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The D (p,[gamma])He³ reaction at low energies 1957

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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 in the Department of PHYSICS accept this thesis as conforming to the standard required from candidates for the degree of MASTER OF ARTS Members of the Department of Physios THE UNIVERSITY OF BRITISH COLUMBIA October, 1957 ABSTRACT A detailed study has been made of the D(p , V)He reaction at proton energies of 300 kev, 600 kev, and 1.0 lev. In order to measure the absolute cross section for this reaction the efficiency of a 2.5 inch by 3.5 inch sodium iodide crystal s c i n t i l l a t i o n counter was measured by simultaneous alpha particle and gamma ray measure- 19 16 ments on the 340 kev resonance of F (p,c<,lQ0 . The efficiency of the counter for the 6.14 Mev gamma radiation from this resonance has a measured value of 0.612 t 0.009. The angular distribution of the gamma radiation from the D(p 9 T)He 2 reaction has been found to have the form A(sin © +-b) where b equals 0.0795 ± 0.010, 0.032 ± 0.004 and Qp24± 0.003 at proton energies of 300 kev, 600 kev and 1.0 Jfev respectively. The absolute cross section of this reaction has been measured at 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 to be (0.8981:0.097) X 10 —30 square centimeters at 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 presenting t h i s thesis i n p a r t i a l fulfilment of the requirements f o r an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the Head of my Department or by his representative. It i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of P'U. y si c _s The University of B r i t i s h Columbia, Vancouver 8, Canada. Date O /tXcK̂ W a (5*5-7 ACKNOWLEDGEMENTS The author wishes to thank Dr. G.M. Griffiths f o r his generous assistance with and attentive supervision of the work described i n this thesis. I would like to thank Mr. L.P. Robertson for his kind assistance during the experimental work. Thanks are also due to Mr. P.J. Riley for operation the Van de Graaff during the f i n a l part of the work and Mr. G.J. Phillips and Dr. B.L. White for many helpful discussions and suggestions. Finally, I wish to thank the National Research Council and the Shell O i l Company of Canada for scholarships which have enabled me to carry out this work. TABLE OF CONTENTS Chapter Title Page I INTRODUCTION . 1 II GAMMA - RAY COUNTER EFFICIENCY MEASUREMENT 1. Introduction 3 2. Apparatus 1 Q 1 6 4 (a) The F (p,<**)0 Target Chamber 4 (b) Fluorine Targets • • 5 (c) Counters 6 (i) Gamma Ray Counter ....................... 6 ( i i ) The Alpha Particle Counter ................ 7 (d) Electronic Counting System 8 3. Experiments 9 4. Calculations 11 5. Results • 13 H I DgO TARGET THICKNESS MEASUREMENTS. 1. Introduction •• 17 2. Apparatus ..................... (a) Target Chamber 17 (b) DgO Dispenser 18 (c) S c i n t i l l a t i o n Counter •• 19 3. Experiment 20 4. Results •• 21 17 THE D(p,7T)He3 REACTION 1. Introduction ......................... 3 24 2. The Angular Distribution of the D(p,,2r)He Gamma Rays • (a) Apparatus • .. 24 (b) Electronics • •• 25 (c) Measurements ................................... 26 (d) Results 3 ...... 29 3. Absolute Cross Section Measurement of D(p,^)He ...... (a) Apparatus 35 (b) Measurements ••••••••••••.••••••••••••••••••••» 36 (c) Calculations •»•••..•.••..•••••••••••...•..»«•• 36 APPENDIX 41 BIBLIOGRAPHY LIST OF ILLUSTRATIONS Number Subject Facing Page Plates I The D(p,?T)He3 Apparatus 24 Figures 19 1. F l Target Pot 4 2. Beam Tube • 5 3. Photo Multiplier Head Amplifier 7 4. Alpha Particle Counter ................................ 8 5. Alpha Spectrum from F 1 9 8 6. Block Diagram of Alpha Counting Apparatus 7 7. Gamma - ray Spectra - 6.14 Mev. from F 1 9 ., 9 - 2.62 Mev. from RdTh 8. l / r 2 Plot for Sodium Iodide Crystal 12 9. DgO Dispenser Calibration Graph ....................... 21 10. D20 Ice Target thickness calibration ..... 22 11. (a) Ice Target Positions 26 (b) Gamma - ray Counter Geometry (c) Geometry for Solid Angle Corrections 12. Gamma Spectra of D(p ,r)He 3, E = 300 kev 27 13. Gamma Spectra of D(p,r)He3, E l =. 1.0 Mev 28 14. Angular Distribution of the D(p,V)He3 35 radiation Tables I Efficiencies of Nal Crystal 14 II Calculation of the D(p,tf)He Angular Distribution 30 III Angular Distribution Results 35 T? Typical Cross Section Calculation 39 .7 Efficiency of Small Nal Crystal 42 - 1 - CHAPTER I INTRODUCTION A detailed study of the three body systems He3 and T should lead to a better understanding of the fundamental internuolear forces than i s possible from a study of the simpler two body system, the deuteron, sinoe He3 and T have approximately 2.5 Mev binding energy per particle inferring that the particles are oloser together than in the deuteron where the binding energy is only about 1 Mev per particle. Also a comparison of the three body nuclei with the deuteron should, i n principle, allow one to determine whether there are many body forces holding the nuoleons together i n addition to two body forces which are the. only ones that oan play a role i n the deuteron. At the moment such a comparison is not possible because the problem i s compli- cated by r e l a t i v i s t i c effects of unknown amounts and due to the existence of uncertain non-central components i n the binding forces. A theoretical inter- pretation of the results of the present experiments should give some under- g standing of the symmetry characteristics of the forces binding the He nucleus together. 3 The D(p )He reaction i s also of interest to astrophysics since i t constitutes an important link in the conversion of hydrogen into helium i n the lower temperature main sequence stars by the so-called proton-proton chain. In the lower temperature stars this process predominates over the carbon- nitrogen cycle sinoe the coulomb barriers involved are smaller. Weak capture radiation from this reaotion was f i r s t reported by Curran and Strothers (1939). Fowler, Lauritsen and Tollestrup (1949) measured the angular distribution f ron a thiok ice target at a bombarding energy of 1.4 Mev and found that i t had the form A(sin^0 +vb ) where b was small. They o also measured the thick target yield at 90 in the energy range 0.5 Msv to 1.7 Mev giving the total cross section && <T 3 0*74 B^*7^ X 10*^ em̂ with a probable error of about 15% i n the exponent and of about 50f* Ixi the coefficient* A detailed study of the angular distribution at proton energies of 1.0 Mev and 1.75 Mev was made previously i n this laboratory (Griffiths and Warren 1955). The angular distribution was of the form A(s>n 20 + b ) where b was small and increased as the proton energy decreased from 1.75 to 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 theoretically and i t was f e l t that more accurate investigation at lower energies would be of interest. ^ None of the previous workers were able to give an accurate value for the absolute cross section of the reaction. The present work has attempted to measure the absolute cross section at 0.3 Mev and 1.0 Mev and to make a detailed -study of the angular distribution coefficient b i n this energy range. In order to do this an accurate measurement of the efficiency 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 in the target were el a s t i c a l l y scattered and collided with other deuterons producing neutrons by the 3 D(d,n)He reaction. The