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The gamma-radiation from the bombardment of heavy ice with low-energy protons 1961

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THE GAMMA-RADIATION PROM THE BOMBARDMENT OP HEAVY ICE WITH LOW-ENERGY PROTONS fey Colin David Scarfe B.Sc. University of B r i t i s h Columbia i 9 6 0 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OP MASTER OF SCIENCE i n the department of PHYSICS We accept t h i s thesis as conforming to the required standard The University of B r i t i s h Columbia October 1961 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for 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 f o r scholarly purposes may be granted by the Head of my Department or by his representatives. 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 The University of B r i t i s h Columbia, Vancouver 8, Canada. ABSTRACT The reaction D(p, y )He was studied at incident proton energies of less than 50 kev. The method was to bom- bard heavy ice targets with the proton beam from the 50 kv accelerator. This machine develops an intense beam of 60 to 80 microamps which i s necessary to produce a substantial y i e l d despite the low reaction cross section. The angular d i s t r i b u t i o n of the y-rays was found p to follow a ( s i n 9 +B) pattern as expected from e a r l i e r work carried out at higher energies. In the neighborhood of 35 kev the value of B was found, by measurements of the y i e l d at 90° and at 0° to the incident beam direction., to be .283+ . 1 1 0 . The t o t a l cross section was found to take on the following values: 2 - 3 2 E(kev) a (cm )x 10 2 9 . 1 4 .87+ 1 . 0 5 3 7 . 5 1 1 . 2 + 2 . 8 4 4 . 0 1 2 . 9 + 4 . 0 ACKNOWLEDGEMENTS The author wishes to express his gratitude to Dr. G. M. G r i f f i t h s who suggested and supervised t h i s work, and whose u n f a i l i n g assistance and advice during the performance of the experiment and with the w r i t i n g of t h i s thesis are greatly appreciated. Thanks also are due to Mr. M. L a i for his valuable advice i n the i n i t i a l stages and to Mrs. E. Nesbitt, who typed t h i s thesis. The author g r a t e f u l l y acknowledges the receipt of a National Research Council of Canada bursary. TABLE OP CONTENTS Page I. Introduction 1 I I . Apparatus 5 1. The 50-kv set 5 2. Counter and Electronics 7 3 . Current Integrator 9 4. E l e c t r o s t a t i c Lenses 10 I I I . Procedure 12 IV. Results 15 1. Angular D i s t r i b u t i o n 15 2. Total Cross-Section 18 V. Conclusions 24 ILLUSTRATIONS Figure To follow page 1. Target Chamber 6 2 . Head Amplifier 8 3 . Photomultiplier Connections 9 4 . Pulse Generator 10 5 . Schematic Diagram of Current Integrator 10 6 . Quadrupole Lens 11 7 . A Typical Background Spectrum 14 8 . Typical D(p, y )He3 Spectra 15 9 . Deterioration of a Target 18 1 0 . The t o t a l Y i e l d 20 11 . The Stopping Cross-Section for Protons i n DgO 22 1 2 . Total Cross-Section for D(p, y )He^ 23 1 3 . Variation of Counting Rate with Distance 25 CHAPTER I - INTRODUCTION 1 The purpose of t h i s thesis i s to discuss an experiment with the reaction D(p,y )He . This reaction i s of s p e c i a l i n t e r e s t i n nuclear physics because i t y i e l d s information about the three body system He . A study of three-body nuclei should lead to a more detailed under- standing of internucleon forces than i s possible from a study of the deuteron, the only bound two-nucleon system, because of the somewhat t i g h t e r binding of the three-body system and because of the p o s s i b i l i t y of finding many- body forces d i f f e r e n t from ordinary two-body forces. Curran and Strothers (1939) were the f i r s t to report detection of the gamma radiation from t h i s reaction. Later, Fowler, Lauritsen and Tollestrup (1949) found that the angular d i s t r i b u t i o n from a thick ice target at a bom- barding energy of 1.4 Mev had the form A(sin 6 +B) where B was small. They also found that the t o t a l cross section i n 0 72 the region 0 .5 to 1.7 Mev obeyed the r e l a t i o n <r = 0.74E *' x -2Q 2 10 cm where E i s i n Mev. Further study by Wilkinson (1952) showed that the main contribution to the radiation i s e l e c t r i c dipole i n character. G r i f f i t h s and Warren (1955) checked the measure- ment of the absolute cross-section made by Fowler e t . a l . and made a detailed study of the angular d i s t r i b u t i o n with the following r e s u l t s . 2 E p(Mev) B 1 .75 07025±0.006 1 . 0 0.046+0.005 0 . 8 0.04+0.015 0 . 6 0 . 0 2 6 + 0 . 0 1 0 With a considerable improvement i n target t h i c k - ness measurements and an accurate measurement of the s c i n - t i l l a t i o n counter e f f i c i e n c y , the angular d i s t r i b u t i o n and absolute cross-section have been remeasured by Larson (1957) and by G r i f f i t h s , Larson and Robertson (to be published) with the following r e s u l t s : E^(Mev) B <rx l0~° 1 . 0 0.024*0.003 3 . 2 4 + 0 . 3 5 0 . 6 0.032+0.004 0 . 3 0 . 0 7 9 + 0 . 0 1 0 0 . 8 9 8 + 0 . 0 9 7 This increase i n B with decreasing energy suggests that the contribution at 0° i s due to an s-wave process rather than to the p-wave capture leading to the s i n 9 distributionj. A more detailed study of t h i s i s of consider- able i n t e r e s t i n the theory of nuclear forces. Because of t h i s and because the reaction Is s i g - n i f i c a n t i n astrophysical processes at very low energies i t was f e l t that an experimental measurement at an energy w e l l below 3 0 0 k e v would be of value, p a r t i c u l a r l y because at the present time, i t i s impossible to predict the cross-section r e l i a b l y at very low energies by extrapolating from the higher energy r e s u l t s . There are three reasons for t h i s . 