,6 3  MeV  Kev  R d T h ~ 2-62MGV  .J IJ  y  CALIBRATION  4000-1  z.  :z i T  6 14  3000H  c  MeV  Ll 0  I- 2 0 0 0 - J D O  IOOO-4  1  30 2-410  3 235  4065  49IO  5 750  CHANNEL NO.  POPPER VOLTS  above the lower edge of the window. The s c i n t i l l a t i o n counter high voltage was supplied by an Atomic Instruments Superstable Power Supply set a t 1080 v o l t s .  The negative pulses  from the cathode follower were f e d into a Northern E l e c t r i c Model No. 1444 amplifier. The discriminator output of t h i s amplifier was put into a Dynatron Scaler.  The bias voltage was set t o be just below the half energy point of  the f l u o r i n e gamma ray as shown i n P i g . 7.  The negative output pulses from  the amplifier were f e d v i a a biased amplifier into a t h i r t y channel Marconi Pulse Amplitude Analyser fkicksorter. ) 11  The biased amplifier was set so that the 6.14 Mev gamma ray was near the top of the kicksorter while the 2.62 gamma ray of RdTh was i n the bottom channels.  Thus a d i r e c t energy c a l i b r a t i o n was available from which the h a l f  energy point of the 6.14 Mev gamma ray was determined.  A t y p i c a l speotrvun  i s shown i n F i g . 7. Gain s h i f t s or n o n l i n e a r i t i e s i n the e l e c t r o n i c system was checked using a mercury relay pulse generator described by Robertson (1957).  Test pulses  were put d i r e c t l y on the grids of the counter's cathode follower.  The ohannel  edges of the kicksorter were set from these pulses through the s c i n t i l l a t o r counter preamplifier.  In t h i s way any non-linearity i n the amplifier-kick-  sorter system was eliminated. The single channel kicksorter l i m i t s f o r the alpha peak were set i n the same manner by t e s t pulses f e d into the alpha counter head a m p l i f i e r .  3.  EXPERIMENTS The University of B r i t i s h Columbia's Tan de Graaff Generator provided  10 -  a w e l l - s t a b i l i z e d beam of up to ten microamperes of protons on the f l u o r i n e target. An excitation curve was f i r s t done over the 340 kev resonance of the 19 P  . The p o s i t i o n of the resonance on the generating voltmeter scale was  obtained.  The shape of the e x c i t a t i o n curve also gave a check on the  uniformity of the f l u o r i n e t a r g e t . If the target was s a t i s f a c t o r y the s c i n t i l l a t i o n c r y s t a l was l e v e l l e d , set at the same height as the beam spot and set perpendicular t o the t a r g e t . A t r i a l at any one position was broken into separate runs.  The spectra was  recorded each time so that a check was kept on the s t a b i l i t y of the equipment.  RdTh c a l i b r a t i o n runs were made a t each p o s i t i o n .  Time and beam  dependent backgrounds were taken so that corrections could be applied i n the c a l c u l a t i o n s . The time taken f o r runs at any one position was set by the necessity of obtaining one percent accuracy i n the counting s t a t i s t i c s .  This required  about ten thousand counts i n the alpha and gamma spectra. At the two closest distances the gamma ray counting rate was extremely f a s t unless a proton current of less than two micro-amperes was used. I t was found that the gain of the Dumont photomultiplier used on the gamma counter tended t o s h i f t with a count rate of about 1500 counts per second or above.  This s h i f t was observed with the accurate t e s t pulse generator  feeding pulses d i r e c t l y into the counter head a m p l i f i e r .  After counting  at a high rate the p o s i t i o n of the spectrum changed while the voltage l e v e l s on the kicksorter and the amplifier gains remained constant, thus confirming that the photomultiplier gain had s h i f t e d .  The gain increased with high  counting rate and amounted t o a 0.3$ change when the high counting rate was  - 11 -  maintained f o r about t h i r t y minutes.  This gain s h i f t had a slow decay time  returning gradually t o i t s o r i g i n a l value a f t e r a few hours.  4.  CALCULATIONS The proportional counter reoords only the 6.14 Mev state alpha p a r t i c l e s .  The gamma spectrum, however, contained the 6.14, 6.91, and 7.12 Mev gamma ray y i e l d s .  The sum of the 6.91 and 7.21 Mev y i e l d i s 2.3$ (Dosso 1957) of  the t o t a l y i e l d a t 340 kev.  The speotra were corrected so that only the gamma  counts from the 6.14 Mev state were considered i n the c a l c u l a t i o n s . The change i n cross section of sodium iodide f o r gamma rays of 7.12 and 6.14 Mev i s approximately 0.004$ and was therefore neglected i n the calculations. 19 The RdTh and the F  spectra were plotted as i n F i g . 7. Knowing the  p o s i t i o n and energy of these peaks the half energy point of the 6.14 Mev gamma ray was calculated. The kicksorter channel readings were summed from the h a l f energy point and corrected f o r the 2.3$ of the 6.91 and 7.12 Mev r a d i a t i o n .  The back-  ground was normalized t o the duration of the run since the background cont r i b u t e d by the beam alone i n the 6 Mev region was almost zero.  See F i g . 7.  The number of 6.14 Mev gamma counts were corrected f o r the 0.3$ absorption i n the aluminium window and the 0.9$ absorption i n the copper target backing. The alpha counter background was about .3$ of the number of alpha counts obtained i n the same time with about two microamperes on the target. The square root of the r a t i o of the alpha counts t o the gamma counts was calculated f o r each of eight positions of the gamma counter and the graph  O 6  H Fig.  05J  O- 4  8  ^ P L O T  FOR  2-5 X 3 - 5 '  Hal  CRYSTAL  -  IS 1 0-3H  O  H  Effective Center  30  DISTANCE  50 70 IN c m T A R G E T  SO TO C R Y S T A L .  110 FRONT  FACE  130  150  - 12 -  of F i g . 8 p l o t t e d . This l i n e , extrapolated to zero, gives the e f f e c t i v e center of the c r y s t a l a t 4.22 ~ 0.23 cm from the f r o n t face of the c r y s t a l .  S o l i d Angle Calculations: (a)  Alpha p a r t i c l e counter: Referring t o F i g . 