neutrons from this secondary reaction affeot the gamma detector and so i t was necessary to investigate this effect and to correct for i t . - 3 - CHAPTER II GAMMA COUNTER EFFICIENCY MEASUREMENT 1. INTRODUCTION In order to have a s c i n t i l l a t i o n oounter of known efficiency for 3 absolute oross seotion measurements of the D(p } Y )He reaction the efficiency of a 2*5 inches by 3.5 inches sodium iodide crystal f o r 6.14 Mev gamma radiation has been measured by simultaneous counting of the alpha and gamma rays from the F 1 9(p,oc, r ) 0 1 6 reaotion. The alpha particles which are isotropieally emitted are counted i n an accurately known geometry* Therefore one oan calculate the total number of alphas emitted in the reaotion. For each alpha emitted there is a 6.14 Mev gamma ray and therefore one has a gamma source of known intensity which oan be used to determine the efficiency of the s c i n t i l l a t i o n crystal as suggested by Van Allen and Smith (1941). The resonant capture of protons by F 1 9 forms Ne 2 0 i n a highly excited 16 state. This state decays by alpha emission forming 0 i n the ground state ( o c 0 ) or in one of the excited states at 6.06 Mev ( ccr ), 6.14 Mev ( oC^)t 6.91 Mev ( o c 2 ) and 7.12 Mev ( oc g ) # (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 intensity ratios of the short range alphas, ( cx ̂  , (K g } CKg) for proton energies between 300 kev and 950 kev obtaining a value of 0.024 for the ratio ^ 2 * ̂ 3 • Chao et al(l950) found that at the 340 kev resonance the ground state group OC 0 and the group to the pair emitting state ^ T T , were not experimentally observable. They also noted that the total number of alpha particles was olosely equal to the total number of gamma rays at the resonances measured. The experimental Fig.I , F 1 9 T A R G E T P O T results of Devon and Hlne (1949) and the spin assignments of Chao (1950) show that the alpha particles and gamma rays are isotropically distributed at the 340 kev resonance* H. Dosso (1957) in this laboratory has measured the relative intensities of the 6.14 Mev gamma ray and the sum of the yields of the 6*91 and 7.12 Mev gamma rays with a four crystal spectrometer. He gives 2,3% * 0,2% as the ratio of 6.91 Mev plus 7.12 Mev to the 6.14 Mev gamma rays. This result i s i n very good agreement with the value of 2.4$ as found by Freeman from relative alpha particle intensity measurements* Van Allen and Smith (1941) used a variable pressure absorption c e l l ionization chamber as an alpha counter and a thin-ended geiger counter for the gamma rays. In the present work the alpha particles were counted by a gas proportional counter sensitive only to the 6.14 Mev state alpha particles. From the known solid angle the t o t a l number of alpha emitted by the source could be calculated and this corresponds to the total number of 6.14 Mev gamma rays emitted by the source. The total number of gamma rays was assumed to be equal to the total number of 6.14 Mev gamma rays plus 2JSt% to allow for the 6.91 and 7.12 Mev gamma rays for which the alpha particles had i n - sufficient energy to enter the proportional counter. The details of the counters are described below. 2. APPARATUS 19 16 (a) The F (p,<*-,T)0 Target Chamber The target chamber used i n this experiment is shown in F i g . 1. The alpha particle oounter was attached to the middle of the three brass tubes of the chamber. This tube had a brass stop located so as to prevent small angle alpha scattering. V a n de G raa f fj B e a m S T O P F i g . 2 B e a m T u b e 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 at an angle of 45° to the beam tube. A light shining into the beam tube could be seen through the beam stops refleoted on the target backing. The target chamber was then adjusted by moveable bellows u n t i l i t was con- centric with a stop i n the main Van de Graaff beam tube. Any further align- ment was done so as to maximize the current on the target and to minimize that soattered i n the beam tube. The target plate was bolted onto a copper frame which was eleotrioally insulated by lucite spacers from the outer chamber. The frame could be rotated for replacement of targets. The experiments were done with the target at 45° to the beam so that the alpha particles came through a minimum thickness of calcium fluoride. The gamma ray oounter "looked" at the back of the target. The absorption of the gamma rays by the 0.029 inch thick aluminium window was about 0,5% and by the 0.015 inch thiok copper target backing was about 0,9%. The gamma ray yield was corrected for this absorption. A liquid nitrogen vapour trap was used in front of the target chamber to prevent carbon from the o i l diffusion pumps of the main vacuum system being l a i d down on the target. See Fig. 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 back- ground. A magnetically controlled quartz beam stop was used to cut the beam from the target except when runs were being made. (b) Fluorine Targets The targets were prepared from powdered calcium fluoride evaporated i n a b e l l jar under vacuum on to thin copper plates. The calcium fluoride was weighed before evaporation and the distances between the boat and the copper sheets measured so that targets could be reproduced. For example, i n one par- ticu l a r evaporation 0.031 gm of oalcium fluoride produced on a sheet of copper 25 cm above the boat a target of three kev thickness for 340 kev protons. The target thickness was approximately inversely proportional to the square of the distance from the boat. The targets were inspected visually for uniformity and any non-.uniform ones were discarded. The shape of the excitation ourve was also noted during the experiments and any nonuniform!ty of the targets was shown by the asym- metry of the ourve. Some targets, especially those used for the high beam current t r i a l s , showed blistering from the heating effeot of the beam. Targets were changed frequently during the experiment to prevent their de- terioration. (o) Counters (i) Gamma Ray Counter The s c i n t i l l a t i o n crystal which was calibrated i s a Harshaw Thallium activated sodium iodide sry3tal. Its dimensions, as supplied by Harshaw, are 2.500 - 0.005 inches diameter by 3.500 - 0.005 inohes long. The crystal was mounted by Harshaw i n an aluminum can with magnesium oxide reflector. The photomultiplier tube was a Dumont No. 6363 with a 2-5/8 inoh diameter photooathode surface. The orystal was held on to the photomultiplier tube by a vulcanized rubber band. Dow Corning 200,000 oentistoke Silicone o i l was used to ensure good optical coupling between the crystal and the photomultiplier tube. The crystal 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 + 3 0 0 V i 4 7 0 3 3 0 K S J _ 3 K V T I 4 7 O X 3 K V D y h o d e s 3 3 0 K 4 7 0 , M l ' 3 KV I O O K < J E s f , 6 0 0 S i MEGQTN' -1 4 7 0 I I J-L—l } _ J _ 3 K V A n o d e ' O O p f V 470< K 10. i »0p4: M-* T pf 6 J 6 OOI I N 3 4 5 K »| 33 0 2 5 — I I — 3 HI •5 K 4 7 0 K <, P h o t o c o t h o d e O U T -11—£) LO F i g . 3 P H O T O M U L T I P L I E R H E A D A M P L I F I E R =3. ^ C O U N T E R PREAMP 1^9 out ECKO AMPLIFIER! 10 4 9 B F i g . 6 B L O C K D I A G R A M OF P C C O U N T I N G A P P A R A T U S pos. out A T O M I C 1NSTR . S I N G L E C H A N N E L K.S. N O . 