3 F i r s t l y , the process occurs by a di r e c t re- action mechanism which i s rather sensitive to external portions of the nuclear wave function which are not very w e l l understood. Secondly, the low Coulomb b a r r i e r means that the energy dependence of the reaction i s Influenced by factors other than the usual exponential p e n e t r a b i l i t y which i s often assumed for low energy reactions. Thirdly, the energy dependence of the angular d i s t r i b u t i o n shown above suggests that two processes contribute to the capture with d i f f e r e n t energy dependences. At the higher energies the p-wave capture with e l e c t r i c dipole emission c l e a r l y predominates. However, i f the small i s o t r o p i c component i s due to an s-wave process, which seems l i k e l y to be the case on the basis of the angular d i s t r i b u t i o n data of Larson (1957) then t h i s process i s l i k e l y to predominate at very low energies. The f i r s t measurements i n the 25 to 45 kev region were made by L a i (1961) who showed c l e a r l y that the y -rays could be observed at these energies and who made a p r e l i m i - nary measurement of the angular d i s t r i b u t i o n . The D(p, y )He^ measurements at the higher energies were hampered by the presence of neutrons produced by the reaction D(d,n)He3 between r e c o i l deuterons and deuterons i n the target. A detailed study of t h i s effect has been made by Singh et a l . ( l 9 5 9 ) . The neutron y i e l d , quite appreciable at 1 Mev bombarding energy, decreases very rapidly with energy and i s expected to be n e g l i g i b l e at 4 energies below 50 kev, which were used i n the present work. The previously mentioned astrophysical importance of the reaction D(p, 7 )He^ i s twofold. F i r s t l y , i t i s a l i n k i n the proton-proton chain, which i s the p r i n c i p a l source of energy i n the lower-temperature main-sequence stars such as our sun. In addition the cross-section at very low energies may be of importance because, as Cameron ( i 9 6 0 ) pointed out, i t i s one of the f i r s t reactions to occur as a star i s condensing from the g a l a c t i c gas onto the main sequence. The res u l t i n g radiation pressure pre- vents further contraction u n t i l the deuterium i n i t i a l l y present i s consumed. Thus the amount of deuterium present i n i n t e r s t e l l a r space affects the time-scale f o r s t e l l a r condensation through the reaction D(p,y )He3„ The present work was undertaken i n an attempt to answer some of these questions. 5 CHAPTER I I - APPARATUS 1. The 50 kv set The proton beam required for t h i s experiment was obtained from the 50 kv accelerator described by Kirkaldy ( 1 9 5 1 ) . Hydrogen from a s t e e l storage b o t t l e was admitted to a pyrex discharge tube by means of an e l e c t r i c a l l y heated thermal leak. The discharge tube was surrounded by the tank c o i l of a 25 mc 300-watt o s c i l l a t o r , which ionised the gas. The protons were drawn from the discharge tube through a small ( . 0 6 " ) hole by means of a bottom extraction probe p o t e n t i a l . They were then accelerated down a column by means of a continuously variable d.c. p o t e n t i a l produced by a Ferranti 50-kv X-Ray transformer r e c t i f i e r set with a se- parate smoothing f i l t e r . The voltage was determined by measuring the current through a 60 megohm r e s i s t o r chain. The beam was focussed by two e l e c t r o s t a t i c lenses i n the accelerating column, the f i r s t just below the extractor and the second several inches lower. Since the second lens operated on the main accelerating p o t e n t i a l , the focus was markedly dependent on the operating voltage, being much better at high energies than at low. Due to incomplete i o n i s a t i o n and recombination i n the ion source the beam consisted p a r t l y of Hg and H^ (the l a t t e r greatly enhanced by the presence of traces of nitrogen). Normal percentages of molecular ions were as follows: 6 Normal Operation With small a i r leak H + 75$ 50$ H2+ 15$ 20$ H 3 + 10$ 30$ Due to t h e i r d i f f e r e n t charge-to-mass r a t i o , however, these components were e a s i l y separated by a water-cooled e l e c t r o - magnet located at the lower end of the accelerating column. This also served to bend the H+ beam through 90° so that i t was t r a v e l l i n g h o r i z o n t a l l y . A 1 .2 cm by 0 . 