1, the dimensions are as follows: -  A  4,8130  s  ±  0.0010 inches  B =  0.1766  t  0.0013  C =  1.4165 "t  0.0009  E =  0.087  -  0.003  t S  0.0152  i  0.002  Total distance from target to center of window defining aperture R r =  A + C + E + B+ t 6.1247 *  0.0082 inches  The alpha counter window was measured across many diagonals by two t r a v e l l i n g microscopes.  Since a l l the readings were approximately the same  the mean diameter was taken as 3.020 — 0.002 mm. The s o l i d angle of the alpha counter i s thus: -  3.020 OJ - ^1 \ ~ • ^VS X 5.1247 X 25.400/ ^oc " 2.956  X  10 "  4  2  ster-radians  -13  (b)  -  Gramma Ray Counter: Diameter of c r y s t a l 2.500 ± 0.005 inches Area  *  AjT  T  (*•£»  31.67 em  x  2.54 )  2  2  Effective S o l i d Angle of counter (J  r  S  31.67 (D + 4.22)  2  Where D i s the distanoe from the target spot t o the c r y s t a l faoe. Efficiency; The e f f i c i e n c y of the c r y s t a l was calculated f o r eaoh distance from the target.  Crystal E f f i c i e n c y =  (Ho. ^-counts above EjJ ( s o l i d angle of oc-counter) (No. of oc-counts)  ( s o l i d angle of T-counter)  as.  5" Results: The r e s u l t s , together with t h e i r estimated errors are given i n the following t a b l e .  - 14 Table D+4.22 £ 0.23 cm. 154.52  I EFFICIENCY  ± 0.28 cm  ERROR  0.6179  ±1.35$  146.82  0.28  0.6146  1.35  120.47  0.30  0.6120  1.35  79.22  0.30  0.6067  1.46  51.47  0.30  0.6105  1.64  33.95  0.28  0.6124  2.04  20.32  0.28  0.6466  2.96  11.72  0.25  0.6433  5.35  Efficiencies  of NaT  Crystal  The error i s estimated from the oounting s t a t i s t i c s  the percentage uncertainty i n the measurement of the distances from the alpha counter aperture t o the target and the uncertainty i n the di3tanoe of gamma counter e f f e c t i v e center t o the target ( £~  iL!jr  percentage uncertainty i n the area of the alpha counter window.  ^ and Thus the  estimated error i n the e f f i c i e n c y i s :  The mean of the f i r s t f i v e values i s 0.612 ± 0.009. The larger estimated error i n the l a s t three values i s due mainly t o the uncertainty i n the p o s i t i o n of the e f f e c t i v e center of the c r y s t a l . The l a s t value i n the table has an uncertainty of three per cent i n the alpha counting s t a t i s t i c s since about one thousand alpha counts were taken  - 15 -  In t h i s run while about ten thousand counts were taken i n the rest of the trials.  The t o t a l 6.14 Mev gamma counts ranged from about t h i r t y thousand  to over two m i l l i o n .  As stated previously the gamma counting rate a t the  short target t o counter distances was extremely f a s t .  Therefore a low  beam current was used which made the alpha p a r t i c l e - y i e l d very small. The one thousand alpha counts of the l a s t t r i a l took several hours of machine operating time.  In conclusion the absolute 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  counter f o r 6.14 Mev gamma rays i s 0.612 £ 0.009. H. Dosso (1957) and P. Singh i n t h i s laboratory have measured the 60 absolute e f f i c i e n c y of t h i s counter f o r the Co 1.17 Mev.  gamma rays of 1.33 and  P. Singh has c a r r i e d out t h e o r e t i c a l calculations the results 60  of which agree with the Co  measurements w i t h i n the accuracy of the  source strength c a l i b r a t i o n done by the National Research Council. * Singh has also calculated the e f f i c i e n c y f o r 6.14 Mev gamma rays which agrees t o w i t h i n f i v e per cent with the r e s u l t s of the present work. Due t o the good agreement between the theory and the experimental observations a t one and s i x Mev i t would appear that the t h e o r e t i c a l estimate of the e f f i c i e n c y between one and eight Mev should be accurate within f i v e percent, p a r t i c u l a r l y i f the t h e o r e t i c a l calculations are adjusted t o f i t the experimental value a t 6.14 Mev which i s accurate t o 1.5$.  In determining the absolute cross section f o r the D(p,y) He  reaction  1 This source was calibrated by National Research Council, Report No. APXNR - 325. The strength was given as 0.178 i 0.007 milliroentgens per hour a t 1 meter ( 0.134 ± 0.005 mc.) s c i n t i l l a t i o n counter,comparison with a C o source giving 1.39 t- 0.05 milliroentgens per hour a t one meter. The l a t t e r source was measured by i o n i z a t i o n chamber comparsion with the Canadian primary radium standard (N.R.C. Report No. C-121). 6 0  - 16 the e f f i c i e n c y i s required f o r gamma rays i n the range 5.7 Mev to 6.2 The e f f i c i e n c y over t h i s energy range has been extrapolated from the experimental value at 6.14 Mev on the basis of the theory.  Mev.  CHAPTER I I I  1.  D 0 ICE TARGET THICKNESS MEASUREMENTS 9  INTRODUCTION The absolute cross section measurements of D(p  s  Y) He  reaction to  be described i n Chapter IV required that the thiokness of the heavy ioe target be measured. This thickness was measured by noting the s h i f t of the 340 kev proton resonance of f l u o r i n e caused by the protons t r a v e l l i n g through the i c e layer.  The number of DO  atoms per sq. cm was then calculated using the  measurements of the stopping power of DgQ i c e f o r protons.  Wenzel and  Whaling (1952) measured, with an accuracy of four per cent, the stopping cross section of D O  i c e f o r protons between 18 kev and 541 kev.  Their  results agree within experimental errors with the t h e o r e t i o a l calculations of Hirschfelder and Magee (1948) f o r energies greater than 300 kev. Prom the experiments described below a c a l i b r a t i o n curve f o r the D^O dispenser has been obtained f o r target thicknesses from 30 kev t o 110 kev f o r 340 kev incident protons.  2.  APPARATUS (a)  Target Chamber The target chamber, shown i n Plate 1, was of a type used  before i n t h i s laboratory ( G r i f f i t h s and Warren 1955). backing was a copper plate  The ioe target  i/B inch by 1 inch and l / l 6 of an inch thiok.  The copper plate was soldered t o a brass l i q u i d nitrogen trap which was  - 18 -  e l e c t r i c a l l y insulated from the outer container by a l u c i t e r i n g .  