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The absolute cross section for the reaction D(p,a)3 He from 400 Kev to 100 Kev 1969

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THE ABSOLUTE CROSS SECTION FOR THE REACTION D(p,tf)3He FROM 400 KeV TO 1100 KeV by RICHARD LLOYD HELMER B.A.Sc, University of Br i t ish Columbia, 1 9 6 6 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in the Department of PHYSICS We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA Apr i l , 1 9 6 9 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 f o r 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 representa- t i v e s . I t i s understood that copying or publication of t h i s thesis f o r f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of Physics The University of B r i t i s h Columbia Vancouver 8, Canada Date: A p r i l , 1969 ABSTRACT 3 The absolute cross section of the reaction D(p,^) He has been measured in the energy range from 400 Kev to 1100 Kev in the laboratory system. A target of deuterated polyethylene was used to measure the relat ive y ie ld of the reaction over this range, and the results were normal- ized to an absolute measurement made with a deuterium gas target. The reaction i s of interest because i t enables some information to be obtained about the forces binding three nucleons together. It also has some significance in a number of astrophysical processes. In order to determine the cross section, the in t r ins ic eff iciency of a 5 inch by 4 inch sodium iodide crystal sc in t i l l a t ion counter was meas- ured by simultaneous alpha part ic le and gamma ray counting on the 340 Kev resonance of the reaction "^F(p,<*#)^0. The int r ins ic eff ic iency of the de- tector was found to be .679 - .03 for the 6.14 Mev gamma rays from this reaction, with the part icular geometry used. The absolute cross section for the reaction D(p,̂ T)̂ He was found by the gas target measurement to be 2.33 - .07 microbarns for an incident proton energy of 643 kev. TABLE OF CONTENTS ABSTRACT i i TABLE OF CONTENTS i i i LIST OF TABLES • ' LIST OF FIGURES . « v i ACKNOWLEDGEMENTS . . v ± 1 CHAPTER I INTRODUCTION 1.1. General Introduction 1 1.2. Previous Work 3 CHAPTER II THEORY 2.1. The Angular Distribution 6 CHAPTER III EXPERIMENTAL APPARATUS 3.1. Target Chamber II 3.2. Targets 13 3.3. Detectors, Collimators, and Shielding 14 3*4* Electronics 16 3.5. Data Analysis , 16 3.6. Proton Beam 17 CHAPTER IV RELATIVE CROSS SECTION MEASUREMENTS 4.1. Experimental Apparatus • • 19 4.2. Procedure 22 4.3. Data Analysis and Results 22 CHAPTER V EFFICIENCY MEASUREMENTS 5.1. Introduction • 30 5.2. Apparatus 31 (a) Target Chamber"i..... •• 31 i i i i v (b) Fluorine Targets 33 (c) Alpha Detector Electronics 35 (d) Gamma Detector Electronics ............... 39 5.3. S o l i d Angle Calculations 39 (a) Alpha Detector ••••• 39 (b) Gamma Detector 42 5.4. Results 46 CHAPTER VI GAS TARGET AND ABSOLUTE CROSS SECTION 6.1. Introduction 48 6.2. The Gas Target 49 6.3. Current Integration 51 6.4. Experimental Procedure • • 54 6.5. Other Correction Factors 55 6.6. Results • 57 BIBLIOGRAPHY 6l APPENDIX COMPUTER PROGRAMS 62 LIST OF TABLES II-l Ratios of coefficients from the angular distr ibut ion measurements 8 II- 2 Smoothing factors 10 III- l Dimensions of the D-detector assembly • ••••• 16 III-2 List of the electronic units used in th is experiment 18 V-l Properties of the alpha detector 31 V-2 Alpha detector sol id angle 39 V-3 Uncollimated gamma detector geometry 46 V- 4 Crystal ef f ic iencies • 47 VI- 1 Current integrator cal ibration 54 VI-2 Absolute cross section measurements • • •• 58 LIST GF FIGURES I I- l Ratios of coefficients from the angular distr ibution measurements •• • 9 III- 1 The rotating target assembly 12 III- 2 A schematic diagram of the detector assembly 15 IV - 1 Detector-target configuration for the relat ive cross section runs 20 IV - 2 Block diagram of the electronic arrangement for the relat ive cross section runs 21 IV - 3 Typical spectrum after analysis by the NAILS computer program •* 24 IV - 4 Target decay from the 800 kev runs 25 IV - 5 Relative y ie ld curve obtained for each detector 27 3 IV - 6 Relative y ie ld for the reaction D(p,tf) He 28 V - 1 Fluorine - 19 target chamber 32 V - 2 Alpha part ic le window 34 19 V - 3 Excitation function for 7 F target used for the eff ic iency measurements 36 V - 4 Block diagram of the electronic arrangement for the crystal ef f ic iency measurements 37 239 V - 5 5.13 Mev Pu alpha part ic le spectrum 38 19 16 V - 6 Typical alpha spectrum from F(p,°00 0 40 V - 7 Typical gamma spectrum from ^F(p,*X )^0 • •• 41 V - 8 Relation of absolute eff ic iency to distance 44 V - 9 Uncollimated gamma detector geometry • 45 VI - 1 The gas target assembly 52 VI - 2 The absolute cross section for the reaction D(p,tf) H e . . . . . . . 