6 cm de f i n i n t s l i t was located 8 | " beyond the magnet e x i t , attached to the bottom of a l i q u i d a i r trap which served to prevent condensable vapors from contaminating the target. The defining s l i t was maintained at +90 volts i n order to i n h i b i t the emission of secondary electrons and also to c o l l e c t the secondary electrons emit- ted by the other metal surfaces i n the tube. A wire gauze prevented charge from c o l l e c t i n g on the areas of glass surface i n the tube. The heavy water target was frozen on a copper backing plate attached to the bottom of another l i q u i d a i r trap and located 72" beyond the defining s l i t . The backing plate and trap could be raised to lay a target or lowered into the beam, as shown In figure 1. The target was held at +15OV to suppress secondary electron emission. The DgO dispenser consisted of a small v i a l of D2O together with an o i l manometer. A volume of D2O vapor at a pressure indicated by the manometer was allowed to FIG. I TARGET CHAMBER i 2 -i »- 3 -+ IN C H E S zz; O- RINGS LI QUID A I R TRAP WINDOW TO D 2 0 DISPENSER *• LUCITE INSULATOR Cu BACKING PLATE STOP 1.2 cm. x 0-6 cm, 7 d i f f u s e through a glass wool plug and to freeze i n a t h i n layer on the backing plate. Since the only requirement f o r th i s experiment was that the target be thick enough to stop the beam e n t i r e l y , no detailed measurement of target t h i c k - ness was required. -5 A pressure of 10 m̂m Hg was required to prevent excessive attenuation of the beam by c o l l i s i o n with a i r molecules. This was maintained by means of a D i s t i l l a t i o n Products 275 l i t e r / s e c . o i l d i f f u s i o n pump together with a Cenco Megavac rotary pump. Condensable vapors were frozen out on a large l i q u i d a i r trap above the d i f f u s i o n pump. An a u x i l i a r y valve system at the ex i t end of the magnet a l - lowed the target chamber and defining s l i t to be removed without l e t t i n g a i r into the source and accelerating column. The system pressure was measured by means of a P i r a n i gauge and a Sylvania VG1 i o n i s a t i o n gauge. The beam current available varied considerably with the accelerating p o t e n t i a l . Above 3 5 k v . , a current of 60 to 80 microamp could be obtained at the target. At 2 4 k v . , however, the best obtainable target current was about 25 microamp. 2 . Counter and Electronics The D(p, / )He3 /-rays were detected by a Harshaw thallium activated sodium Iodide s c i n t i l l a t i o n counter. The c r y s t a l was c y l i n d r i c a l , 4 . 5 0 + 0 . 0 0 5 inches long and 2 . 7 5 + 0 . 0 0 5 inches i n diameter. I t s front surface was located O.407+O.O3O inch from the front of i t s aluminum container. 8 The c r y s t a l was o p t i c a l l y coupled to a Dumont K1213 photo- m u l t i p l i e r tube, whose output was fed into a preamplifier. The preamplifier c i r c u i t and the wiring diagram of the photomultiplier are shown i n figures 2 and 3 . The c r y s t a l , photomultiplier and preamplifier were a l l housed i n a 16" length of 4" diameter brass tube. The output from preamp- l i f i e r was further amplified and fed into the laboratory's Computing Devices of Canada one hundred-channel Kicksorter for spectrum analysis. The counter e f f i c i e n c y had previously been mea- sured using the P 1^(p,ay reaction. The e f f i c i e n c y i s defined as the r a t i o of the number of counts above the h a l f - energy bias to the number of gamma rays incident on an area equal to that of the c r y s t a l face and located at the effec- t i v e center of the c r y s t a l . The depth of the e f f e c t i v e center i s defined as the distance which must be added to the source-to-crystal face distance to give an inverse-square law r e l a t i o n between number of counts and distance. For 6.14 Mev y-rays the e f f e c t i v e center i s 5»5±P«5 cm behind the front of the aluminum can and i t s e f f i c i e n c y i s . 7 6 1 . This corresponds to an e f f e c t i v e center depth of 5.4+0.5 cm and an e f f i c i e n c y of . 7 3 for the 5 . 5 Mev y-rays detected i n t h i s experiment. The gain of the system and the k i c k s o r t e r bias varied with time and so i t was necessary to c a l i b r a t e the system before and a f t e r each run. This was done by measuring the spectrum of a radiothorium (Th ) source. The f i n a l step i n t h i s decay chain i s the emission of a 2 . 6 1 5 Mev 3.9K 4 7 0 K , VALOR PT 5 3 0 D 27 K TEST lOOpf , N H h IOO a A A A i i 7 ^ I N 4 5 9 1 — w - - 1 - H T 2 9 5 V • 0 5 / » f ^ L i O U T ( -VE) I N T O i o o n FIL. 2 2 0 pf £ T > F T CLIPPING CABLE =J=.02 1.5 K 470 O- ' |0K I 0 2 J _ & 8 0 pf FIG. 2 HEAD AMPLIFIER 9 gamma ray. The l i n e a r i t y of the system was checked by turning o ff the high tension on the photomultiplier and connecting a mercury relay pulse generator (figure 4) to the input of the preamplifier. This pulse generator works as follows: The . 1 fxf condenser i s kept charged by the battery. When the relay i s switched to pin 2 , the 470 pf condenser charges through 470 ohms i n . 2 microsecond. When the relay swit- ches over to pin 4 , the same condenser discharges through 100 K to ground i n 47 microsecond. Since the relay operates on the l i n e voltage, t h i s y i e l d s a long pulse of 6 0-cycle frequency. The d i f f e r e n t i a t i o n c i r c u i t on the output pro- duces a short, sharp pulse ( r i s e time . 2 microsecond, f a l l time 50 microsecond). The opposite p o l a r i t y pulses are in h i b i t e d In the preamplifier. The pulse height i s accur- atel y controlled by the 100 K helipot. Pulses of various sizes can be fed to the kicksorter, producing sharp peaks one or two channels wide. The generator i s l i n e a r and can be used to cal i b r a t e the kic k s o r t e r spectra. 