The target  was operated at 4-135 v o l t s to suppress secondary eleotrons and thereby prevent erroneous beam current readings. The adjustable bellows used i n the e f f i c i e n c y measurements was also used on the f r o n t of t h i s chamber.  A l u c i t e r i n g e l e c t r i o a l l y insulated the  beam tube from the bellows.  Thus the amount of beam current s t r i k i n g the  beam tube could be measured.  This was of great assistance i n the rather  c r i t i o a l alignment necessary with t h i s chamber.  Molybdenum stops with 6 mm  and 8 mm aperture were put i n the beam tube t o reduce scattering of the incident beam onto the target.  A degree c i r c l e was attached t o the bottom  of the outer chamber so that horizontal angles could be read during the angular d i s t r i b u t i o n measurements. A l i q u i d nitrogen vapour trap was used between the target chamber and the main vacuum system of the Van de Graaff•  I t had a copper stop with a  one inch hole through which the beam passed.  This trap was always removed  from the beam tube at the end of the runs while i t was s t i l l c o l d .  In t h i s  way D vapour frozen onto the trap was kept out of the main vacuum system. Any D i n the system would have added greatly t o the beam dependent  background.  There was no noticeable increase i n beam dependent background during t h i s series of experiments. A magnetically controlled quartz stop was used to keep the beam from the D target except when readings were being taken.  (b)  DgO  Dispenser The D 0 9  dispenser shown i n Plate 1 was made of glass. I t s  - 19  three taps had been i n d i v i d u a l l y ground so that a vacuum t i g h t f i t was ensured.  The dispenser was mounted on plywood so that i t could be attaohed  by a bracket to the target chamber. cemented behind the monometer.  A piece of centimeter graph paper was  The l e v e l of the o i l i n the TJ-tube was read  d i r e c t l y from t h i s scale. O i l was chosen as the indicating f l u i d . used i n t h i s laboratory.  Mercury had previously been  However, with a density of 0.9 gm/cc, o i l has  about f i f t e e n times greater s e n s i t i v i t y than mercury.  O c t o i l Vacuum Pump -7  F l u i d from D i s t i l l a t i o n Produots Industries with a vapour pressure of 10 mercury at 20° C. was used. The o i l was heated under vacuum to remove water and other v o l a t i l e impurities.  Both the o i l and the dispenser were pumped f o r two days t o  remove a l l v o l a t i l e vapours. penser U-tube.  About f o r t y co. of o i l were put i n the d i s -  This allowed the f u l l vapour pressure of D O at room  temperature (about 24 cm) t o be measured on the monometer.  The top glass  tube of the dispenser f i t t e d into an 0-ring j o i n t on the outer target chamber. (c)  S c i n t i l l a t i o n Counter The s c i n t i l l a t i o n counter whose e f f i c i e n c y was measured i n  Chapter I I was used to count the gamma rays.  I t was set at 90°  to the  proton beam and was shielded by two inches of lead on the top and at the sides to cut down background r a d i a t i o n . Negative pulses from the head amplifier of the s c i n t i l l a t i o n counter  mm  -20  -  were put into a Northern E l e c t r i c Model No. 1444  amplifier.  The discrimin-  ator output of t h i s amplifier was fed into a Tracerlab Inc., Model SC-34A count rate meter. above the 2.62  The discriminator bias of the amplifier was  set just  Mev RdTh peak since a large percentage of the room background  was  due to thorium i n the concrete of the walls and f l o o r .  3.  EXPERIMENT  F l u o r i n e targets of thicknesses between three and ten kev were prepared as described i n Chapter I I .  The copper sheets were indium coated on the  backs before the f l u o r i n e evaporation.  After preparation they were soldered  onto the copper target plate described above using low melting point (155°  C)  indium so as not to disturb other soldered j o i n t s . As the runs were made a careful cheok was  kept on the e x c i t a t i o n curves.  Asymmetry of the e x c i t a t i o n curve would have indicated a non uniform t a r g e t . Targets were changed when any deterioration was  noted.  A low proton ourrent  of less than two microamperes was used f o r these experiments. deterioration of the heavy ice layer was  In thi3  way  kept at a minimum.  After the f l u o r i n e target had been soldered into place and the target chamber and monometer allowed to pump down as low as possible the was  shut o f f by the top tap.  The target chamber was  f l u o r i n e target was f a c i n g and perpendicular inner pot was f i l l e d with l i q u i d nitrogen. the two arms of the U tube was  closed.  dispenser  rotated u n t i l the  to the dispenser The dispenser tap  The lower tap was  inlet.  The  connecting  opened allowing  a suitable amount of vapour as indicated by the o i l l e v e l s to enter the  Fig. 9  Dp  DispenserCalibrotion  Curve  - 21 -  enclosed volume.  The o i l l e v e l s were recorded.  opened and the vapour was  The top tap was  slowly-  pumped out of the dispenser through a brass  which had a l / l 6 inch diameter hole d r i l l e d through i t .  rod  The vapour then  diffused through a l/8 inch t h i c k glass wool plug held by a copper screen and sprayed out^freezing over the f l u o r i n e t a r g e t .  After the o i l l e v e l s  had come back to t h e i r o r i g i n a l positions the tap was The above procedure was  closed.  repeated i n a standard manner f o r each heavy  ice target with reproducible r e s u l t s . A uniform spot about 1.5  cm i n  diameter was formed on the target p l a t e . A f t e r each of the c a l i b r a t i o n t r i a l s the i c e target was  removed and a  resonance oheck made on the bare f l u o r i n e target.  4.  RESULTS  The c a l i b r a t i o n graph i s shown i n F i g . 9. f o r one p a r t i c u l a r t r i a l . bare f l u o r i n e .  F i g . 