5 IO neg. B E R K L E Y S C A L E R pos . o ut O Y N A T R O N S C A L E R M O D E L l O O | counter is shown i n Plate 1. The single cyclindical unit made preoise levelling and positioning of the counter as described later relatively easy. A mu metal shield was put around the photomultiplier tube to shield 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 ci r c u i t diagram is given in Pig. 3. This s c i n t i l l a t i o n counter has now operated well for a year with no noticeable change in i t s energy resolution. A resolution of about seven per cent for the photo-peak of the 2.62 Mev RdTh gamma ray has been obtained. ( i i ) The Alpha Particle Counter The alpha counter was attached to the target chamber as shown i n F i g . 1. The proportional counter is a stainless steel tube 1.5 inches i n diameter and five inches long. It is f i l l e d with eleven cm of argon and one cm of alcohol. The counter size and gas pressure was chosen so that the alpha particles associated with the 6.14 Mev gamma rays of the reaotion would stop in the gas of the counter. The counter has a 6.1 mm ai r equivalent mica window cemented as shown in F i g . 4. This window thickness was chosen so as to stop a l l scattered protons from the target and as a result i t also stops the 6.91 and 7.12 Mev state alpha partloles from entering the counter. The 6.14 Mev state alpha particles 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 is offset from the center of the entrance aperture so that alpha particles would not hi t the centre wire. The centre wire is 0.005 inches in diameter made of a copper-nickel alloy and was diamond drawn to ensure uniformity along i t s entire length. For the precise P R O P O R T I O N A L C O U N T E R 0-005CU-NI W I R E B R A S S C A P M I C A " WO-18 •+ 3-5 mmi^ 1 ' 6 7 m m \ ^ 5 \ 3 0 2 mm C E M E N T E D S C A L E X 5 W INDOW D E T A I L F i g . 4 Alp no P o r t i l e Counter  - 8 ~ calibration of the Nal crystal i t was essential that the solid angle of the alpha counter be well defined* The entrance window is shown in Fig . 4. The entranoe aperture dimensions and the counter to 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. In this way the mica window was protected from atmospheric pressure when the counter was not in operation. The proportional counter centre wire was operated at a potential of 800 volts which gave a gas multiplication factor of ten. The guard rings which define the sensitive volume of the counter were at the same voltage as the centre wire. A typical alpha particle spectrum is shown in Fig . 5. A resolution of 12.5% was obtained for the alpha particle group associated with the 6.14 Mev gamma ray of the fluorine reaction. (d) Electronic Counting System A block diagram of the alpha particle counting system i s shown in Fig . 6. Negative pulses from the alpha - counter were fed via a 6AK5 cathode follower into an E.K. Cole Model 1049 B amplifier. Positive pulses from this unit were put into an Atomic Instruments Single Channel Pulse Height Analyzer Model 510. The single ohannel "kicksorter" window was set to give out only those pulses in the 1.85 Mev alpha particle peak corresponding to the 6.14 Mev gamma ray as shown in Fig. 5. The positive output pulses from the window were fed into a deoade scaler. The negative output from the base line discriminator was fed into a Dynatron Model 100 scaler. In this way a record was kept of a l l alpha pulses 5 0 0 0 H 4 0 0 0 - 1 .J IJ z. :z i T 3 0 0 0 H c Ll 0 I- D O 2 0 0 0 - J IOOO-4 F ( P , a , y ) 0 , D F R 0 M 6 1 4 MeV y R A Y E p = 3 4 0 K e v R d T h ~ 2 - 6 2 M G V C A L I B R A T I O N 5 ,6 3 MeV 6 14 MeV 1 C H A N N E L 3 0 NO. P O P P E R V O L T S 2-410 3 2 3 5 4 0 6 5 4 9 I O 5 7 5 0 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 at 1080 volts. The negative pulses from the cathode follower were fed into a Northern Electric Model No. 1444 amplifier. The discriminator output of this amplifier was put into a Dynatron Scaler. The bias voltage was set to be just below the half energy point of the fluorine gamma ray as shown i n Pig. 7. The negative output pulses from the amplifier were fed via a biased amplifier into a thirty channel Marconi Pulse Amplitude Analyser fkicksorter. 1 1) 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 direct energy calibration was available from which the half energy point of the 6.14 Mev gamma ray was determined. A typical speotrvun is shown i n F i g . 7. Gain shifts or nonlinearities i n the electronic system was checked using a mercury relay pulse generator described by Robertson (1957). Test pulses were put directly 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 this way any non-linearity i n the amplifier-kick- sorter system was eliminated. The single channel kicksorter limits for the alpha peak were set in the same manner by test pulses fed into the alpha counter head amplifier. 3. EXPERIMENTS The University of British Columbia's Tan de Graaff Generator provided 10 - a well-stabilized beam of up to ten microamperes of protons on the fluorine target. An excitation curve was f i r s t done over the 340 kev resonance of the 19 P . The position of the resonance on the generating voltmeter scale was obtained. The shape of the excitation curve also gave a check on the uniformity of the fluorine target. If the target was satisfactory the s c i n t i l l a t i o n crystal was levelled, set at the same height as the beam spot and set perpendicular to the target. 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 equip- ment. RdTh calibration runs were made at each position. Time and beam dependent backgrounds were taken so that corrections could be applied i n the calculations. The time taken for 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 fast unless a proton current of less than two micro-amperes was used. It was found that the gain of the Dumont photomultiplier used on the gamma counter tended to shi f t with a count rate of about 1500 counts per second or above. This shift was observed with the accurate test pulse generator feeding pulses directly into the counter head amplifier. After counting at a high rate the position of the spectrum changed while the voltage levels on the kicksorter and the amplifier gains remained constant, thus confirming that the photomultiplier gain had shifted. The gain increased with high counting rate and amounted to a 0.3$ change when the high counting rate was - 11 - maintained for about thir t y minutes. This gain shift had a slow decay time returning gradually to i t s original value after a few hours. 4. CALCULATIONS The proportional counter reoords only the 6.14 Mev state alpha particles. The gamma spectrum, however, contained the 6.14, 6.91, and 7.12 Mev gamma ray yields. The sum of the 6.91 and 7.21 Mev yield is 2.3$ (Dosso 1957) of the total yield at 340 kev. The speotra were corrected so that only the gamma counts from the 6.14 Mev state were considered in the calculations. The change in cross section of sodium iodide for gamma rays of 7.12 and 6.14 Mev is approximately 0.004$ and was therefore neglected in the calculations. 19 The RdTh and the F spectra were plotted as in Fig. 7. Knowing the position 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 half energy point and corrected for the 2.3$ of the 6.91 and 7.12 Mev radiation. The back- ground was normalized to the duration of the run since the background con- tributed by the beam alone i n the 6 Mev region was almost zero. See Fig. 7. The number of 6.14 Mev gamma counts were corrected for the 0.3$ absorption i n the aluminium window and the 0.9$ absorption in the copper target backing. The alpha counter background was about .3$ of the number of alpha counts obtained in the same time with about two microamperes on the target. The square root of the ratio of the alpha counts to the gamma counts was calculated for each of eight positions of the gamma counter and the graph O 6 H 05J O- 4 - IS 1 0 - 3 H O H F i g . 