3. Current Integrator The t o t a l beam s t r i k i n g a target was integrated over a run using the current integrator described by Edwards ( 1 9 5 1 ) . This device measured the voltage on a condenser which was charged by the incoming current. When the con- denser reaches a certain voltage i t i s discharged and the cycle repeats. Two of these condensers were connected i n p a r a l l e l and only one was discharged, while the other con- tinued to c o l l e c t current.A schematic diagram i s shown i n FIG. 3 PHOTOMULTIPLIER CONNECTIONS 10 figure 5 . Since the currents to be integrated were too large for the device to handle, they were divided into two parts, one going to ground through a 50K 1$ carbofilm re- s i s t o r and the other going to the instrument v i a a 470K Vfo wire-wound r e s i s t o r . The device was calibrated each day, as the voltage measurement c i r c u i t and the zero setting tended to d r i f t . 4. E l e c t r o s t a t i c Quadrupole Lenses In an attempt to increase the current s t r i k i n g the target, a p a i r of e l e c t r o s t a t i c quadrupole lenses were constructed. The theory of these lenses i s discussed by Enge ( 1 9 5 9 ) . An e l e c t r o s t a t i c quadrupole lense normally consists of four right hyperbolic c y l i n d r i c a l pole faces arranged i n opposing pairs at right angles. To each p a i r i s applied the same p o t e n t i a l , one p a i r being charged p o s i - t i v e l y and the other negatively. A charged p a r t i c l e enter- ing the lens w i l l be focused toward the axis i n the plane of two of the electrodes and away from i t i n the perpendi- cular plane, since i n these planes the e l e c t r i c f i e l d strength i s proportional to the distance from the axis, to a very good approximation. Two such lenses arranged i n series with corresponding poles oppositely charged produce a net focusing effect as shown by Enge. A p a i r of lenses were constructed as shown i n figure 6. The electrodes were made c i r c u l a r instead of hyperbolic, as c i r c u l a r sections of brass pipe were a v a i l - able, and mounted on rods through kovar seals. FIG. 4 PULSE GENERATOR POLARITY REVERSING SWITCH MOV 6 0 ~ —-o WE 2 7 6 D Hg RELAY 4?on f A A - I 4 7 0 <? FIG. 5 CURRENT INTEGRATOR (SCHEMATIC) IN RELAY O A O- VOLTAGE MEASURING CIRCUIT Due to the diffuseness of the beam entering the lenses, the electrodes picked up considerable current. Hence low Impedance North East Instrument Company power supplies were used. Since the energy of the beam was small, the voltage required on the lenses as constructed was ex- pected, using Enge's figures, to be less than 1000 volts even f o r a 45 kev beam. The lenses were tested by placing them together a f t e r the magnet and also by placing one above and one below the magnet. When both followed the magnet, a strong fo- cusing effect was observed. The beam could be reduced to a th i n l i n e l / l 6 " across either h o r i z o n t a l l y or v e r t i c a l l y , or into an i r r e g u l a r spot about i n diameter on the target. However, the increase i n the t o t a l current was very small, i n d i c a t i n g that even without the lenses, a l l the current coming through the magnet struck the target, a l b e i t i n a much larger spot than with them. A lens above the magnet had very l i t t l e focusing effect at a l l . Hence the lenses were not used during the experimental runs. 0 FIG. 6 QUADRUPOLE LENS - SECTIONAL VIEWS CHAPTER I I I - PROCEDURE 12 In order to f i n d out how many f i l l i n g s of the dispenser would be necessary to produce a target thick enough to stop the beam, a rough estimate of the volume of the dispenser (65cm ) was made. This, together with a knowledge of the vapor pressure of DgO at room tempera- ture (l.7cmHg), the density of ice and the stopping power of ice as given by Wenzel and Whaling (1952), enabled the required number of f i l l i n g s to be calculated. A crude guess was made that only one f i f t h of the DgO a c t u a l l y froze on to the target and that t h i s froze uniformly on the backing plate. In t h i s manner i t was estimated that at 40 kev three f i l l i n g s would be required. This was pro- bably more than enough but f o r the purposes of t h i s experi- ment i t was better to have the target too thick than too t h i n . After a target had been l a i d on the backing plate i t was lowered into bombarding p o s i t i o n and set at 30° to the beam d i r e c t i o n , so that no y-rays emitted into the s o l i d angle subtended by the counter at the 90° p o s i t i o n would be attenuated by passing through the copper pl a t e . For most of the runs the counter was moved back so that i t s front face was 4.5cm from the target chamber, i n an attempt to improve the angular resolution at the expense of the measured y i e l d . o In t h i s manner the y i e l d at 90 to the beam was measured for Ep=24.0, 34.2, 40.7 and 47.2 kev. Angular d i s t r i b u t i o n measurements were made at 34.2 and 40.7 kev. The target current was measured by connecting 13 the top of the l i q u i d a i r trap on which the target was mounted through a microammeter to the current integrator. I t was found, despite the system of stops that prevented any of the d i r e c t beam from s t r i k i n g the walls of the target chamber, that a current equal to about 20$ of the target current was picked up on the chamber. This was believed to be due to i o n i s a t i o n of the residual gas i n the chamber by the beam. The p o s i t i v e ions thus produced go to the chamber walls while