10 shows the  readings  The f i r s t curve i s the e x c i t a t i o n curve f o r the  The resonance peak i s at 338 kev as measured on the Van  de  Graaff generating voltmeter  scale.  12.10  put on top of the f l u o r i n e and a second e x c i t a t i o n  i : .05 cm of o i l was  An ice target corresponding to  curve done with the protons passing through the ice l a y e r .  The resonance  had s h i f t e d to 412 kev as shown i n the second curve of F i g . 10. that a change of 12.10  This indicates  cm on the o i l monometer gives a target thickness of  74 kev as shown on the graph. The c a l i b r a t i o n was  not c a r r i e d out f a r beyond a 100 kev  thickness,  since f o r the absolute y i e l d measurements the maximum target thickness required was  100 kev f o r 300 kev incident protons.  Protons  Proton  o n Fl u o r i n e  Through  2 0 0 0  onFluorinft lc§ Layer  1500  Q) 3 C  itooo a  09 Q 050 0  0  i 330  1 3 4 0  I  l  39 5  350  G.V.M.  F f g . 10  Q£)  Ice  1  Target  Scale  Thickness  405  Kev  Calibration  1 415  • 4 25  - 22  I t w i l l be noticed from F i g . ice  10 that the resonance curve taken with the  layer on the f l u o r i n e i s lower and broader than the one taken on the hare  fluorine.  The f u l l width at half height has, i n f a c t , increased from 7.5  to 14 kev.  The width of the f i r s t curve i s contributed by the width of the  f l u o r i n e resonanoe, the thickness of the f l u o r i n e target and the proton beam energy spread. fluorine  These e f f e c t s give a width of 7.5 kev as seen from the bare  measurement.  The increased width from the protons passing through  the ioe i s due t o straggling of the protons i n the i c e and to non-uniformities i n the ioe target. Since the integrated areas of the two curves are approximately the same the centers of the curves were taken as the resonance peak and the dispenser c a l i b r a t i o n graph was obtained on t h i s b a s i s . The thickness of the targets i n atoms per sq. cm. was calculated i n the following manner using the results of Wenzel and Whaling  (1952).  T X 10 X 2 5  e where: T  -  e =  Target thickness i n kev  Molecular stopping power f o r protons -15 i n D_0 i c e i n 10  ev-cm.2  i s obtained from Table I I of the above paper. Using the example c i t e d previously f o r a target of 74 kev thickness we have: -  - «3 -  For  t—  t p of approximately  nj,  atoms /cm  e  400 kev  -15 13.9 X 10 ev-c^a  74 X 10 X 2  2  3  s  13.9 X 10 "  1  s  ~  1.06 X 1 0 ^  1 5  atoms /cm  2  19 Thus f o r a D 0 i c e target of 74 kev thickness one has 1.06 X 10  . o atoms /cm .  Target thicknesses f o r the absolute cross section measurements t o be discussed i n Chapter TV were calculated i n t h i s manner.  PLATE  I.  THE  D(p,y)He*APPARATUS  - 24  CHAPTER IV  THE  1.  D(p,TT)He  REACTION  5  INTRODUCTION A f t e r the determination  of the c r y s t a l e f f i c i e n c y (Ch. I i ) and the  target thickness (Ch. I l l ) i t was possible t o determine the absolute section and angular d i s t r i b u t i o n f o r the D(p,tf)He  3  cross  reaction as described  below.  2. (a)  THE ANGULAR DISTRIBUTION OF  D(p,T)He  3  GAMMA RAYS  Apparatus The target chamber used f o r the measurements and the  of the DgO targets are described i n Chapter I I I above:  preparation  The gamma counter  whose e f f i c i e n c y was measured i n Ch. I I , hereafter c a l l e d the "large" counter, was used t o measure the i n t e n s i t y of the gamma r a d i a t i o n at the d i f f e r e n t angles. A monitor counter, hereafter c a l l e d the "small* counter, was used during the angular d i s t r i b u t i o n runs.  This counter i s described i n Appendix 1.  The large counter was fastened t o an aluminum frame which could be rotated i n a horizontal plane around the target chamber as shown i n Plate I . The counter was set so that the o r y s t a l center was at the same height as the proton beam spot on the target, the counter was horizontal and swung'in a horizontal plane with the c r y s t a l always set the same distance from the target.  The small counter was held by an adjustable X-ray stand as close  - 25 -  to the target as possible and a t an angle of approximately 90°  t o the beam  as seen i n Plate I . The low gamma y i e l d a t 0°,  e s p e c i a l l y a t a proton energy of 300 kev,  made i t e s s e n t i a l that the background during the experiments be kept at a minimum,  A moveable rack holding a s i x inch t h i c k lead b r i c k layer approx-  imately eighteen inches square was r o l l e d over the gamma counter a t 0° t o cut down the time dependent background.  Since contaminants, e s p e c i a l l y  f l u o r i n e with i t s 6 Mev gamma rays, i n the target chamber would have added to the background the copper target plate and the end of the inner chamber were electroplated with gold using Caro-Perfection Gold Solution. The gold layer lowered the background r a d i a t i o n observed from the copper and brass.  (b)  Electronics The gamma ray pulses from the large counter were put onto the  t h i r t y channel kicksorter as desoribed i n Chapter I I . An Isotopes Developements Limited E.H.T. Unit Type 532 supplied the high voltage f o r both the large counter (1000 v o l t s ) and the small oounter (960 v o l t s ) . The monitor counter had a delay l i n e pulse shaping head amplifier described by P h i l l i p s (1957).  Pulses from the head amplifier were f e d  through a Dynatron 1049B Amplifier i n t o two decade scalers whose discrimination l e v e l s were set such that the "lower" scaler counted from just below the gamma-ray peaks and the "upper" counted from just above the peaks so that the D(p/tf}He  gamma - ray y i e l d was proportional t o the difference  i n the readings of the two s c a l e r s .  A l l discrimination l e v e l s were set and  { 0 T a r g e t '  i  90°  Positions  •  B  eff.  center  c m.  R  Target  2 - 5 x 3 5" cylindrical crystal {b)  y  Detector  Solid  Proton, Beam  Detector 9CT  Gammo Radiation Distribution < "> S o l i d c  Angle  Correotion  Fi  9-11  Angle  - 26 l i n e a r i t y of the electronics was checked using the accurate mercury pulser mentioned i n Chapter I I , (c)  Measurements The angular d i s t r i b u t i o n of the gamma r a d i a t i o n was measured f o r  proton energies of 300 kev,  600 kev and 1.0 Mev.  