8 ^ P L O T F O R 2-5 X 3-5' Hal C R Y S T A L Effective Cente r 3 0 5 0 7 0 S O 110 1 3 0 DISTANCE IN cm T A R G E T T O C R Y S T A L . F R O N T F A C E 150 - 12 - of F i g . 8 plotted. This line, extrapolated to zero, gives the effective center of the crystal at 4.22 ~ 0.23 cm from the front face of the crystal. Solid Angle Calculations: (a) Alpha particle counter: - Referring to Fig. 1, the dimensions are as follows: - A s 4,8130 ± 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 travelling microscopes. Since a l l the readings were approximately the same the mean diameter was taken as 3.020 — 0.002 mm. The solid angle of the alpha counter is thus: - 3.020 2 OJ - ^1  \ ~ • ̂ VS X 5.1247 X 25.400/ ^oc " 2.956 X 10 " 4 ster-radians -13 - (b) Gramma Ray Counter: - Diameter of crystal 2.500 ± 0.005 inches Area * T (*•£» x 2.54 ) 2 AjT 31.67 em 2 Effective Solid Angle of counter - ( J r S 31.67 (D + 4.22) 2 Where D i s the distanoe from the target spot to the crystal faoe. Efficiency; The efficiency of the crystal was calculated for eaoh distance from the target. Crystal Efficiency = (Ho. ̂ -counts above EjJ (solid angle of oc-counter) (No. of oc-counts) (solid angle of T-counter) as. 5" Results: The results, together with their estimated errors are given i n the following table. - 14 - T a b l e I D+4.22 £ 0.23 cm. EFFICIENCY ERROR 154.52 ± 0.28 cm 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 is estimated from the oounting stat i s t i c s the percentage uncertainty i n the measurement of the distances from the alpha counter aperture to the target and the uncertainty in the di3tanoe of gamma counter effective center to the target ( £~ iL!jr ^ and percentage uncertainty in the area of the alpha counter window. Thus the estimated error in the efficiency i s : The mean of the f i r s t five values is 0.612 ± 0.009. The larger estimated error i n the last three values is due mainly to the uncertainty in the position of the effective center of the crystal. The last value in the table has an uncertainty of three per cent in the alpha counting statistics since about one thousand alpha counts were taken - 15 - In this run while about ten thousand counts were taken in the rest of the t r i a l s . The total 6.14 Mev gamma counts ranged from about t h i r t y thousand to over two million. As stated previously the gamma counting rate at the short target to counter distances was extremely fast. Therefore a low beam current was used which made the alpha particle- yield very small. The one thousand alpha counts of the last t r i a l took several hours of machine operating time. In conclusion the absolute efficiency of the s c i n t i l l a t i o n counter for 6.14 Mev gamma rays is 0.612 £ 0.009. H. Dosso (1957) and P. Singh in this laboratory have measured the 60 absolute efficiency of this counter for the Co gamma rays of 1.33 and 1.17 Mev. P. Singh has carried out theoretical calculations the results 6 0 of which agree with the Co measurements within the accuracy of the source strength calibration done by the National Research Council. * Singh has also calculated the efficiency for 6.14 Mev gamma rays which agrees to within fiv e per cent with the results of the present work. Due to the good agreement between the theory and the experimental observations at one and six Mev i t would appear that the theoretical estimate of the efficiency between one and eight Mev should be accurate within fiv e percent, particularly i f the theoretical calculations are adjusted to f i t the experimental value at 6.14 Mev which is accurate to 1.5$. In determining the absolute cross section for 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 at 1 meter ( 0.134 ± 0.005 mc.) s c i n t i l l a t i o n counter,comparison with a Co 6 0 source giving 1.39 t- 0.05 milliroentgens per hour at one meter. The latter source was measured by ionization chamber comparsion with the Canadian primary radium standard (N.R.C. Report No. C-121). - 16 - the efficiency is required for gamma rays in the range 5.7 Mev to 6.2 Mev. The efficiency over this energy range has been extrapolated from the experimental value at 6.14 Mev on the basis of the theory. CHAPTER III D90 ICE TARGET THICKNESS MEASUREMENTS 1. INTRODUCTION The absolute cross section measurements of D(p s Y) He reaction to be described in Chapter IV required that the thiokness of the heavy ioe target be measured. This thickness was measured by noting the shift of the 340 kev proton resonance of fluorine caused by the protons travelling through the ice layer. The number of DO atoms per sq. cm was then calculated using the measurements of the stopping power of DgQ ice for protons. Wenzel and Whaling (1952) measured, with an accuracy of four per cent, the stopping cross section of DO ice for protons between 18 kev and 541 kev. Their results agree within experimental errors with the theoretioal calculations of Hirschfelder and Magee (1948) for energies greater than 300 kev. Prom the experiments described below a calibration curve for the D̂ O dispenser has been obtained for target thicknesses from 30 kev to 110 kev for 340 kev incident protons. 2. APPARATUS (a) Target Chamber The target chamber, shown in Plate 1, was of a type used before i n this laboratory (Griffiths and Warren 1955). The ioe target backing was a copper plate i/B inch by 1 inch and l / l 6 of an inch thiok. The copper plate was soldered to a brass liquid nitrogen trap which was - 18 - ele c t r i c a l l y insulated from the outer container by a lucite ring. The target was operated at 4-135 volts to suppress secondary eleotrons and thereby prevent erroneous beam current readings. The adjustable bellows used in the efficiency measurements was also used on the front of this chamber. A lucite ring electrioally insulated the beam tube from the bellows. Thus the amount of beam current striking the beam tube could be measured. This was of great assistance in the rather c r i t i o a l alignment necessary with this chamber. Molybdenum stops with 6 mm and 8 mm aperture were put in the beam tube to reduce scattering of the incident beam onto the target. A degree c i r c l e was attached to the bottom of the outer chamber so that horizontal angles could be read during the angular distribution measurements. A liquid nitrogen vapour trap was used between the target chamber and the main vacuum system of the Van de Graaff• It 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 cold. In this way D vapour frozen onto the trap was kept out of the main vacuum system. Any D in the system would have added greatly to the beam dependent background. There was no noticeable increase in beam dependent background during this 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 D90 dispenser shown in Plate 1 was made of glass. Its - 19 three taps had been individually ground so that a vacuum tight 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. A piece of centimeter graph paper was cemented behind the monometer. The level of the o i l in the TJ-tube was read directly from this scale. Oil was chosen as the indicating f l u i d . Mercury had