the elctrons are attracted to the target, causing the microammeter to read less than the actual beam current. To correct for t h i s , the outer w a l l of the chamber was connected to the integrator as w e l l as the target i t s e l f . I t was observed that the y i e l d decreased gradu- a l l y during the course of a run, This e f f e c t , known as target deterioration, was probably caused by deposition of a f i l m of o i l or other contaminant on the target. I t appeared to be p a r t l y beam dependent as i f the contaminant molecules were carried along by the beam. To correct for t h i s deterioration the bombardment of each target was separated into a series of short runs over an integrated current of about t h i r t y - f i v e millicoulombs, and the yields extrapolated back to zero time. The y i e l d generally de- creased by h a l f a f t e r about two hundred millicoulombs or an hour and a h a l f of bombardment, a f t e r which period a target was discarded. Before and a f t e r bombardment of each target the counter and electronics were calibrated by measuring the 14 spectrum of a 0 . 0 2 9 mc RdTh source superposed on one pro- duced by the pulse generator described previously. Several measurements of the room background were made, leaving the counter on for several hours at a time both during the day and overnight. A t y p i c a l background spectrum i s shown i n figure 7- A t o t a l of 38 hours yielded an average value of 9 . 8 1 + 0 . 0 7 counts per minute i n the energy range 2 . 7 6 to 5 - 8 Mev. A measurement of the beam- dependent background made by bombarding the backing plate for 100 integrator cycles ( 170 millicoulombs) yielded a result of 0 . 0 + 0 . 1 5 counts per millicoulomb, so that the beam dependent background was considered to be n e g l i - g i b l e . The time-dependent background was subtracted from a l l the runs which were also corrected for absorption i n the target chamber and for counter e f f i c i e n c y . The e f f i - ciency, as defined, has been shown to be independent of source distance, so no additional correction was necessary for the short range used. Since the v e l o c i t y of the He-1 nuclei formed was expected to be small, the Doppler s h i f t correction discussed by G r i f f i t h s and Warren (1955) was neglected. 600 BACKGROUND RUN JULY 21 5 hrs. 5 0 0 - NUMBER OF COUNTS 400 - 3Q0h 200l - IOOL CHANNEL NUMBER FIG. 7 A TYPICAL BACKGROUND SPECTRUM CHAPTER IV - RESULTS 15 1. Angular D i s t r i b u t i o n As the angular d i s t r i b u t i o n was expected to conform to the ( s i n 6 +B) r e l a t i o n found at higher ener- gies by Fowler et a l . , the chief interest i n measuring i t lay i n the determination of the size of the i s o t r o p i c component. In any case, due to the low y i e l d and r e s u l - t i n g poor s t a t i s t i c s , i t was expected that an attempt to detect deviation from t h i s r e l a t i o n would lead to incon- clusive r e s u l t s . Therefore, a simple estimate of the value of B was obtained by measuring the yields at 90° and zero degrees. To permit correction for target deterioration the counter was moved back and forth from 90° to 0° several times during the bombardment on each target. One measure— o 2n ment at 45 gave a result i n accord with the s i n Q d i s t r i - bution, to within the s t a t i s t i c a l error. Angular d i s t r i b u - t i o n measurements were made at 3 4 . 2 and 4 0 . 7 kev but not at 24 .0 and 4 7 . 2 kev, since at 2 4 . 0 the y i e l d was very low, and at 4 7 . 2 the apparatus became unstable, tending to produce high tension sparks or discharges from the o s c i l - l a t o r c o i l , which sent large surges back into the supply l i n e s , blowing fuses, cutting o f f the ion source discharge, and sometimes even stopping the kick s o r t e r . Spectra at 90° and 0° are shown i n figure 8 . Since the counter subtended a f i n i t e s o l i d angle at the target, the measured angular d i s t r i b u t i o n was somewhat smeared. That i s , the measured number of CHANNEL NUMBER TYPICAL D ( p , y ) H e 3 SPECTRA 16 counts at 90° was somewhat less than the d i f f e r e n t i a l y i e l d exactly at 9 0 ° , and the number at 0° correspon- dingly too high, leading to a high estimate of B. This was corrected by using a modification of a method devised by Rose (1953) for correcting angular c o r r e l a t i o n data for the same ef f e c t . I f the d i s t r i b u t i o n i s of the form (1) W(0) = ^ a ^ c ' o s f l ) n and i s measured by a c y l i n d r i c a l c r y s t a l of length t and radius r, distant h from the source, the measured d i s t r i b u t i o n w i l l be /w ( 0')(l-e" T X)d& (2) W(0)= -7- / ( l - e _ r x ) d i l where XI i s the c r y s t a l s o l i d angle,r i s i t s absorption c o e f f i c i e n t (Grodstein 1957) and x i s the distance t r a - v e l l e d through i t by the y-ray. I f /J i s the angle between the ray and the c r y s t a l axis, x i s given by x( j8) = t secj3 0 < fi < t a n " 1 r = £* x( £ ) = r esc ft -h sec £ £'< 0 < t a n - 1 r =/.