At 600 kev measurements  were made with the gamma counter at 0° and 90° only,while at 300 kev and 1.0 Mev measurements were also made a t ± 45° and 135°, measured as shown i n F i g . 11 ( a ) .  angles being  During the various runs the target was  set at position A and B so that corrections could be applied f o r any asymmetry due t o target absorption.  The y i e l d was corrected f o r target  absorption; the correction was 6% f o r gamma rays passing through the target at 45°. The lead s h i e l d i n g described above was used f o r the 0° runs and thereo fore separate time dependent background measurements had t o be taken a t 0 and 90° as w e l l as separate beam dependent background measurements. The DgO targets ranged i n thickness from 75 kev t o about 200 kev t h i c k f o r 340 kev incident protons. The proton beam was clipped by the molybdenum stops i n the beam tube so that p o s i t i o n f l u c t u a t i o n s i n the beam would not cause i t t o move over the target.  The beam was defocussed so that no "hot spots"  target which would have, caused d e t e r i o r a t i o n .  occurred on the  Target d e t e r i o r a t i o n was  checked by comparing the r a t i o of the counts i n the monitor t o the integrated beam current f o r successive runs and since the target deteriorated rapidly a t 300 kev, the y i e l d dropping by two-thirds  a f t e r one hour of  2001  (a ) Coun ter  at IOO  Q> S O C  O' Integrators  c o £ o  £ioo| c  3  o o  50  i i I  10  15 Channel  15 . Chonnel F.Q-12  Dft>,y)He  No.  K l  No.  S p e c t r a ,  20 Ep = 3 0 0  Kev.  -27-  running of a 100 kev thick target; the targets were changed whenever appreciable deterioration was noted.  At 1.0 Mev, however, the protons lose  less energy i n the target and targets up t o 120 kev t h i c k f o r 340 kev protons showed no noticeable deterioration a f t e r three hours of running time.  Proton  currents of about f i v e microamperes were used on a l l the angular d i s t r i b u t i o n runs. An experimental check was made on the s o l i d angle e f f e c t a t 1.0 Mev by doing angular d i s t r i b u t i o n measurements f o r a distance of 15.82 cm from the target (10.01 cm. from the counter face t o the outside of the target chamber), 22.37 cm. from the target (16.56 cm. from the counter face t o outside target chamber).  Comparison of the results a t the two d i f f e r e n t distances were  used t o check s o l i d angle corrections computed from the geometry as discussed below. A correction was made f o r the neutron e f f e c t from D + D reactions caused by deutrons e l a s t i o a l l y scattered by the incident protons during the D(p,t) )He  reaction.  The number of neutrons produced a t 0 p . o  bombarding the heavy i c e target, N  n  by protons  N  (0 ) was measured by a gamma ray insensit  t i v e neutron counter described by Ssu (1955).  During the same run the number  of gamma-ray counts i n the large counter was obtained a t 90° , H ^(90°). From the observed angular d i s t r i b u t i o n s the number of gamma ray counts a t 0° p from the p + D reaction,  H  r  o (0 ), could be Inferred.  Now the gamma ray  count a t 0° was due t o the true counts from the p + D reaction, plus the counts due t o neutrons,  N ^  D+ D  ^(0°).  i  n  I?P (P )(o°) + D  order t o determine the  number of counts i n the gamma - ray counter due t o neutrons the s e n s i t i v i t y of the gamma ray counter t o neutrons was measured by placing both the neutron and gamma ray counters a t 0° and bombarding the heavy ice target with 1.0 Mev  C honnel  Channel F i q.\Z D f p , y ) H e  No.  No Spectra  Ep = 10  Mev  - 28 deuterons*  Thus the number of counts i n the neutron counter, N ^ (0°) and n  the number of counts i n the gamma ray counter,  4  (0°) were obtained. Since  no capture gamma rays are produced d i r e c t l y by the D(d,n)He  reaction the r a t i o  3  of these two counts determines the r e l a t i v e e f f i c i e n c i e s of the two counters f o r neutrons alone.  B  I  Therefore: -  P ( D . D )  (  O  0  )  .  ,  (  O  0  )  X  , °(Q°)  V °  (0°)  This number of counts observed i n the gamma ray counter must be subtracted from the number of counts observed i n the gamma counter from the 3 D(p,Y)He  reaction.  The e f f i c i e n c y of the neutron counter i s dependent on the energy of the neutrons and the average energy of the neutrons due t o the secondary reaction when protons bombard the target i s l i k e l y t o be less than the energy of the D(dn)He  neutrons at 0 ° .  The r e l a t i v e e f f i c i e n c i e s of the  neutron oounter and gamma ray counter were also measured using the lower energy neutrons produoed by the D(dn)He  reaction at 90 .  In the calcu-  lations given below the average value f o r the e f f i c i e n c y obtained a t 0° o and 90  was used i n making t h i s correction. o The e f f e c t of the neutrons at 0 could also be seen by the d i s t o r t i o n  produced i n the lower portion of the gamma ray spectrum at 0° when compared o to the gamma ray spectrum at 90  where the neutron e f f e c t was very small  as shown i n P i g . 13. Since the shape of the d i s t o r t i o n to the zero degree curve has much the same shape as the spectrum produced i n t h i s counter produced by neutrons i t has been assumed that t h i s d i s t o r t i o n i s produced  - 29 -  by the secondary neutrons.  Therefore a correction f o r t h i s neutron effeot  can be made by subtracting a s u f f i c i e n t number of counts from the zero o degree spectrum to give i t the same shape as the 90  spectrum.  Reasonable  agreement was obtained f o r these two d i f f e r e n t methods of making the neutron correction.  The e f f e c t of the neutrons at 1.0 Mev. appears t o  have been somewhat greater than that used by G r i f f i t h s and Warren (1955) at the same energy, possibly because the l a t t e r authors compared curves taken at 0° and 45° .  