59 v i ACKNOWLEDGEMENTS I wish to express my gratitude to a l l the members of the Van de Graaff group for t h e i r help during the course of t h i s work. Par t i c u l a r thanks go to Dr. G. M. Bailey f o r his supervision of the experimental part, and to Dr. G. M. G r i f f i t h s for his assistance and very helpful suggestions during the w r i t i n g of t h i s t h e s i s . v i i CHAPTER I INTRODUCTION 1.1 General Introduction One key to understanding the properties of nuclei would be to d i s - cover the characteristics of the internucleon force. A correlation exists between various parts of the nuclear force and the detailed character of nuclear bound state wave functions. Since many th e o r e t i c a l studies have been made to relate d e t a i l s of the force system i n a quantitative way to the properties of few nucleon systems, i t i s important to obtain as much experi- mental information as possible about the bound states of n u c l e i , and particu- l a r l y l i g h t n u c l e i , where the many body aspects of the problem do not obscure the s p e c i f i c relations between nuclear structure and characteristics of the internucleon force. Direct radiative capture reactions provide a r e l a t i v e l y simple way of determining some of the properties of nuclear bound states and assessing nuclear models through comparing t h e o r e t i c a l l y predicted and experimentally measured cross sections. The s i m p l i c i t y i n comparison to other reactions arises because the t r a n s i t i o n which proceeds d i r e c t l y from a free nucleon state to a bound state i s produced by a r e l a t i v e l y weak coupling to the electromag- netic radiation f i e l d which does not produce a large perturbation on the system. Other direct reactions might be used to study the bound states, for example, the stripping reaction, i n which one nucleon from an incoming complex p a r t i c l e i s stripped o f f the complex and moves d i r e c t l y to a f i n a l bound state without forming an intermediate compound state. In t h i s case the interaction between p a r t i c l e s occurs through the medium of another p a r t i c l e and involves strong 1. 2" nuclear forces. This makes i t much more d i f f i c u l t to extract information about the nuclear forces since a knowledge of the nuclear forces i s required to understand the nature of the t r a n s i t i o n from one nuclear state to another. For the above reason and for further reasons noted below, a study 3 of the dir e c t radiative capture of protons by deuterium to form He should prove useful i n understanding the 3 nucleon system. F i r s t , t h i s reaction r e - 3 s u i t s i n the formation of He, which i s more t i g h t l y bound than the deuteron, 3 the only bound two body nucleus. Also He has both singlet and t r i p l e t two- nucleon spin configurations while the deuteron has only the t r i p l e t configura- 3 t i o n . Thus the structure of He should be more sensitive to the short range components of the nuclear force as w e l l as to the components which depend on the singlet spin configuration. Therefore a study of three body nuclei should provide more information about the internucleon force than can be obtained from the deuteron. Another reason why t h i s reaction i s of interest i s related to astro- 3 physics. The reaction D(p,#) He i s the second step i n the chain of reactions which supplies most of the energy i n the hydrogen-burning stage of the smaller main-sequence stars. This chain i s as follows: p + p — D + /3*+ T> 3 p + D — He + Y 3 3 4 He + ^He —- He + 2p Now although the rate of energy release of a main sequence star i s controlled by the f i r s t reaction since i t occurs by means of the very weak /3- i n t e r a c t i o n , i t i s l i k e l y that the reaction D(p,2f) He i s the f i r s t to supply nuclear energy as the star contracts, and i t may consequently have consider- able effect on the rate at which the star condenses to the main sequence, at least i f there i s as high a deuterium to hydrogen r a t i o i n the i n t e r s t e l l a r gas as i s found i n the earth. 3 In the early stages of s t e l l a r condensation, the reaction D(p,<5") He competes with the reaction D(d,n)^He which has a much larger cross section, but a smaller p r o b a b i l i t y of occurring since the concentration of hydrogen i s much greater than the concentration of deuterium. The l a t t e r reaction supplies neutrons to the i n t e r s t e l l a r gas which are then captured by the heavy elements and thus there may be sig n i f i c a n t changes i n some isotope r a t i o s from the p r i - mordial r a t i o s depending on the number of neutrons supplied. Clearly the num- ber of neutrons available for t h i s process i s dependent upon the i n i t i a l con- centration of deuterium and the amount of i t that survives long enough to pro- duce neutrons. Thus the isotope r a t i o s among the heavy elements could be affected by the reaction D(p, ZO^He, since much of the deuterium which would otherwise be available for the release of neutrons i s removed by t h i s reaction. 