-i h Furthermore, since 9' = 9 + /9,P-L(cos 9')= P 1 ( c o s 0 )P 1(cos /8 azimuthal terms which do not contribute to the i n t e g r a l . By substituting ( l ) into (2) i t i s easy to see that a"n the c o e f f i c i e n t of P n i n W( 9 ) should be corrected by 17 a factor ^o/J n. where (3) J n = y r X P n ( c o S / 8 ) ( l - e - r x ( ^ ) ) s i n i 9 d / 3 . JQ Only two terms of the series, P Q and P 2, are required to f i t a slrfiQ d i s t r i b u t i o n since A ( s i n 2 0 +B) = l+aP 2(cos Q ) = l+ | . ( 3 c o s 2 0 - l ) y i e l d s a • - j- 4 or B = - 2 U * a ) 3B+T 3 a 2 Therefore i f a =Jo a, B= - 2-- 2_= - 2 + 2 J 2 _ ( 2g +1) 3 3 a 3 2 W = - 2 + 2 J 2 + E J 2 Values of J Q and J 2 were found by graphical i n - tegration f o r the values of h used i n t h i s experiment. For the value at which the angular d i s t r i b u t i o n s were mea- sured, 801 cm from the center of the target to the front face of the c r y s t a l , the value of J 2/J0 l s 0 . 9 1 4 . The measurements at 0° had also to be corrected f o r absorption i n the backing plate which was found to be 0 . 0 3 1 9 + 0 . 0 0 7 or 0 . 0 8 1 1 + 0 . 0 0 1 8 cm thick. The absorption c o e f f i c i e n t s f o r t h i s and for the brass of the target chamber were taken from Davisson and Evans ( 1 9 5 2 ) . The values of B obtained were Ep(kev) B 3 4 . 2 0 . 2 7 + 0 . 1 1 40 .7 0 . 2 9 5 + 0 . 1 1 The errors quoted are s t a t i s t i c a l i n nature. Thus the percentage of i s o t r o p i c contribution i s consider- ably larger at these energies than i t was i n the 300 kev to 1 Mev range. The evidence i s inconclusive as to whether or not i t i s s t i l l increasing as the energy decreases. 2 . The Absolute Cross Section The absolute cross section f or a reaction i s defined as the i n t e g r a l of the d i f f e r e n t i a l cross section over a l l angles. Hence to obtain the absolute cross sec- t i o n i t i s f i r s t necessary to know the t o t a l thick-target y i e l d per incident proton, integrated over a l l angles. Since the angular d i s t r i b u t i o n i s approximately known, the t o t a l y i e l d can be obtained d i r e c t l y from the d i f f e r e n t i a l y i e l d at 90° by integration. For t h i s purpose, at each energy, a series of runs was taken on a single target and the number of counts per miHicoulomb, with background subtracted, was plotted against time and extrapolated back to the s t a r t of bombard- ment (see figure 9 ) . The angular d i s t r i b u t i o n runs were plotted s i m i l a r l y and served as an I n i t i a l check on the deterioration. The i n i t i a l y i e l d figures f o r each energy were averaged and corrected f o r counter e f f i c i e n c y (multi- p l i c a t i o n factor j~ 1 .37) and for absorption i n the l / l 6 " brass of the target chamber (factor 1 . 0 4 ) using an average (weighted 67 Cu33 Zn) of the absorption c o e f f i c i e n t s given by Davisson and Evans (1952) for copper and zinc. The error introduced by the f i n i t e s o l i d angle subtended by the counter at the target was corrected by the following method. Let N=A(sin 9 +B) be the number  of /-rays per unit s o l i d angle. I f x i s the number emit- o ted at 90 into the counter s o l i d angle,0^ , then a value of A may be obtained from x using x=A e(l+B)o) 0 . This value i s incorrect, however, as i t assumes uniform i n t e n s i t y over the entire area of the counter. Correctly, A may be obtained from r o x = A c y ^ ( s i n 9 +B)S|. = A c l c where dS i s the unit of surface area on the plane p a r a l l e l to the counter face through i t s e f f e c t i v e center. By changing variables from r, 9 , and <f> , the angle of rotation about the beam d i r e c t i o n , to D the distance from the t a r - get to the ef f e c t i v e center of the c r y s t a l , x the distance i n the e f f e c t i v e center plane away from the center, and /3 the angle i n t h i s plane we obtain: R r2.iT 2 CO r  dir - Jo Jo J r ! § = + \ ) Dc+ xc D- and R r 2ir 2 I = / / D xdxdjB +Bco0 0 / O ( D 2 + X 2 ) ( D S + X 2 O O S 2 / 9 ) where R i s the c r y s t a l radius. I can be integrated by p a r t i a l fractions and expansion of log(l+Z ) to obtain a solution i n series form. Substitution for a l l the terms greater than. .1% of the largest term yi e l d s the following r e s u l t s . A c = ofa (B+i:) = c I A T D(cm) <*>n (steradians) c _e c_ 7 . 7 . 5 9 2 . 7 3 2 1 . 0 3 7 + . 0 0 3 8 . 9 . 4 5 1 . 5 6 3 1 . 0 2 8 + . 0 0 3 1 1 . 8 . 2 6 5 . 3 3 4 1 . 0 1 8 + . 0 0 2 1 2 . 4 . 2 4 1 . 3 0 4 I .OI6+.OO15 The l a s t coluraiis included to indicate the size of the error incurred by assuming that the i n t e n s i t y i s constant over the counter s o l i d angle. In t h i s c a l c u l a t i o n B was assumed to take on the value 0 . 2 8 3 , the average of the two values previously obtained. This assumption that B i s con- stant throughout the narrow energy range of t h i s experi- ment should not lead to serious errors. Values of A at each energy were calculated using A = (1^")" ^ Now the t o t a l y i e l d i s given by r 2 w r w 2 Y = A / / ( s i n 9 +B)sin0 d 0 d<£ Jo Jo 4 = 3"irA(2+3B) Values of Y were calculated using (6) Y = 4 7 r 3 ^ j 2 | 3 E ) 1 .6 x 1 0 " 1 6 r-rays/proton. These are tabulated below Y( y -rays per A( Y -rays per unit s o l i d incident proton kv angle per millicoulomb) x 10"^) 24.0 1 7 . 4 + 3 . 