If at 45°  there was some neutron d i s t o r t i o n of  the curve then the correction they applied would have been too small. (d)  Results Since the gain of the system and the position of the spectrum  on the kicksorter was not the same f o r a l l runs the number of counts f o r each run was obtained by summing the number o f counts i n the kicksorter channels corresponding t o a d e f i n i t e energy range.  For 1.0 Mev t h i s  energy range was chosen as 4.5 to 6.5 Mev which included the main peaks due t o the D(p^Y)He  gamma rays and excluded as much of the low energy  spectrum as possible, since t h i s portion was distorted by background and neutron e f f e c t s . The energy region over which the k i c k s o r t e r counts were summed was o chosen s l i g h t l y higher a t 0  o than a t 90  by an amount necessary t o correct  f o r the Doppler s h i f t i n the emitted gamma rays ( G r i f f i t h s & Warren, 1955).  - 30 -  A t y p i c a l c a l c u l a t i o n 1B shown below: Table I I Calculation of the D(p,r)He E • 1.0 Mev.  s  Target a t  p  + 45°  e=  • =0°  90°  Time  13.9 min.  Beam  50 integrators  10 integrators  2679  7941  Time background  150  36  Beam background  677  99  Neutron e f f e c t correction  122  —  Total correction  949  135  1730  7806  No. of counts i n peak  D (p,y) yield Absorption correction  3.3 min.  —  1730/.94 - 1842  Monitor uncorrected  65030  12057  Time background  63  16  Beam background  948  145  64019  11896  Monitor corrected N f  V  /N monitor  Y i e l d Ratio  s  V -  0.0287  90°  0.656  Y  Y 90  0.0287  =  0.656  0.0437  - 31 -  The experimentally observed angular d i s t r i b u t i o n s consisted of a 2 predominant oomponent proportional t o s i n ©  plus a non zero contribution  o at 0  suggesting the presence of an i s o t r o p i c component.  I f we assume  that the true d i s t r i b u t i o n i s of the form N(«)duJ =• A(sin Q b)doJ 2  as shown i n F i g . 11(c), then the experimentally observed d i s t r i b u t i o n w i l l be distorted from t h i s form by the f i n i t e s o l i d angle of the deteotor. In order t o determine b w  n  i t i s necessary t o correct f o r t h i s d i s t o r t i o n .  Integration of t h i s angular d i s t r i b u t i o n f u n c t i o n over the whole sphere determines the t o t a l y i e l d as  No  = 4TA(2/3 + b)  which w i l l be used i n computing the y i e l d of the reaction i n s e c t i o n 3. If the angular aperture of the large gamma ray counter has a half angle of 6  C  subtended at the target as shown i n F i g . 11(b) then a t 0°  the counting rate should be  3 where G i s the c r y s t a l e f f i c i e n c y as defined i n Ch. I I . At 90°  i f we assume that the gamma ray f l u x i s constant across the  32 -  whole face of the c r y s t a l and has the value obtained from the above angular d i s t r i b u t i o n f u n c t i o n at 90°, then the observed count at 90° should be -  N  ( 0°) 9  c  =  2 7 r e A ( l + b ) ( l - cos  The r a t i o of the observed counts at 0°  9) 0  and 90° i s then -  2/3 - OOS ©  COS  +  a  3  ©  c  + 1 - cos ©  K (0)  b  c  o  K (90)  1 -Hb  c  cos 2/3 - cos ©  < <  e  0  +  1 - cos  since b  3  -f- b ©  A  c  1 as w i l l be seen from the r e s u l t s below.  Thus the value of  b which i s of interest can be obtained from the observed r a t i o by subtracting from that r a t i o the f i r s t term above depending on the counter s o l i d angle. This term represents the counting rate i n the c r y s t a l at G  from the s i n ©  component due to the f i n i t e s o l i d angle of the counter. There was some uncertainty concerning the value of © used i n the above expressions.  c  that should be  The s o l i d angle to the e f f e c t i v e centre ©  as shown i n P i g . 11(b) i s s a t i s f a c t o r y f o r the i s o t r o p i c component since  c  - S3 -  t h i s produced a tiniform f l u x across the c r y s t a l face which corresponds to the conditions used to determine the e f f i c i e n c y and e f f e c t i v e centre (Ch. I i ) . But the s i n  9  the c r y s t a l ; the f l u x was  component did not produce a uniform f l u x over greatest at the outer edges so that the e f f e c t i v e  s o l i d angle could have been between 9  order to check the v a l i d i t y of using 9 of the r a t i o of counts at 0°  and 9  Q  Q  shown i n P i g . 11(b).  Q C  as the s o l i d angle, measurements  to counts at 90° were taken f o r two  target to counter distances as described i n section C. corresponded to 9  In  different  These two distanoes  f o r D_.r 15.82 cm. and 9 = 8°5 f o r D, = 22.37 cm. 10 c 16 o o The r a t i o s f o r the y i e l d at 0 to the y i e l d at 90 obtained at 1.0 Mev f o r  the D(p^"*)He  S  C  = 11°20  reaction were  R  10  =  °*  0 5 8 7  R  = 1 6  °'  0 4 6 1  These r a t i o s were obtained after background and neutron offebt corrections and except f o r s o l i d angle effects should have been the same.  S o l i d angle  corrections were computed f o r the above angles using formula A above giving f o r the f i r s t term on the r i g h t side the value 0.0194 f o r the smaller distance and 0.0099 f o r the larger one. "b" are 0.0393 and 0.0362.  Thus the two values obtained f o r  These are i n agreement to about 10$; the accuracy  of the measurements was not greater than t h i s and consequently we oan conclude that the s o l i d angle e f f e c t has been properly corrected f o r to t h i s order of accuracy. 2' Then, using t h i s value of the s i n 9 value of the isotropic component b.  d i s t r i b u t i o n we can calculate  the  - 34 -  For the example cited i n Table I I we have -  b  = 0.0437 - 0.0194  •=• 0.0243  The other r e s u l t s are calculated s i m i l a r l y f o r the other t r i a l s .  The  means of the r e s u l t s are given i n Table I I I .  Estimated Errors: Distance  15.82  S o l i d Angle  ± .2 cm  -  15.82  £ Z<%  t 5$  Neutron effect  +. 