previously been used in this laboratory. However, with a density of 0.9 gm/cc, o i l has about f i f t e e n times greater sensitivity than mercury. Octoil Vacuum Pump -7 Fluid from D i s t i l l a t i o n Produots Industries with a vapour pressure of 10 mm mercury at 20° C. was used. The o i l was heated under vacuum to remove water and other volatile impurities. Both the o i l and the dispenser were pumped for two days to remove a l l v o latile vapours. About forty co. of o i l were put in the dis- penser U-tube. This allowed the f u l l vapour pressure of DO at room temperature (about 24 cm) to be measured on the monometer. The top glass tube of the dispenser f i t t e d into an 0-ring joint 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 efficiency was measured i n Chapter II was used to count the gamma rays. It 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 radiation. Negative pulses from the head amplifier of the s c i n t i l l a t i o n counter -20 - were put into a Northern Electric Model No. 1444 amplifier. The discrimin- ator output of this amplifier was fed into a Tracerlab Inc., Model SC-34A count rate meter. The discriminator bias of the amplifier was set just above the 2.62 Mev RdTh peak since a large percentage of the room background was due to thorium in the concrete of the walls and f l o o r . 3. EXPERIMENT Fluorine 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 fluorine 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 joints. As the runs were made a careful cheok was kept on the excitation curves. Asymmetry of the excitation curve would have indicated a non uniform target. Targets were changed when any deterioration was noted. A low proton ourrent of less than two microamperes was used for these experiments. In thi3 way deterioration of the heavy ice layer was kept at a minimum. After the fluorine target had been soldered into place and the target chamber and monometer allowed to pump down as low as possible the dispenser was shut off by the top tap. The target chamber was rotated u n t i l the fluorine target was facing and perpendicular to the dispenser i n l e t . The inner pot was f i l l e d with liquid nitrogen. The dispenser tap connecting the two arms of the U tube was closed. The lower tap was opened allowing a suitable amount of vapour as indicated by the o i l levels to enter the F i g . 9 D p D i s p e n s e r C a l i b r o t i o n C u r v e - 21 - enclosed volume. The o i l levels were recorded. The top tap was slowly- opened and the vapour was pumped out of the dispenser through a brass rod which had a l / l 6 inch diameter hole d r i l l e d through i t . The vapour then diffused through a l/8 inch thick glass wool plug held by a copper screen and sprayed out^freezing over the fluorine target. After the o i l levels had come back to their original positions the tap was closed. The above procedure was repeated in a standard manner for each heavy ice target with reproducible results. A uniform spot about 1.5 cm i n diameter was formed on the target plate. After each of the calibration t r i a l s the ice target was removed and a resonance oheck made on the bare fluorine target. 4. RESULTS The calibration graph is shown in Fig. 9. F i g . 10 shows the readings for one particular t r i a l . The f i r s t curve is the excitation curve for the bare fluorine. The resonance peak is at 338 kev as measured on the Van de Graaff generating voltmeter scale. An ice target corresponding to 12.10 i : .05 cm of o i l was put on top of the fluorine and a second excitation curve done with the protons passing through the ice layer. The resonance had shifted to 412 kev as shown in the second curve of Fi g . 10. This indicates that a change of 12.10 cm on the o i l monometer gives a target thickness of 74 kev as shown on the graph. The calibration was not carried out far beyond a 100 kev thickness, since for the absolute yield measurements the maximum target thickness required was 100 kev for 300 kev incident protons. P r o t o n s o n F l u o r i n e P r o t o n o n F l u o r i n f t 2 0 0 0 T h r o u g h l c § L a y e r 1 5 0 0 Q) 3 C i t o o o a 09 Q 0 5 0 0 0 i 1 l I 1 1 • 3 3 0 3 4 0 3 5 0 3 9 5 4 0 5 415 G . V . M . S c a l e K e v 4 2 5 F f g . 10 Q£) Ice T a r g e t T h i c k n e s s C a l i b r a t i o n - 22 It w i l l be noticed from Fi g . 10 that the resonance curve taken with the ice layer on the fluorine is lower and broader than the one taken on the hare fluorine. The f u l l width at half height has, in fact, 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 fluorine resonanoe, the thickness of the fluorine target and the proton beam energy spread. These effects give a width of 7.5 kev as seen from the bare fluorine measurement. The increased width from the protons passing through the ioe is due to straggling of the protons in the ice and to non-uniformities in 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 calibration graph was obtained on this basis. The thickness of the targets in atoms per sq. cm. was calculated i n the following manner using the results of Wenzel and Whaling (1952). T X 10 5 X 2 e where: T - Target thickness in kev e = Molecular stopping power for protons in D_0 ice i n 10 -15 .2 ev-cm i s obtained from Table II of the above paper. Using the example cited previously for a target of 74 kev thickness we have: - - « 3 - t— -15 For t p of approximately 400 kev e s 13.9 X 10 e v - c ^ a nj, atoms /cm2 s 74 X 10 3 X 2 13.9 X 10 " 1 5 1 ~ 1.06 X 10^ atoms /cm2 19 . o Thus for a D 0 ice target of 74 kev thickness one has 1.06 X 10 atoms /cm . Target thicknesses for the absolute cross section measurements to be discussed in Chapter TV were calculated i n this manner. P L A T E I. T H E D ( p , y ) H e * A P P A R A T U S - 24 CHAPTER IV THE D(p,TT)He5 REACTION 1. INTRODUCTION After the determination of the crystal efficiency (Ch. I i ) and the target thickness (Ch. I l l ) i t was possible to determine the absolute cross section and angular distribution for the D(p,tf)He3 reaction as described below. 2. THE ANGULAR DISTRIBUTION OF D(p,T)He3 GAMMA RAYS (a) Apparatus The target chamber used for the measurements and the preparation of the DgO targets are described in Chapter III above: The gamma counter whose efficiency was measured in Ch. II, hereafter called the "large" counter, was used to measure the intensity of the gamma radiation at the different angles. A monitor counter, hereafter called the "small* counter, was used during the angular distribution runs. This counter is described i n Appendix 1. The large counter was fastened to an aluminum frame which could be rotated i n a horizontal plane around the target chamber as shown in Plate I. The counter was set so that the orystal 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 crystal 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 at an angle of approximately 90° to the beam as seen i n Plate I. The low gamma yield at 0°, especially at a proton energy of 300 kev, made i t essential that the background during the experiments be kept at a minimum, A moveable rack holding a six inch thick lead brick layer approx- imately eighteen inches square was rolled over the gamma counter at 0° to cut down the time dependent background. Since contaminants, especially fluorine with i t s 6 Mev gamma rays, in 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 radiation observed from the copper and brass. (b) Electronics The gamma ray pulses