3 3.34+0 .45 34.0 41.0+5.8 7.82+0.65 40 .7 75.9+10 .9 14.5+1.3 47.2 114.3+14.6 21.8+1.6 The t o t a l t hick target y i e l d Y i s plotted against incident proton energy i n figure 10. To obtain the cross-section as a function of energy from the thick target y i e l d , the theory of a thick target must be considered. A th i c k target i s defined as one In which a l l the bombarding p a r t i c l e s come to rest. At any distance x into the target where the bombarding p a r t i c l e s are s t i l l moving with energy E, dY = 2Ndx <r(E) = 2N |£ <r(E)dE 2C4 TOTAL YIELD Y x 10 X-rays per proton -14 I5f 5h t / / /1 / A / / o FIG. 10 10 20 30 ENERGY OF BOMBARDING PROTONS ( k e v . ) TOTAL YIELD CURVE 40 50 21 where N i s the number of DgO molecules per cubic c e n t i - meter of target and o'CE) i s the cross-section i n square centimeters. The factor 2 appears because there are two deuterium atoms i n each DgO molecule. The stopping power dE i s d e f i n e a i n terms of dx the molecular stopping cross-section e by ̂ 5== -N e (E) dx Using t h i s stopping cross-section, the y i e l d i s given by f E l (7) Y(Ex) = / 2 q-(E) dE €(E) There have been several attempts made to deter- mine €(E) for protons i n water. Hirschfelder and Magee (19^8) calculated, using a theory due to Bethe, the values of the stopping number B for hydrogen and oxygen, where « = 2 ir e 4 M B(E) m E In t h i s equation e i s the electronic charge and M/m i s the r a t i o of the mass of the proton to that of the electron. A simple addition (Bragg theory) of the stopping cross - sections thus obtained gives a value of « for HgO In ex- celle n t agreement with the experimental results of Wenzel and Whaling (1952) for D 2 0 i c e . In t h i s l a t t e r work, i t was assumed that the cross-section for 0 1 ^ ( p , p ) 0 1 ^ scatter- ing was given by Rutherford's formula and « calculated from the y i e l d of scattered protons from DgO i c e . However, l a t e r work by P h i l l i p s (1953) and Reynolds et a l . (1953) on hydrogen, oxygen and water vapor suggests that the stop- ping cross-section for water vapor i s 1 5 - 2 0 $ higher than Hirschfelder and Magee estimated and, furthermore, that i t i s not equal to a simple sum of those for hydrogen and 22 oxygen. The various estimates are plotted i n figure 11 with the errors quoted for them. Since Wenzel and Whaling's values for D^O i c e were for conditions closest to those employed i n t h i s work, they have been used i n the following calculations. There are several ways to calculate <r from equa- t i o n ( 7 ) . One i s simply to d i f f e r e n t i a t e Y so that dY| = 2 <r(Ex) This gives cr at once. However, the slope of the y i e l d curve i s not c l e a r l y determined, especially at the end points 2 4 . 0 and 4 7 . 2 kev. The errors thus incurred are rather large and indeterminate, so t h i s method was abandoned. An estimate of the slope of the y i e l d curve with a better known error can be obtained by taking the difference between the measured points and by assuming that theAY/ ^-g thus obtained i s the slope at the mid-point of the i n t e r v a l . Since the curve i s smooth and nearly a straight l i n e , espe- c i a l l y at the upper energies, t h i s should give a good estimate of the energy at whichAY/^ E i s supposed to take on the value obtained. Then A Y / ^ E can be equated to 2 cr / € at the midpoint. This, of course, cuts by one the number of cross-section points obtained, but i t i s expected that the s t a t i s t i c a l errors quoted are accurate estimates. These results are plotted as Method 1 i n figure 1 2 . I f the cross-section i s assumed to be controlled by p e n e t r a b i l i t y considerations, as i t i s expected to be € X 10 ev-cm { FROM WENZEL AND WHALING (1952) | FROM PHILLIPS ( l 9 5 3 ) FROM HIRSCHFELDER AND MAGEE (1948) _j i 10 2 0 PROTON ENERGY (kev) 3 0 4 0 5 0 FIG. STOPPING CROSS-SECTION FOR PROTONS IN D 20 at the energies involved i n th i s experiment, i t should have an energy dependence of the form <r = KE^exp - [ J L ^ t E"*) where M i s the proton mass and K i s a constant. Values of CT/k can be calculated and i f plotted as a function of Ke energy. This can be integrated using a planimeter and a value of X. obtained f o r any desired energy. Using the ex-K perimental values of Y, values of K can be obtained. The results are given below: E(kv) Y/K x 10 1 2(kev cm 2)" 1 Y x l O " 1 4 Kxl0~ 2 8kev cm2 24.0 57.5+2.3 3.34+0.45 5.81+1.02 34.2 161.3+6.5 7.82+O.65 4.84+0.58 40.7 256.3+IO.3 14.7+1.3 5.65±0.73 47.2 370.0+14.8 21.8+1.6 5.89+0.67 Ave rage 5.5 2+0.77 Using these values of K and the calculated values of <f/K, the following values of <f were obtained and plotted i n figure 9 as Method 2. E(kv) o-ACkev" 1 ) crxlO~ 3 2cm 2 24.0 6 . 9 l x l 0 " 5 4.09+0.71 34.2 1.47X10"11" 6.63+0.81 40.7 1 . 7 9 x 1 0 I O . 1 1 + 1 . 3 1 47.2 2.22x10"4 13.04+1.48 As can be seen these give a reasonable agreement with Method 1.. A plot of the function o- =5.52xl0- 2 8E- 1 exp " ( 1' 254xl0-3 E-ij i s included i n figure 9. 