10$  The uncertainty i n the counting s t a t i s t i c s was calculated as f o l l o w s : Uncertainty i n counts  Percentage error i n  N is  N^m  Ny  i s the sum of t o t a l number of counts i n the uncorrected gamma spectra  plus the t o t a l number of time dependent counts plus the t o t a l number of beam dependent counts, the l a s t two being considered before normalizing faotor3  Ep  =3 0 0  kev  E p = 10  Mev  _ 20  ><^r\  0 O w >  .15  /  \  o 1- -  x> N  o  1 45  1^ O  V  (-)Dearees  1  1  45  90  io\  _  5  Angular  I  \  1  135  45  0 ( — )Degrees(+)  of  Gamma  A  /  l  Distribution  \  /  1  l+l  F i g . 14  \  -  Radition  1  1  45  90  from  D(p.)f/He  1 135  - 35 -  were used.  N m  i s a similar sum f o r the monitor counts,  The percentage error i n the and oalled  and Eg  N*-  o r a t i o was calculated at 0  N m  c  and 90  respectively.  Thus the percentage error due t o counting uncertainties i n the f i n a l ratio i s E - ±  / V 4- E  2 2  This percentage error was calculated f o r each energy and the f i n a l estimated percentage error i s  Ab=Y< ) +• (5) +• (10) +• (E) 2  2  J  3  The f i n a l r e s u l t s : Table I I I Angular E  3. (a)  P  D i s t r i b u t i o n Results Distribution  1.0 Mev  sin 9  + .024 - .003  .043  .005  0.6  sin ©  + .032 x. .004  .052  *• .006  0.3  s i n G 4- .0795 £ .010  2  2  2  ABSOLUTE CROSS SECTION MEASUREMENT OF  .099 £ .013  D(p,r)He"  Apparatus The apparatus used f o r these measurements was the same as used  f o r the angular d i s t r i b u t i o n measurements except that the monitor counter was  - 36  not used and the large counter was held on a l a r g e r , heavier stand since i t was shielded by about seven inches of lead above i t and on the sides. o The oounter was set at 90  to the beam and about 13 cm. from the target  so that the center counter l i n e was horizontal with the target spot.  The  o target plate was set at 45  to the beam, p o s i t i o n A i n F i g . 11(a).  The  large counter electronic system was i d e n t i c a l t o that used during the angular d i s t r i b u t i o n measurements. (b)  Measurements The absolute cross section was measured at a proton energy of 300  kev and 1.0 Mev f o r several D^O  targets of thicknesses from 41 kev to 76 kev  f o r 340 kev incident protons using the DgO dispenser F i g . 9.  c a l i b r a t i o n curve of  A careful check was kept on target deterioration by d i v i d i n g the  runs into separate t r i a l s and noting the r a t i o of gamma ray y i e l d t o i n t e grated beam current.  I f t h i s y i e l d started t o decrease, as i t d i d a f t e r 40  integrators at 300 kev, the target was removed and another target made. Beam dependent and time dependent backgrounds were taken.  The target spot  was clipped by the stops i n the beam tube of the target chamber and the beam was defocussed so that the beam formed a uniform spot on the t a r g e t . The beam could be seen very e a s i l y as a bright blue glow on the ice target. A low current of about one microampere was used so that target d e t e r i o r a t i o n from the heating e f f e c t of the beam was reduced.  (c)  Calculations The absolute  cross section was calculated f o r each target  thickness  by taking into account the number of D atoms per square centimeter using the  - 37 -  f i g u r e s of Wenzel & Whaling (1952), the number of protons from the known c a l i b r a t i o n of the current integrator,  and the s o l i d angle and e f f i c i e n c y of  the counter* Cross Section 0~C9) =A(sin © -r-b)dco  If  2  where A has the dimensions square centimeters per unit s o l i d angle when integrated over a l l angles t h i s gives the t o t a l cross section i n square centimeters.  (Zj- -  4 TrA (2/3 + b)  Then A oan be related to the observed count at 90°  N  ( 9 c  °  } =  as follows: -  £N N COfA(l+b) p  Then: -  D  4  cr ^  (90°)  N  [2/3  •  T  ±b\  \ H-b  p D  /  «  where: - N N  P D  — No. of incident protons - No. of D atoms /  cm  2  £ = e f f i c i e n c y of counter  — .61  COy.=solid angle of counter E f f i c i e n c y of counter 0.61 f o r 6.14 Solid angle,  ^  3"  Mev gamma rays: -  Area of c r y s t a l  2 (Distance from e f f . center t o target)  =  51*67  2 (15.82 £.2)  - 38 -  N  I  X  106  1-602  X 10  N  -13  2T  D — e  X x  c o s  10 4 5  3  o  where I t= Beam current i n integrators (106 microcoulombs per integrator) T = e  Thickness of targets i n kev from F i g . 9,  =. Molecular Stopping power f o r protons i n DgO  ice i n 10  -15  ? ev - cm  Collecting a l l the.constants i n the cross section expression we have: -  N (90) c  6  2/3  IT  b l  (.871  b  From Table I I I , we have the values  At  E  E  P  -  -300 kev,  b  - 0.0795  =  1.0 Mev,  b  — 0.0239  A t y p i c a l c a l c u l a t i o n follows:  X  10  -31  )  2  cm  Table  17  Typical Cross Section Calculation E. =300 kev P  63 kev t h i c k target  15 integrators  17.3 minutes  No. of Gamma Rays above E i  1155  Time dependent background  176  Beam dependent background  25  No. of Gammas (corrected)  954  Corr. f o r absorption i n l / l 6 inch brass  954  Target thickness  ~  1 0  15  63 kev  Molecular stopping power  13.8  X  -15 10  ev—cm  Substituting values, we have -  —31 CT  r-r °T  9  5  4  x  1 3  15  X  =  ^ 0.891  '  ^  8  0.6667 -r- 0.0795  63  X  -30 10  1 +- 0.0795  2  cm  X .871 X 10  ci  - 40  Estimated'Errors: Counter to target distance  15.82  ± 0.2 cno  =15.82 ±  1.2$  Counting s t a t i s t i c s Molecular Stopping Power  ± 4$  Current Measurements  2$  Counter EfficiencyTarget thickness  ± 10$  Thus the percentage uncertainty i n the t o t a l cross section i s the square root of the sum of the squares of the above percentage uncertainties and i s eleven per cent f o r both the 300 kev and 1.0 Mev runs (ignoring the less than one percent error due to the uncertainty i n b ) .  The estimated error of the  target thickness was obtained by noting the consistency between the cross section values f o r the d i f f e r e n t runs.  