from the large counter were put onto the thirty channel kicksorter as desoribed i n Chapter II. An Isotopes Developements Limited E.H.T. Unit Type 532 supplied the high voltage for both the large counter (1000 volts) and the small oounter (960 v o l t s ) . The monitor counter had a delay line pulse shaping head amplifier described by Phillips (1957). Pulses from the head amplifier were fed through a Dynatron 1049B Amplifier into two decade scalers whose discrim- ination levels 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 yi e l d was proportional to the difference in the readings of the two scalers. A l l discrimination levels were set and { 0 T a r g e t P o s i t i o n s ' 9 0 ° i • B e f f . c e n t e r c m. T a r g e t R 2 - 5 x 3 5 " c y l i n d r i c a l c r y s t a l {b) y D e t e c t o r S o l i d A n g l e P r o t o n , B e a m D e t e c t o r 9CT G a m m o R a d i a t i o n D i s t r i b u t i o n < c"> S o l i d A n g l e C o r r e o t i o n F i 9-11 - 26 - linearity of the electronics was checked using the accurate mercury pulser mentioned in Chapter I I , (c) Measurements The angular distribution of the gamma radiation was measured for 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 at ± 45° and 135°, angles being measured as shown in F i g . 11 (a). During the various runs the target was set at position A and B so that corrections could be applied for any asymmetry due to target absorption. The yield was corrected for target absorption; the correction was 6% for gamma rays passing through the target at 45°. The lead shielding described above was used for the 0° runs and there- o fore separate time dependent background measurements had to be taken at 0 and 90° as well as separate beam dependent background measurements. The DgO targets ranged in thickness from 75 kev to about 200 kev thick for 340 kev incident protons. The proton beam was clipped by the molybdenum stops in the beam tube so that position fluctuations in the beam would not cause i t to move over the target. The beam was defocussed so that no "hot spots" occurred on the target which would have, caused deterioration. Target deterioration was checked by comparing the ratio of the counts in the monitor to the inte- grated beam current for successive runs and since the target deteriorated rapidly at 300 kev, the yield dropping by two-thirds after one hour of 2 0 0 1 ( a ) C o u n t e r a t O ' S O Q> C c o £ o £ioo| c 3 o o 5 0 I O O I n t e g r a t o r s i i I 10 15 C h a n n e l N o . 15 . K l 2 0 C h o n n e l No. F . Q - 1 2 Dft>,y)He S p e c t r a , E p = 3 0 0 K e v . - 2 7 - running of a 100 kev thick target; the targets were changed whenever ap- preciable deterioration was noted. At 1.0 Mev, however, the protons lose less energy in the target and targets up to 120 kev thick for 340 kev protons showed no noticeable deterioration after three hours of running time. Proton currents of about five microamperes were used on a l l the angular distribution runs. An experimental check was made on the solid angle effect at 1.0 Mev by doing angular distribution measurements for a distance of 15.82 cm from the target (10.01 cm. from the counter face to the outside of the target chamber), 22.37 cm. from the target (16.56 cm. from the counter face to outside target chamber). Comparison of the results at the two different distances were used to check solid angle corrections computed from the geometry as discussed below. A correction was made for the neutron effect from D + D reactions caused by deutrons elastioally scattered by the incident protons during the D(p,t) )He reaction. The number of neutrons produced at 0 by protons p . o N bombarding the heavy ice target, N n (0 ) t was measured by a gamma ray insensi- tive neutron counter described by Ssu (1955). During the same run the number of gamma-ray counts i n the large counter was obtained at 90° , H ^(90°). From the observed angular distributions the number of gamma ray counts at 0° p o from the p + D reaction, H r (0 ), could be Inferred. Now the gamma ray count at 0° was due to the true counts from the p + D reaction, I?P (P + D)(o°) plus the counts due to neutrons, N ̂ D + D^(0°). i n order to determine the number of counts i n the gamma - ray counter due to neutrons the sensitivity of the gamma ray counter to neutrons was measured by placing both the neutron and gamma ray counters at 0° and bombarding the heavy ice target with 1.0 Mev C h o n n e l N o . C h a n n e l No F i q.\Z Dfp,y)He S p e c t r a E p = 1 0 M e v - 28 - deuterons* Thus the number of counts i n the neutron counter, N n^ (0°) 4 and the number of counts i n the gamma ray counter, (0°) were obtained. Since no capture gamma rays are produced directly by the D(d,n)He3 reaction the ratio of these two counts determines the relative efficiencies of the two counters for neutrons alone. Therefore: - B I P ( D . D ) ( O 0 ) . , ( O 0 ) X , °(Q°) V ° (0°) This number of counts observed i n the gamma ray counter must be sub- tracted from the number of counts observed in the gamma counter from the 3 D(p,Y)He reaction. The efficiency of the neutron counter is dependent on the energy of the neutrons and the average energy of the neutrons due to the secondary reaction when protons bombard the target i s l i k e l y to be less than the energy of the D(dn)He neutrons at 0°. The relative efficiencies 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 for the efficiency obtained at 0° o and 90 was used in making this correction. o The effect of the neutrons at 0 could also be seen by the distortion produced in the lower portion of the gamma ray spectrum at 0° when compared o to the gamma ray spectrum at 90 where the neutron effect was very small as shown in Pig. 13. Since the shape of the distortion to the zero degree curve has much the same shape as the spectrum produced in this counter produced by neutrons i t has been assumed that this distortion i s produced - 29 - by the secondary neutrons. Therefore a correction for this neutron effeot can be made by subtracting a sufficient number of counts from the zero o degree spectrum to give i t the same shape as the 90 spectrum. Reasonable agreement was obtained for these two different methods of making the neutron correction. The effect of the neutrons at 1.0 Mev. appears to have been somewhat greater than that used by Griffiths and Warren (1955) at the same energy, possibly because the latter authors compared curves taken at 0° and 45° . If at 45° there was some neutron distortion 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 for a l l runs the number of counts for each run was obtained by summing the number of counts in the kicksorter channels corresponding to a definite energy range. For 1.0 Mev this energy range was chosen as 4.5 to 6.5 Mev which included the main peaks due to the D(p^Y)He gamma rays and excluded as much of the low energy spectrum as possible, since this portion was distorted by background and neutron effects. The energy region over which the kicksorter counts were summed was o o chosen slightly higher at 0 than at 90 by an amount necessary to correct for the Doppler shift i n the emitted gamma rays ( Griffiths & Warren, 1955). - 30 - A typical calculation 1B shown below: - Table II Calculation of the D(p,r)Hes E p • 1.0 Mev. Target at + 45° • =0° e = 90° Time 13.9 min. 3.3 min. Beam 50 integrators 10 integrators No. of counts i n peak 2679 7941 Time background 150 36 Beam background 677 99 Neutron effect correction 122 — Total correction 949 135 D (p,y) yield 1730 7806 Absorption correction 1730/.94 - 1842 — Monitor uncorrected 65030 12057 Time background 63 16 Beam background 948 145 Monitor corrected 64019 11896 N f /N monitor V s 0.0287 Y = 0.656 90 Yield Ratio V - 0.0287 - 0.0437 Y90° 0.656 - 31 - The experimentally observed angular distributions consisted of a 2 predominant oomponent proportional to sin © plus a non zero contribution o at 0 suggesting the presence of an isotropic component. If we assume that the true distribution is of the form - as shown i n F i g . 