1.2 Previous Work Previous work on the reaction by Fowler, Lauritsen and Tollestrup (FO 49) indicated that the angular d i s t r i b u t i o n was of the form a + b s i n -e- 2 where the i s o t r o p i c part a was small but not zero. The presence of the s i n -©• component i n the angular d i s t r i b u t i o n l ed these workers to advance the hypoth- esis that the capture was mainly the re s u l t of an e l e c t r i c dipole t r a n s i t i o n 3 of a p-wave proton to the ground S - state of He. Their investigation of the y i e l d at 90^ for various bombarding energies showed that the reaction was non- resonant i n character, indicative of a direct capture process. In an ingenious experiment, Wilkinson (WI 52) showed that the gamma radiation at 90° was plane polarized with the e l e c t r i c dipole i n the reaction plane. This confirmed the hypothesis of Fowler et. a l . that the capture was the res u l t of_an EL t r a n s i t i o n . Wilkinson also suggested that the small i s o - t r o p i c component could arise from a small amount of spin-orbit coupling. How- ever, G r i f f i t h s and Warren (GR 55) found that the energy dependence of the y i e l d was different at 90° from what i t was at 0°, and t h i s raised the possib- i l i t y that the i s o t r o p i c component might arise from S-wave capture of the incoming protons. Verde (VE 50) had shown that magnetic dipole t r a n s i t i o n s could occur between S-states of the continuum and the bound three nucleon S- state as a r e s u l t of small non-central components i n the nuclear force. Further measurement by G r i f f i t h s et. a l . (GR 63) i n the energy range from 25 Kev to 45 Kev confirmed the hypothesis that the y i e l d at 0 ° followed an en- ergy dependence characteristic of incoming S-waves. The ground state of ^He i s known to have = and thus can con- t a i n the components (SA 55): 2 2 2 However, Derrick (De 60) has shown that the amplitudes of the P 4 and P components are n e g l i g i b l e . The continuum states a r i s i n g from the un- bound p + D system contains the following components which can give r i s e to electromagnetic t r a n s i t i o n s to the bound state components: 4s 2 > 4 P \ ^ 7 2 Thus the E l radiation i s the result of t r a n s i t i o n s from P to Si p states which gives r i s e to the main s i n •&• part of the angular d i s t r i b u t i o n . The i s o t r o p i c part arises mainly from Ml radiation, which results from trans- 4 2 i t i o n s from S to S^ states. Other tra n s i t i o n s which could be of some signif- icance are the following: E2 ( 2D - 2 S ) , E1( 4P - S>), EL( 4F - ^D) and 4 4 E2( S - D). There are also some interference terms. The most important of these i s the E l ( 2 P - 2S)/E2( 2D - 2S) interference. Donnelly (DO 68) has investigated the effects of these t r a n s i t i o n s and t h e i r interferences t h e o r e t i c a l l y . His results are based mainly on a two body model describing the interaction between a proton and deuteron but incor- porating some three body parameters i n an empirical way. I t i s important that his findings be checked experimentally to determine whether t h i s i s a useful 5. model for the reaction, and i f so, to t r y to extract some t h e o r e t i c a l l y s i g - n i f i c a n t parameters from the data. I t i s of p a r t i c u l a r importance to i n v e s t i - gate the cross sections predicted by t h i s semi-empirical theory, since i f these do not compare favorably with experiment, i t i s u n l i k e l y that any of the other parameters w i l l be p a r t i c u l a r l y s i g n i f i c a n t . Other work has been done recently i n t h i s laboratory to measure the angular d i s t r i b u t i o n of the emitted radiation, however the main object of the present work was to measure the absolute cross section of the reaction as accurately as possible. CHAPTER I I THEORY A b r i e f description of the parameters required f o r the determination of the cross section i s given i n t h i s chapter. 