These values varied by ten percent  so t h i s was taken as an estimate of the uncertainty i n the thickness of the DgO targets. The measured values of the absolute cross section of the D ( p , y ) H e  3  reaction are -30 (0.898 t 0.097) X and  (3.24 ±  0.35)  10  X 10"  30  s  q . centimeters at E^:=  sq. centimeters at 1.0  300 kev  Mev  These values are s l i g h t l y smaller than those quoted by G r i f f i t h s and Warren (1955) and Fowler (1949) but are w i t h i n the ± 5 0 $ error stated by these authors.  The estimated error f o r the present results i s about  f i v e times less than that quoted by the above workers.  - 41 -  APPENDIX  E f f i c i e n c y Measurement of a 1.75 inch X 2 inch Nal Crystal  The e f f i c i e n c y of the monitor counter used i n the angular d i s t r i bution measurements of Chapter IV has been measured f o r the 6.14 Mev gamma 19 rays from the 340 kev resonance of F  16 (p»°S Y)0  •  This counter had a  1.75 inch diameter by 2 inch long Harshaw sodium iodide t h a l l i u m activated s c i n t i l l a t i o n c r y s t a l mounted on a RCA No. 6342 two inoh photomultiplier tube inside a brass cylinder three inohes i n diameter and ten inches long*) 6 Dow  Corning No. 200 S i l i c o n e o i l with a v i s c o s i t y of 10  25° C held by a slefve cut from a toy balloon  centistokes at  was used to ensure good o p t i c a l  coupling between the c r y s t a l and the phototube.  The counter i s shown i n  Plate I. The e f f i c i e n c y of the counter was measured using the same equipment and procedure described i n Chapter I I . Measurements were made at three target to counter distances.  The e f f e c t i v e center of the c r y s t a l was determined  from the inverse square p l o t . The e f f i c i e n c y at each of the distances was calculated i n the same manner as f o r the large c r y s t a l . The results are given i n Table TV. The e f f e c t i v e center was found to be 2.18 t .71 cm. from the front of the c r y s t a l .  - 42 -  Table  .V  E f f i c i e n c y of Small Nal C r y s t a l  D + 2.18±.71 C m  Efficiency  43.83 ± 1.0 cm  0.379  62.98  1.0  0.402  79.68  1.0  0.384  The estimated error i s about five percent giving a mean value for the efficiency of this counter for 6.14 Mev gamma rays of 0.388 - 0.019.  - 43 Bibliography  Ajzeriberg, F. and Lauritsen, T., (1955), Rev. Mod. Fhys., 27,  77 - 166.  A l l i s o n , S.K., and Warshaw, S.D., (1953) Rev. Mod. Phys., 25, 779. Chao, C.Y., (1950) Phys. Rev., 80, 1035. Chao, C.Y., Tollestrup, A.V., Phys. Rev., 79, 108.  Fowler, W.A.,  Lauritsen, C.C., (1950),  Crenshaw, CM., (1942), Phys. Rev. 62, 54. Curran, S.C., and Strothers, J . ,  (1939),  Proc. Roy. S o c , 172 ,  Davisson, D.M., and Evans, R.D.,  (1952),  Rev. Mod. Phys.  Devons, S. and Hines, M.G.N., (1949), Dosso, H.W.,  (1957),  72.  2A, 79.  Proo. Roy. Soo. (London),  199 A,  56.  M.A. Thesis, University of B r i t i s h Columbia  Freeman, J.M., (1950), P h i l . Mag. _41, 1225. French, A.P.,'and S e i d l , F.G.P., Fowler, W.A.,  (1951), P h i l . Mag. 42,  Lauritsen, C.C., and Tollestrup, A.V., (1949),  G r i f f i t h s , G.M., and Warren, J.B., (1955), Pt. 9, 781 - 92. Hirschfelder, J.O., and Magee, J.L., Huby, R.,  (1953),  Phys. Rev. J76, 1767.  Proc. Phys. Soc. A, 68,  (1948),  Progr. Nuclear Phys.,  Lauritsen, T., (1950), P h i l l i p s , G.  537.  Phys. Rev.  73. 207.  _3, 177.  Phys. Rev. 77, 617.  (1957), PhD. Thesis, University of B r i t i s h Columbia  Robertson, L.P., (1957), M.A. Thesis, University of B r i t i s h Columbia Ssu, W.,  (1955),  M.So. Thesis, University of B r i t i s h  Tollestrup, A.W., Fowler, W.A., and Lauritsen, C.C., Phys. Rev. 76, 428. Van A l l e n , J.A., and Smith, N.M., Wenzel, W.A.,  and Whaling, W.  (1941),  (1952),  Columbia (1949),  Phys. Rev. J59,  Phys. Rev. 87,  501.  3499.  G l o s s Wind ov#  Br o s s S pacer  Pnoportional Counter  cc-Winoow  Fig.I . F  /  T A R G E T  L-J  PQT  F U L L  SIZE Beam  In  V a n d e G r a a f fi  3 S—i Liquid / V a p o u r  BftHOws  r—] m  N Trap Gold  Stop  A l p h a Counter  M L M a get  mi Tartf&f  C h a i n ber  Qua rtz Beam STOP  F ig. 2  Beam  Tube  Box  PROPORTIONAL  Fig. 4  COUNTER  Alp h o P o r t i l e C o u n t e r  CHANNEL  NO-  (T)  L 4r  H T  470  ^ 3 3 0 K_  3KV  470 3KV  ,  .600  :-00l <1 ' W W I00K  1  I MEG 0«^ T  1470  X  +300V  3 KV  ~T_470 J 3 KV  L 'Anod«  1  10. 4 »qp4  S  »0&pf  Dyhodes  0-25  <i—3HI  OUT  3 3 0 K,  1—3L.  4 7 0 K s Photocothode FiQ.S  PHOTOMULTIPLIER  HEAD  AMPLIFIER  PRE AMP "J  out  ^COUNTER  ECKO  AMPLIFIER]  I Q 4 9 B pos. out  Fig. 6  BLOCK DIAGRAM OF **C0UNTlNG  APPARATUS  ATOMIC INSTR. SINGLE CHANNEL K.S. NO. 510  neg.  SCALER  pos. o u t  DYNATRON SCALER MODEL  BERKLEY  IOO  FiftT 5000-  V  SPECTRA,-!  F(p,o,y)0 Ep R d T h  J IJ ;z  -  , 6  FROM  6-14 fteV /  RAY  5,63  MeV  = 3 4 0 KeV 2-62 Mev  CALIBRATION  400CH  z I  'c  6 14 M e V  •> 3 0 0 0 -  c 0  z2 0 0 0 D D  2-62 M e V t  lOOO-  ' 30 2-4IO  3 235  4-06*5  4-9IO  5 750  CHANNEL NO. POPPER VOLTS  Fig. 8 fe. P L O T  FOR Nal  30  2»5X  3-5  CRYSTAL  50 70 O S T A N C E IN c m T A R G E T  .  I 90 TO CRYSTAL.  110 FRONT  FACE  130  Fig. 9  Dp  DispenserColibrotion  Curve  G<V.M. F i g . 10  Op  Ice  Target  Scale  Thickness  Kev  Calibration  (g)lee  Target  Positions  90° i  !-90°  A  '  B  C «ff.  L- ' 4  2 2  -J  center  2001  (0)  Counter ot IOO  10  15 Channel  Q ° Integrators  20  25  20  25  30  No.  200. ( b) C o u n t e r 45  at  9 0 °  Integrators  - 150 o> c c o  o IOO u a  3  5  50I  I  i  I -i  i_  F i f l . |2  '  •  '  IO  •  D(p,y)He  •  '  •  l  15 , Chonnel  No.  K 1  S p e c t r a ,  Ep « 3 0 O  kev.  30  SOC Counter  4 l  \  100  at  p,  0 °  J  Integrators  1  375 "3 c c o 250  5  V  Q. «0 +-  c  J  \  125 i I 5  1  j  ^D(d,n)He  '  J  »  i  i ' 10  *  - « -—  i i  i • i 15  Channel  0 2000  Effect  3  -  Counter  21  at  -  \  i  -1  20  i  i  i  i i 25  i  i  i  i 30  No.  9 0 °  /A  1 n te g r o * o r s  /  \  1500 c c o o ,.1000 a c O  o  500 1—1—i—i  5  i  i  i  10  f  •  i  •  i  15  Channel 0  FiQ.I3  D(p,y?He  i  i  i  i  i  1  20  i  i  i  i  25  No. Spectra  E  p  = |.Q M e v  i  i  i  ,  i  30  F  i  q  "  1  4  Angular  Distribution  of  Gamma  Radition  from  D(p.y/He  

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