11(c), then the experimentally observed distribution w i l l be distorted from this form by the f i n i t e solid angle of the deteotor. In order to determine w b n i t is necessary to correct for this distortion. Integration of this angular distribution function over the whole sphere determines the total yield as which w i l l be used i n computing the yield of the reaction i n section 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 Fig. 11(b) then at 0° the counting rate should be 3 where G is the crystal efficiency as defined i n Ch. II. At 90° i f we assume that the gamma ray flux is constant across the N(«)duJ =• A(sin 2Q b)doJ No = 4TA(2/3 + b) 32 - whole face of the crystal and has the value obtained from the above angular distribution function at 90°, then the observed count at 90° should be - N c( 90°) = 2 7 r e A ( l + b ) ( l - cos 9 0) The ratio of the observed counts at 0° and 90° is then - 3 2/3 - OOS © a + COS © c + b K o(0) 1 - cos © c Kc(90) 1 -Hb cos 3 e0 2/3 - cos © + -f- b A 1 - cos © c since b < < 1 as w i l l be seen from the results below. Thus the value of b which is of interest can be obtained from the observed ratio by subtracting from that ratio the f i r s t term above depending on the counter solid angle. This term represents the counting rate in the crystal at G from the sin © component due to the f i n i t e solid angle of the counter. There was some uncertainty concerning the value of © c that should be used i n the above expressions. The solid angle to the effective centre © c as shown in Pig. 11(b) is satisfactory for the isotropic component since - S3 - this produced a tiniform flux across the crystal face which corresponds to the conditions used to determine the efficiency and effective centre (Ch. I i ) . But the sin 9 component did not produce a uniform flux over the crystal; the flux was greatest at the outer edges so that the effective solid angle could have been between 9 Q and 9 Q C shown in Pig. 11(b). In order to check the v a l i d i t y of using 9 Q as the solid angle, measurements of the ratio of counts at 0° to counts at 90° were taken f o r two different target to counter distances as described i n section C. These two distanoes corresponded to 9 C = 11°20 for D_.r 15.82 cm. and 9 = 8°5 for D, = 22.37 cm. 10 c 16 o o The ratios for the yield at 0 to the yield at 90 obtained at 1.0 Mev for the D(p^"*)HeS reaction were R10 = ° * 0 5 8 7 R 1 6 = ° ' 0 4 6 1 These ratios were obtained after background and neutron offebt corrections and except for solid angle effects should have been the same. Solid angle corrections were computed for the above angles using formula A above giving for the f i r s t term on the right side the value 0.0194 for the smaller distance and 0.0099 for the larger one. Thus the two values obtained for "b" are 0.0393 and 0.0362. These are i n agreement to about 10$; the accuracy of the measurements was not greater than this and consequently we oan con- clude that the solid angle effect has been properly corrected for to this order of accuracy. 2 ' Then, using this value of the sin 9 distribution we can calculate the value of the isotropic component b. - 34 - For the example cited in Table II we have - b = 0.0437 - 0.0194 •=• 0.0243 The other results are calculated similarly for the other t r i a l s . The means of the results are given in Table III. Estimated Errors: Distance 15.82 ± .2 cm - 15.82 £ Z<% Solid Angle t 5$ Neutron effect +. 10$ The uncertainty in the counting stat i s t i c s was calculated as follows: Uncertainty in counts N is Percentage error in N̂ - m Ny is the sum of total number of counts i n the uncorrected gamma spectra plus the total number of time dependent counts plus the total number of beam dependent counts, the last two being considered before normalizing faotor3 E p = 3 0 0 k e v 0 O w > o 1- - x> N o 1 1 ^ 1 1 1 E p = 1 0 M e v _ 2 0 > < ^ r \ . 1 5 / \ \ I \ - i o \ / A _ 5 \ / l 1 1 1 1 4 5 O 4 5 9 0 135 ( - ) D e a r e e s l + l V 4 5 0 4 5 9 0 135 ( — ) D e g r e e s ( + ) F i g . 14 A n g u l a r D i s t r i b u t i o n o f G a m m a R a d i t i o n f r o m D(p.)f/He - 35 - were used. N is a similar sum for the monitor counts, m N*- o c The percentage error i n the ratio was calculated at 0 and 90 N m and oalled and Eg respectively. Thus the percentage error due to counting uncertainties in the f i n a l ratio i s - E - ± / V 4- E 2 2 This percentage error was calculated for each energy and the f i n a l estimated percentage error is Ab=Y<3) +• (5) 2 +• (10) 2 +• (E) J The f i n a l results: - Table III Angular Distribution Results E P Distribution 1.0 Mev 0.6 0.3 sin 29 + .024 - .003 sin 2© + .032 x. .004 sin 2G 4- .0795 £ .010 .043 .005 .052 *• .006 .099 £ .013 3. ABSOLUTE CROSS SECTION MEASUREMENT OF D(p,r)He" (a) Apparatus The apparatus used for these measurements was the same as used for the angular distribution measurements except that the monitor counter was - 36 not used and the large counter was held on a larger, 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 line was horizontal with the target spot. The o target plate was set at 45 to the beam, position A in Fig. 11(a). The large counter electronic system was identical to that used during the angular distribution measurements. (b) Measurements The absolute cross section was measured at a proton energy of 300 kev and 1.0 Mev for several D̂ O targets of thicknesses from 41 kev to 76 kev for 340 kev incident protons using the DgO dispenser calibration curve of Fi g . 9. A careful check was kept on target deterioration by dividing the runs into separate t r i a l s and noting the ratio of gamma ray yield to inte- grated beam current. If this yield started to decrease, as i t did after 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 target. The beam could be seen very easily as a bright blue glow on the ice target. A low current of about one microampere was used so that target deterioration from the heating effect of the beam was reduced. (c) Calculations The absolute cross section was calculated for each target thickness by taking into account the number of D atoms per square centimeter using the - 37 - figures of Wenzel & Whaling (1952), the number of protons from the known calibration of the current integrator, and the solid angle and efficiency of the counter* Cross Section If 0~C9) =A(sin2© -r-b)dco where A has the dimensions square centimeters per unit solid angle when integrated over a l l angles this gives the total cross section i n square centimeters. (Zj- - 4 TrA (2/3 + b) Then A oan be related to the observed count at 90° as follows: - N c ( 9 ° } = £N pN DCOfA(l+b) Then: - 4 crT ^ • N (90°) p D « [2/3 ±b\ \ H-b / where: - N — No. of incident protons P N D - No. of D atoms / cm2 £ = efficiency of counter — .61 COy.