2.1 The Angular D i s t r i b u t i o n 3 The measured angular d i s t r i b u t i o n of the reaction D(p,y) He can be described as a series of Legendre polynomials i n the form W( ) = J Q B 1 PA (cos (2.1-1) where -©-' i s measured i n the center of mass system. Before the experimental angular d i s t r i b u t i o n can be compared with the theory, i t must be corrected f o r the f i n i t e s o l i d angle of the detector. I t has been shown by Rose (RO 53) that for an angular d i s t r i b u t i o n of the form (2.1 - l ) , these corrections are p a r t i c u l a r l y simple. The corrected angular d i s t r i b u t i o n i s given by W (•&') * £ A£ Pn (cos (2.1 - 2) where - B x /Qi • The so-called smoothing factors, QA take into account the smearing of the angular d i s t r i b u t i o n which re s u l t s from the f i n i t e s o l i d angle of the detector. They are given by / J c , where i s obtained from the following i n t e g r a l . " f K&s $)[l-t-MXa)]M^U$ (2.1 - 3) o where A i s the half angle of the detector jU i s the l i n e a r attenuation coeffi c i e n t X$ i s the distance traversed by radiation incident on the c r y s t a l at an angle ^ to the axis and P. are the Legendre polynomials of order H. Now the angular d i s t r i b u t i o n given by (2.1 - 2) i s e s s e n t i a l l y the d i f f e r e n t i a l cross section , and from t h i s one can determine the expec- ted gamma ray y i e l d , Ny (-«•), at a par t i c u l a r angle by integrating over the s o l i d angle subtended by the detector at the source. The expression ob- tained from t h i s integration i s N, W * NpA/0 £ j i 0 i t A0 [ i t k ?,Q, + £ P2Q, + £ p ^ j (2.1 - 4) where A/p = number of incident protons No - number of target atoms per square centimeter £ = ef f i c i e n c y of the detector J l f e t = s o l i d angle subtended by the detector at the source. Terms for angular momentum 1 greater than three have not been i n - cluded since i t has been shown (DO 67) that the cross section f o r the Jl = 4 2 2 term, which would arise from an E2 ( D - S) t r a n s i t i o n i s very small com- /2 2 x pared to the main E l ( p - S) t r a n s i t i o n . The form of the angular d i s t r i b u t i o n given i n Chapter I implies that the maximum y i e l d i s obtained at a laboratory angle of 90° to the incident pro- ton beam, and hence from the point of view of the s t a t i s t i c a l significance of the number of counts obtained, i t i s best to measure the gamma ray y i e l d at t h i s angle. Now the t o t a l cross section i s obtained from an integration over a l l angles of (2.1 - 2), and the re s u l t i s 0~r = (2.1 - 5) where A0 i s given by (2.1 - 4)» Thus the t o t a l cross section f o r a given energy E , 0~T(i) i s computed by combining the l a s t two equations to obtain 8. CTT(E) » ND £ A D E F [l + th. p, Q, + 4j p z ( ? 2 + ^ P j Q l (2.1 - 6) where A/y Ĉ :̂ » i s the gamma ray y ie ld obtained at •& = 90° for a given energy E and the Legendre polynomials , P2 and P̂  are evaluated for = 90°. The other parameters are as previously described. The expression (2.1 - 6) shows that before the tota l cross section can be determined i t i s necessary to measure the angular distr ibution i n order to obtain the rat io of the coefficients (j-^j , and ^ ~ j for a given energy E at which the cross section i s to be measured. The measurements of the angular distr ibution has been made at laboratory proton energies of 500 Kev 650 Kev and 800 Kev (BA 69). From a least squares f i t of these angular d i s t r i b - ution measurements, the ratios of the coefficients were determined. The results are l i s t ed in Table II - 1. and are shown in Figure II - 1. The other results shown in this figure are from data obtained by previous workers. Table II - 1 : Ratios of Coefficients from the Angular Distribution Measurements. Ep (lab) A 1 /A Q = -A 3/A Q A 2 /A Q 455 kev .072 - .012 -.940 - .012 595 kev .115 - .013 -.965 - .013 760 kev .127 - .016 -.958 - .013 The values of the smoothing factors for the detector geometry used in this experiment are l i s t ed in Table II - 2. These were obtained from the com- puter program DEWF, which was written previously (LE 64) to evaluate numerically the integral given in (2.1 - 3) 9 X PRESENT WORK OLIVO (OL 68) T WOLFLI et. al l(WO 67) GRIFFITHS et. al. (GR 61) T 0.4 0.8 1.2 1.6 LABORATORY PROTON ENERGY (Mev) 2.0 F i g . I I - l : Ratio of the coeff i c i e n t s from angular d i s t r i b u t i o n measurements. 10 Table I I - 2: Smoothing Factors. T. 2 3̂ .9884 .9655 .9317 Thus the cross section can now be determined, i n p r i n c i p l e , i f the gamma ray y i e l d i s measured at 90° to the incident proton beam i n an accurately known geometry. But before the description of t h i s measurement, attention w i l l f i r s t be focussed on the apparatus used i n the experiment, followed by a d i s - cussion of the measurement of a series of r e l a t i v e cross-sections, and f i n a l l y the determination of the gamma detector e f f i c i e n c y , which i s required for the computation of the absolute cross section. CHAPTER I I I EXPERIMENTAL APPARATUS 3.1 Target Chamber The target chamber used for most of the angular d i s t r i b u