15 0» « 1 1 1 1_ O 10 2 0 3 0 4 0 5 0 PROTON ENERGY (kev) FIG. 12 TOTAL CROSS-SECTION FOR D(p,y)He 3 CHAPTER V - CONCLUSIONS The errors quoted i n the above results and i n - dicated i n the graphs are purely s t a t i s t i c a l i n nature. Some other errors have been discussed and corrected. However, there are some uncertainties incurred i n t h i s experiment which should be discussed. The e f f e c t i v e center depth and e f f i c i e n c y of the counter were measured for a broad p a r a l l e l f l u x of / -rays. In our experiment, due to the close proximity of the counter to the target, t h i s was not the case because the y -rays emanated from a small source. Hence a few y -rays might be detected i n a larger s o l i d angle than that quoted. Since they passed through a r e l a t i v e l y small thickness of c r y s t a l , however, they were less l i k e l y to be detected. Hence the error incurred here Is l i k e l y to be not bigger than the s o l i d angle corrections involved i n the angular d i s t r i b u t i o n function c a l c u l a t i o n , say about 5$. There i s a small uncertainty (2mm) i n the p o s i - tioning of the spot on the target where the beam struck, leading to an error of about 2$ i n D the distance to the eff e c t i v e center. This added to the 0.5 cm uncertainty i n the p o s i t i o n of the e f f e c t i v e center makes an error of about 10$. Runs were made at three d i f f e r e n t distances (and corrected for target deterioration)to check the po s i - t i o n of the ef f e c t i v e center for the small counter—to- 25 target distances used i n t h i s work. The results are p l o t - ted i n figure 13. The e f f e c t i v e center deduced from these results agrees, to within the s t a t i s t i c a l error, with the 5.5cm+0.5cm eff e c t i v e center depth found for the counter previously. I t has been mentioned that there was a consi- derable current detected on the walls of the target chamber despite the fact that the beam was collimated so that i t f e l l e n t i r e l y on the target. This current was believed to be due to i o n i s a t i o n of the residual gas i n the chamber, and to correct for i t the chamber was connected to the target. However, some of the ions thus formed may have been repelled by the +150V on the target chamber and c o l - lected elsewhere. Furthermore, the chamber may have collected a small number of secondary electrons from other parts of the tube, increasing the difference between the actual beam i n t e n s i t y and that calculated from the measured current. The magnitude of t h i s uncertainty i s estimated to be not more than 5$. Due to the lack of energy-defining s l i t s i n the magnet system, the precise k i n e t i c energy of the protons incident on the target i s unknown. Errors due to the size of the beam above the magnet and the magnet dispersion, together with uncertainties i n the c a l i b r a t i o n of the 60 megohm r e s i s t o r chain, fluctuations i n the high tension supplies and the Maxwellian v e l o c i t y d i s t r i b u t i o n i n the Ion source, lead to a further 5$ uncertainty i n the energy of the bombarding protons. .4 DISTANCE FROM TARGET TO FRONT OF COUNTER HOUSING ( c m ) FIG. 13 VARIATION OF COUNTING RATE "WITH DISTANCE N = COUNTS PER MILLICOULOMB Thus the following errors have not been accounted for i n our estimate of the cross-section. Point source effect 5$ Source to counter distance 10$ Unmeasured current 5$ Dispersion 5$ Total estimated error 14$ The error i n the angular p o s i t i o n of the counter- was about 2$, too small to increase t h i s t o t a l . Other small uncertainties such as d r i f t i n electronics, and fluctuations i n the magnet current are expected to c o n t r i - bute no more than 1$ to the error. Hence we may conclude from t h i s experiment that at low bombarding energies the cross-section for D(p,y )He^ increases rapidly with energy, as i s expected i f i t depends c h i e f l y on exponential p e n e t r a b i l i t y . The s-wave component of the gamma ray y i e l d i s much larger r e l a t i v e to the p- wave contribution than i t was found to be at higher energies i n d i c a t i n g a d i f f e r e n t energy dependence for each component. A more detailed study would be required to separate the two components as functions of energy. I t seems l i k e l y from the fact that the " i s o t r o p i c " component decreases less rapidly with energy, that i t actu- a l l y i s an s-wave contribution and hence i s r e a l l y i s o t r o p i c and that i t s true angular dependence i s not obscured by the p-wave dependence. However, a much more accurate measure- ment of the angular d i s t r i b u t i o n , taken more slowly to permit larger y i e l d s and at many more angles would be re- quired to prove t h i s . Suffice i t to say, however, that t h i s work yie l d s results i n f a i r agreement with t h e o r e t i - c a l predictions and serves as a basis f o r further i n v e s t i - gations, both experimental and t h e o r e t i c a l i n nature. BIBLIOGRAPHY 1. Cameron, A.G.W., Private Communication, with Dr. G.M. G r i f f i t h s , i960 2. Curran, S.C. and Strothers, J . , Proc. Roy. Soc. 172, 72, 1939 3. Davisson, CM., and Evans, R.D. Rev. Mod. Phys. 24, 79> 1952 4< Edwards, M.H., M.A. Thesis, U.B.C. 1951 5. Enge, H.A., Rev. S c i . Inst., 30, 248, 1959 6. Fowler, W.A., Lauritsen, C.C., and Tollestrup, A.V., Phys. Review. 76, 1767, 1949 7. G r i f f i t h s , G.M. and Warren, J.B., Proc. Phys. Soc. 68, 78I, 1955 8. Grodstein, G.W., N.B.S. Report 583. 1957 9. Kirkaldy, J.S., M.A. Sc. Thesis, U.B.C. 1951 10. L a i , M., Ph.D. Thesis, U.B.C. 1961 11. Larson, E.A.G., M.A. Thesis, U.B.C. 1957 12. P h i l l i p s , J.A., Phys. Rev. 90, 532, 1953 13. Reynolds, H.K., Dunbar, D.N.F., Wenzel, W.A., and Whaling, W., Phys. Rev. 92, 742, 1953 14. Rose, M.E., Phys. Rev., 91, 610, 1953 . 15. Singh, P.P., G r i f f i t h s , G.M., Ssu, Y.I., and Warren, J.B. Can. J . Phys., 3J_, 866, 1959 16. Wenzel, W.A., and Whaling W., Phys. Rev., 8_J_, 6l0, 1952 17. Wilkinson, D.H., P h i l . Mag. 43, 659, 1952

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