=solid angle of counter Efficiency of counter 0.61 for 6.14 Mev gamma rays: - Solid angle, ^ Area of crystal = 51*67 3" 2 2 (Distance from eff. center to target) (15.82 £.2) - 38 - N I X 106 N 2T X 103 -13 D — 1-602 X 10 e x c o s 4 5 o where I t= Beam current in integrators (106 microcoulombs per integrator) T = Thickness of targets in kev from F i g . 9, e =. Molecular Stopping power for protons -15 ? i n DgO ice in 10 ev - cm Collecting a l l the.constants in the cross section expression we have: - N (90) 6 c 2/3 b -31 2 (.871 X 10 ) cm IT l b From Table III, we have the values At E - -300 kev, b - 0.0795 P E = 1.0 Mev, b — 0.0239 A typical calculation follows: Table 17 Typical Cross Section Calculation E. =300 kev P 63 kev thick target 15 integrators 17.3 minutes No. of Gamma Rays above Ei 1155 Time dependent background 176 Beam dependent background 25 No. of Gammas (corrected) 954 Corr. for absorption in l / l 6 inch brass 954 ~ 1 015 Target thickness 63 kev Molecular stopping power -15 13.8 X 10 ev—cm Substituting values, we have - —31 CT = 9 5 4 x 1 3 ' 8 ^ 0.6667 -r- 0.0795 X .871 X 10 ci 15 X 63 1 +- 0.0795 r-r -30 2 ° T ^ 0.891 X 10 cm - 40 Estimated'Errors: - Counter to target distance 15.82 ± 0.2 cno =15.82 ± 1.2$ Counting statistics Molecular Stopping Power ± 4$ Current Measurements 2$ Counter Efficiency- Target thickness ± 10$ Thus the percentage uncertainty i n the t o t a l cross section is the square root of the sum of the squares of the above percentage uncertainties and is eleven per cent for 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 for the different runs. These values varied by ten percent so this 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)He 3 reaction are -30 (0.898 t 0.097) X 10 s q . centimeters at E^:= 300 kev and (3.24 ± 0.35) X 10" 3 0 sq. centimeters at 1.0 Mev These values are sli g h t l y smaller than those quoted by Griffiths and Warren (1955) and Fowler (1949) but are within the ±50$ error stated by these authors. The estimated error for the present results i s about fi v e times less than that quoted by the above workers. - 41 - APPENDIX Efficiency Measurement of a 1.75 inch X 2 inch Nal Crystal The efficiency of the monitor counter used i n the angular d i s t r i - bution measurements of Chapter IV has been measured for the 6.14 Mev gamma 19 16 rays from the 340 kev resonance of F (p»°S Y)0 • This counter had a 1.75 inch diameter by 2 inch long Harshaw sodium iodide thallium activated s c i n t i l l a t i o n crystal mounted on a RCA No. 6342 two inoh photomultiplier tube inside a brass cylinder three inohes in diameter and ten inches long*) 6 Dow Corning No. 200 Silicone o i l with a viscosity of 10 centistokes at 25° C held by a slefve cut from a toy balloon was used to ensure good optical coupling between the crystal and the phototube. The counter is shown in Plate I. The efficiency of the counter was measured using the same equipment and procedure described i n Chapter II. Measurements were made at three target to counter distances. The effective center of the crystal was determined from the inverse square plot. The efficiency at each of the distances was calculated in the same manner as for the large crystal. The results are given in Table TV. The effective center was found to be 2.18 t .71 cm. from the front of the crystal. - 42 - Table .V Efficiency of Small Nal Crystal D + 2.18±.71 Cm Efficiency 43.83 ± 1.0 cm 62.98 1.0 79.68 1.0 0.379 0.402 0.384 The estimated error is 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. Allison, 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., Fowler, W.A., Lauritsen, C.C., (1950), Phys. Rev., 79, 108. Crenshaw, CM., (1942), Phys. Rev. 62, 54. Curran, S.C., and Strothers, J., (1939), Proc. Roy. Soc, 172 , 72. Davisson, D.M., and Evans, R.D., (1952), Rev. Mod. Phys. 2A, 79. Devons, S. and Hines, M.G.N., (1949), Proo. Roy. Soo. (London), 199 A, 56. Dosso, H.W., (1957), M.A. Thesis, University of British Columbia Freeman, J.M., (1950), P h i l . Mag. _41, 1225. French, A.P.,'and Seidl, F.G.P., (1951), P h i l . Mag. 42, 537. Fowler, W.A., Lauritsen, C.C., and Tollestrup, A.V., (1949), Phys. Rev. J76, 1767. Gri f f i t h s , G.M., and Warren, J.B., (1955), Proc. Phys. Soc. A, 68, Pt. 9, 781 - 92. Hirschfelder, J.O., and Magee, J.L., (1948), Phys. Rev. 73. 207. Huby, R., (1953), Progr. Nuclear Phys., _3, 177. Lauritsen, T., (1950), Phys. Rev. 77, 617. Phillips, G. (1957), PhD. Thesis, University of British Columbia Robertson, L.P., (1957), M.A. Thesis, University of British Columbia Ssu, W., (1955), M.So. Thesis, University of British Columbia Tollestrup, A.W., Fowler, W.A., and Lauritsen, C.C., (1949), Phys. Rev. 76, 428. Van Allen, J.A., and Smith, N.M., (1941), Phys. Rev. J59, 501. Wenzel, W.A., and Whaling, W. (1952), Phys. Rev. 87, 3499. G l o s s Wind ov# Br o s s S p a c e r Pnopo r t i ona l Counter cc-Winoow / L-J Fig.I . F T A R G E T P Q T F U L L S I Z E B e a m In L i q u i d N / V a p o u r T r a p BftHOws r—] m A l p h a Counter G o l d S t o p M L mi T a r t f & f C h a i n ber Q u a r t z B e a m S T O P V a n de G r a a f fi 3 S—i M a get B o x F i g . 2 B e a m T u b e P R O P O R T I O N A L C O U N T E R F i g . 4 Alp ho P o r t i l e Counter C H A N N E L NO- ( T ) H T + 3 0 0 V ^ 3 3 0 K_ L 4 7 0 4r 3 K V 1 4 7 0 X 3 K V D y h o d e s 3 3 0 K, 4 7 0 , 3 K V I00K I MEG 0T«̂ S 1 :-00l < . 6 0 0 1 ' WW 1 10. 4 »qp4 ~ T _ 4 7 0 L J 3 K V ' A n o d « » 0 & p f 4 7 0 K s P h o t o c o t h o d e 0-25 <i—3HI O U T 1—3L. F i Q . S P H O T O M U L T I P L I E R H E A D A M P L I F I E R ^ C O U N T E R PRE AMP "J out E C K O A M P L I F I E R ] I Q 4 9 B F i g . 6 BLOCK DIAGRAM OF **C0UNTlNG APPARATUS pos. out ATOMIC INSTR. SINGLE CHANNEL K.S. N O . 510 neg. pos . o u t D Y N A T R O N S C A L E R M O D E L I O O B E R K L E Y S C A L E R 5 0 0 0 - 400CH J I J ;z z I ' c •> 3 0 0 0 - c 0 - z D D 2 0 0 0 l O O O - F i f t T V S P E C T R A , - ! F ( p , o , y ) 0 , 6 F R O M 6-14 fteV / R A Y E p = 3 4 0 K e V R d T h - 2 - 6 2 M e v C A L I B R A T I O N 5 , 6 3 M e V 2-62 M e V t 6 14 MeV ' C H A N N E L 3 0 N O . P O P P E R V O L T S 2-4 IO 3 2 3 5 4-06*5 4-9IO 5 7 5 0 F i g . 8 fe. P L O T F O R 2 » 5 X 3-5 N a l C R Y S T A L . I 3 0 5 0 7 0 9 0 110 1 3 0 O S T A N C E IN cm T A R G E T T O C R Y S T A L . F R O N T F A C E F i g . 9 D p D i s p e n s e r C o l i b r o t i o n C u r v e G<V.M. S c a l e K e v F i g . 10 Op Ice T a r g e t T h i c k n e s s C a l i b r a t i o n ( g ) l e e T a r g e t P o s i t i o n s 9 0 ° i ! - 9 0 ° ' A B C « f f . c e n t e r L - 4 ' 2 2 - J 2 0 0 1 (0) C o u n t e r o t Q ° I O O I n t e g r a t o r s 10 15 C h a n n e l N o . 20 2 5 3 0 2 0 0 . ( b ) C o u n t e r a t 9 0 ° 4 5 I n t e g r a t o r s - 1 5 0 o> c c o o IOO u a 3 5 50 I I i I -i i_ ' • ' • • ' • l IO 15 , K 1 2 0 C h o n n e l No . 2 5 3 0 F i f l . |2 D(p,y)He S p e c t r a , E p « 3 0 O k e v . S O C 3 7 5 "3 c c o 5 2 5 0 V Q. «0 +- c J 125 0 4 C o u n t e r a t 0 ° p, l\ 1 0 0 I n t e g r a t o r s J 1 \ ^ D ( d , n ) H e 3 E f f e c t \ i i - « - — - 1 I j J ' » i ' * i i i • i - 1 i i i i i i i i i i 5 10 15 2 0 2 5 3 0 C h a n n e l N o . 2 0 0 0 1 5 0 0 c c o o , .1000 a c O o 500 0 - C o u n t e r a t 9 0 ° / A 21 1 n te g ro* o r s / \ 1—1—i—i i i i f • i • i i i i i 1 i i i i i i i i , i 5 10 15 2 0 2 5 3 0 C h a n n e l No. F i Q . I 3 D(p,y?He S p e c t r a E p = |.Q M e v F i q " 1 4 A n g u l a r D i s t r i b u t i o n o f G a m m a R a d i t i o n f r o m D(p.y/He


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