t i o n runs and for the measurement of the r e l a t i v e cross sections was developed i n t h i s labora- tory by the author i n conjunction with G.M. Bailey and M.A. Olivo. The target consisted of a rotating copper disk covered by a t h i n layer of deuterated* poly- ethylene, (C 2 D^)n» The polyethylene was obtained i n powdered form from Merck, Sharp and Dohme of Canada Limited, Montreal, Canada. The chamber was made of brass and the dimensions were approximately eight inches high by s i x inches i n diameter. In order to reduce the gamma ray absorption through the walls of the chamber, the l / 8 inch w a l l thickness was machined to a thickness of .040 inch i n the region over which gamma rays from the reaction could enter the detector. The target chamber was mounted on an angular d i s t r i b u t i o n table. A l u c i t e i n s u l a t i n g disk was attached to the bottom of the chamber, so that the chamber would be i s o l a t e d e l e c t r i c a l l y from the table. Figure I I I - 1. shows the chamber and the means of locating i t on the table. The nut on the concentric rod attached to the bottom of the chamber enabled the chamber to be raised or lowered. A l u c i t e i n s u l a t i n g r i n g was placed on the top of the chamber, and the assembly containing the target disk and the motor which rotated i t was placed on top of the l u c i t e . Provision was made to water cool the disk to reduce out- gassing. The top part could be rotated to place the plane of the disk at any desired angle to the incoming beam. The gas target which was used for the measurement of the absolute cross section w i l l be described i n a l a t e r section. 11. 12 F i g . I I I - l : The rotating target chamber. 3.2 Targets The method of making the targets was as follows. F i r s t the deuterated polyethylene was dissolved i n xylene by b o i l i n g the mixture gently f o r approx- imately three minutes. The resultant solution was then poured onto the disk and was prevented from running over the edge by an 0-ring which was clamped to the edge of the disk with a metal r i n g . A smaller 0-ring surrounding the cen- t r a l part of the disk l i m i t e d the deposit to a band about 3 cm. wide. The xylene was then allowed to evaporate slowly at room temperature i n a dust free atmosphere, leaving behind a f a i r l y uniform layer of polyethylene. Note: A superior method of making the targets has since been found and a b r i e f description of t h i s technique follows. The t a r - get i s machined out of l/U inch thick brass leaving two rings of brass to contain the xylene instead of using G-rings for t h i s purpose. The target thickness after machining was ap- proximately 0.066 inches. The disk i s then preheated to a temperature at which xylene w i l l b o i l and the mixture of xylene and polyethylene i s then poured into the container and i s allowed to b o i l u n t i l a l l the xylene has evaporated. The disk i s f i n a l l y removed from the heat and i s allowed to cool. This method of preparing the target has three d i s t i n c t advan- tages. F i r s t , the deposited layer of polyethylene i s smoother and hence more uniform than was obtained before. Second, there are no losses of the xylene solution through spaces which form- e r l y occurred between the 0-ring and the disk, and t h i s method reduces the time taken to make a target from twenty hours to approximately one half hour. To reduce the background from the copper backing which could be expec- ted at proton energies above approximately 1 Mev, a .001 inch thick platinum 14. f o i l was attached, to the target base with a high thermal conductivity epoxy (Delta Bond 152, obtained from Wakefield Engineering Inc., Wakefield, Massa- chusetts) before depositing the polyethylene. The deuterated polyethylene target was rotated while a run was in progress in order to reduce the rate of deterioration. 3.3 Detectors. Collimators, and Shielding. Two ident ical 5 inch diameter by 4 inch deep Nal (Tl) gamma ray detectors (HARSHAW type 20 MBS 16/B) mounted on 3 inch photomultipliers (RCA 8054) were used in th is experiment. In order to reduce the background and to keep to a minimum the num- ber of gamma rays scattered into the detectors, they were shielded in the following manner. One, cal led the D detector during the angular distr ibution runs, was placed inside a heavy lead shielding, the dimensions of which are shown in Figure III - 2., and l i s t ed in Table III - 1. This detector was also shielded by an 8 inch diameter lead col lar with a 1 5/8 inch thick wall which f i t t ed over the photomultiplier. Mounted in front of the detector was a lead collimator which l imited the acceptance angle for gamma rays coming from the source. This collimator was not used during the relat ive cross section runs, however; instead a l/8 inch thick f l a t lead sheet was placed in front of the detector to reduce the intensity of low energy gamma rays. The other crystal cal led the M detector, was placed inside a c y l i n - dr i ca l col lar with a l/4 inch thick wal l , and was shielded in front by a l/l6 inch thick lead sheet. The back of th is detector was shielded by a l/8 inch thick lead covering which extended over and hence gave further protection to the sides of the crysta l . Fig. III-3 : A schematic diagram of the detector assembly. The dimensions are given i n Table I I I - l . 16 Table I I I - 1. Dimensions of the D-dector assembly Collimator Half-angle e 12.0 - 0.2 degrees Source to Crystal Face R 19.52 + 0.05 cm Source to Collimator Face p 12.46 + 0.05 cm Collimator Thickness S 6.54 + 0.05 cm Crystal Diameter D 12.70 + 0.02 cm Crystal Thickness L 10.16 + 0.02 cm Collimator Face Inner Diameter I 5.30 + 0.05 cm Collimator Face Outer Diameter 0 11.6 + 0.1 cm Thickness of Lead Shielding T 4.0 cm 3.4 Electronics The electronic equipment used i n the experiment i s discussed i n some d e t a i l i n the section to which a p a r t i c u l a r configuration i s relevant. C i r - c u i t diagrams of the photomultipliers and preamplifiers f o r the detectors have previously been presented (0L 68). A complete l i s t of the electronics used during the experiment i s given i n Table I I I - 2. The numbers i n parentheses i n the block diagrams refer to the numeral order i n Table I I I - 2. 3*5 Data Analysis Several computer programs were written for the U.B.C. IBM 7044 com- puter t o ass i s t i n the analysis of the data. The rather complex analysis pro- cedure was required i n order to separate from the gamma ray spectra background radiations f a l l i n g i n the same energy range as the D(p,y)-%e gamma rays. The main contributions to t h i s background were 6 and 7 Mev gamma rays from the reaction "^F(p,<xtf)^0 , and 8 Mev gamma rays from the reaction "J"^C(p,y)'^N A l i s t of the computer programs, with a b r i e f description of each, i s given i n the Appendix. 17. 3.6 Proton Beam The proton beam was obtained from the U.B.C. Van de Graaff accelerator. This machine i s capable of delivering a beam of approximately 20 microamps on target f o r the energy range covered during t h i s experiment. 18. TABLE I H - 2 : L is t of the electronic units used in this experiment 1. FLUKE Model 412-B High Voltage Power Supply 2. HARSHAW Type 20MBS16/B 5"^x 4" Nal(TL) crystal coupled to an RCA 8054 3 inch photomultiplier 3. U. B. C. Power Supply 4. U. B. C. Preamplifier 5. U. B. C. Pulse generator 6. NUCLEAR DATA ND-160 Dual Parameter Analyzer 7. NUCLEAR DATA ND-120 Pulse Height Analyzer 8. NUCLEAR DATA ND-500 Dual Amplifier and Single Channel Analyzer 9. ORTEC Model 430 Scaler 10. - ORTEC Model 210 Detector Control Unit 11. RCA Type C-3-75-0.2 Diffused Junction Detector 12. ORTEC Model 101 Low Noise Preamplifier 13. ORTEC Model 201 Biased Amplifier 14. CANBERRA INDUSTRIES Model 1410 Linear Amplifier 15. FLUKE Model 881A DC Dif ferent ia l Voltmeter 16. ELECTRO SCIENTIFIC INDUSTRIES Model 250 DE Impedance Bridge 17. ELECTRO SCIENTIFIC INDUSTRIES Model 300 Potentiometric Voltmeter-Bridge 18. ELDORADO ELECTRONICS Model CI-110 Current Integrator CHAPTER IV RELATIVE CROSS SECTION MEASUREMENTS 4.1 Experimental Apparatus The absolute cross section measurement was made with a gas target which could only take a small amount of beam and therefore required a long run. To measure cross sections at a l l energies with this' target would have required a very long time. Thus i t was decided to determine the r e l a t i v e y i e l d of the reaction at several energies from 400 kev to 1100 kev with the deuterated polyethylene target, and then to measure the absolute cross section at only one energy, thereby e f f e c t i v e l y determining the absolute cross section over the entire energy range explored. The target was prepared as discussed i n the previous chapter, and i t s thickness was estimated to be approximately 2 50 micrograms per cm corresponding to an energy loss of 14 kev for 800 kev i n - cident protons. The rotating disk was set at an angle of 45° to the incoming beam as shown i n Figure IV - 1. Also shown i n t h i s figure are the two detectors placed at 90° to the incoming beam, which were shielded i n the manner discussed i n the l a s t chapter. The distance from the target centre to the c r y s t a l face was 4g inches. The rotating disk was e l e c t r i c a l l y connected to the rest of the t a r - get chamber so that electrons which were ejected from the target by secondary emission caused by the incoming protons would not cause an error i n the measure- ment of the current, since these emitted electrons would eventually reach the chamber walls. There would also be some protons scattered o f f the target to the walls and t h i s e l e c t r i c a l tieup insured that these protons would also be meas- ured. The current was integrated by an Eldorado Electronics Current Integrator, Model CI-110, which was checked f o r leakage current at the completion of the run. A block diagram of the electronics used i s shown i n Figure IV - 2. 19. Fig. TV-1 : Detector target configuration for the r e l a t i v e cross section runs. 21. H. V. P O W E R S U P P L Y (0 DETECTOR'W (2) S O U R C E D E T E C T O R "M" (2) P U L S E (5) G E N E R A T O R P R E - (4) A M P L I F I E R M A I N (14) A M P L I F I E R K I C K S O R T E R (6) P O W E R S U P P L Y (3) A M P L I F U " I E R - B 3) S . C . A . - B (8) S C A L E R (9) P R E - A M P L I (4) F I E R A M P L I F I E R - A (8) S. C . A . - A (8) S C A L E R (9) K I C K S O R T E R (7) Fig. IV-2 : Block diagram of the electronic arrangement for the relative cross section runs. 22. The pulse generator was used to check the l i n e a r i t y of the kicksorter and for setting the windows on the single channel analyzers. The scalers were used to monitor the deterioration rate of the target, but were not used at a l l i n the analysis of the data. 4.2 Procedure I t was known that the target would decay appreciably during the runs so i t was necessary to constantly remeasure the y i e l d at one p a r t i c u l a r energy so that the y i e l d at other energies could be normalized to t h i s . These norm- a l i z a t i o n measurements were taken at a proton laboratory energy of 800 kev, and the other measurements were taken at proton energies of 400 kev, 470 kev, 520 kev, 620 kev, 700 kev, 1000 kev, and 1100 kev. A l l the runs were taken for an integrated charge of from 6000 to 22,500 microcoulombs. The data was analyzed by the method discussed i n the next section. 4.3 Data Analysis and Results Rather than add together the data collected by the two detectors and determine the r e l a t i v e y i e l d from t h i s , i t was decided to analyze the re s u l t s separately, thereby determining a r e l a t i v e y i e l d curve for each detector. These two y i e l d curves were then blended together to obtain the r e l a t i v e y i e l d at the various energies. The two sets of data are referred to as the M c r y s t a l and D c r y s t a l r e s u l t s . The spectra were f i r s t gain-shifted to a standard gain and zero by the computer program TREAT. This program was also used to subtract a time dependent room background from the data. The modified data was then processed by NAILS, a complex analysis program, which analyzed the data into a specified set of components. From t h i s , one could determine the number of gamma 23. • 3 rays i n the spectrum which originated from the D(p,tf) He reaction. A t y p i c a l output of the NAILS program i s shown i n Figure IV - 3, which gives the r a t i o of the number of counts i n a preselected range of the spectrum introduced by various components as l i s t e d (M5.224 gives D(p,tf) He component^, F19MHI gives 1 9F(p,°a) l 60, C135M gives 1 3 C ( p , t f ) 1 4 N , NBGSM gives neutron background, and 15 12 M4.439 gives N(p,°0Q C ). The curve shows the t o t a l spectrum f i t t e d to the data. The spectrum represented i n t h i s figure i s for a proton bombarding energy of 1100 kev. From the r e l a t i v e i n t e n s i t i e s l i s t e d , i t i s clear that a considerable amount of the spectrum arose from gamma rays originating from the other reactions, and from the neutron background which arose p a r t l y from D on D knock-on reactions i n the target and p a r t l y from D on D reactions i n the magnet box. 3 The number of gamma rays from the D(p,2f) He reaction was corrected for dead time losses i n the kicksorter, and f o r absorption of gamma rays by the target backing, t h i s l a t t e r correction being applied only i n the case of the D cr y s t a l r e s u l t s . Now i t was necessary to normalize a l l the results to a given target thickness since the target was decaying while the runs were i n progress. In order to monitor t h i s decay, several r e p e t i t i o n runs were made at a proton energy of 800 kev. The results of these runs are shown i n Figure IV - 4. The yield s shown were those obtained from the analysis as described so f a r . The error bars indicate the s t a t i s t i c a l uncertainty r e s u l t i n g from the number of counts. A small correction was added to allow for errors i n the computer •pro- gram NAILS (part of the output of t h i s program was an estimate of the e r r o r ) . The fourth run was omitted as being inconsistent with the r e s t . Probably the beam spot shifted during t h i s run. I t i s seen that the M c r y s t a l y i e l d i s about 20 percent higher than Fig, IV-3 : Typical spectrum after analysis by the NAILS computer program. 25. I800-J UJ _ l < o OT 1600- >- <t rr CD rr < 1400H UJ CD rr < x U 1200- 5 T + 1 i z ZD rr UJ o- 1000- o _ i UJ T +• 1 UJ > H <t _ J UJ rr 8 0 0 - f 6 0 0 ~1 3 0 "~1 6 0 T 9 0 120 150 A C C U M U L A T E D C H A R G E C x l O O O MICROCOULOMBS) 180 Fig. IV-4 : Target decay from the 800 kev runs. The c i r c l e s r e f e r to the M c r y s t a l . The crosses refer to the D c r y s t a l . 26. the D crystal y i e ld . This i s the result of the more scanty shielding of the M crysta l , and of the absorption of gamma rays by the target backing which af fec - ted only the D crysta l . The results of the normalization runs were fed into the computer pro- gram POLY-D, which f i t t ed each curve separately as the sum of two exponentials. The y ie ld per unit charge for each of the relat ive cross section runs was then determined and the counts obtained for each run were multipl ied by the appro- priate amount to allow for the target decay. A small correction was also applied to allow for the eff ic iency change of the detectors with the changing energy of the gamma ray. The result of this normalization procedure was to obtain relat ive cross section curves, one for the D crystal and one for the M crysta l . These curves are shown in Figure IV - 5» The error bars indicate part ly the s ta t i s t i ca l error resulting from the number of counts. This was typ ica l l y of the order of 3 percent. Again, a small amount was added to this to allow for errors in the computer program NAILS. The rest of the error results from an uncertainty of about 3 percent in the target decay. The root mean square sum of these errors was approximately 5 percent. The two results were then blended together in the following way. F i r s t , each set of results was f i t ted with a cubic least squares curve. The D curve was then multipl ied by a constant factor to give the best f i t with the M curve. This analysis was done with the computer program CSFIT. A small correc- t ion was then applied to allow for the change of the angular distr ibution with energy. The resultant relat ive cross section curve i s shown in Figure IV - 6. The errors arise from two sources. F i r s t , there i s the error out- l ined above for the results from each crysta l . Added to th is i s a 1 percent error for the blending procedure done by CSFIT. The tota l error then i s • 27. 240CH 1600- o CO > 2000- <E cc K CD GC UJ CD Ct <r x o Z CC UJ Q. Q _1 ^ I200- UJ > t-< _J UJ cc 1 M CRYSTAL +D CRYSTAL 1 i T 1 I i T + 1 T 1 800 —I— 0.4 —I 0.5 — r — 0.7 I.I I 0.8 0.6 0.9 LABORATORY PROTON ENERGY (Mev) 1.0 Fig. IV-5 : Relative yield curve obtained for each detector. 28. 2400- UJ _J < O CO >-cc <t cc H CD CC < CC I o 2IOO- $ 1800- 1500- CC UJ Cu Q ui >- £ 1200- P _j UJ CC I 900 T ~I— l.O 0.4 X 0.5 0.6 0.7 0.8 0.9 LABORATORY PROTON ENERGY (Mev) F i g . IV-6 : Relative y i e l d for the reaction D(p,tf) He. 29. approximately 6 percent. With t h i s section of the work completed, i t now remained only to f i x the l o c a t i o n of the curve by measuring the absolute cross section. Before t h i s could be done, however, i t was necessary to determine the c r y s t a l e f f i c i e n c y , which i s the subject of the next chapter. CHAPTER V EFFICIENCY MEASUREMENTS 5.1 Introduction I t was necessary to determine an accurate detection e f f i c i e n c y of the s c i n t i l l a t i o n counters for gamma rays before the absolute cross section could be obtained. The reaction "^F(p,«y)"^0 was u t i l i z e d f o r t h i s purpose. 19 In t h i s reaction the protons can be captured by F at several resonances to 20 form excited states of Ne, which subsequently decay by alpha emission to the ground state of "^0 (°<»)* or to one of the excited states of t h i s nucleus. These l a t t e r states are the 6.06 Mev state (<Xrr)> which decays by electron p a i r emission to the ground state, the 6.14 Mev state ( ° 0 the 6.91 Mev state and the 7«12 Mev state (<*j) which a l l decay by gamma ray emission to the ground state. I t has been shown (FR 50) that f o r the 340 kev resonance where the present measurements were made, the r a t i o of i s 0.024. I t has also been found that at 340 kev bombarding energy, the alpha decay to the ground state ( <*<>) and to the pair emitting state (̂ cV) were not experimentally observ- able (CH 50). This same experiment showed that the number of alpha p a r t i c l e s emitted was i n close agreement with the number of gamma rays, and that the angular d i s t r i b u t i o n of both reaction products was i s o t r o p i c . Devons and Hiney (DE 49) had previously shown that the gamma rays were i s o t r o p i c . The foregoing discussion implies that to determine the e f f i c i e n c y of a gamma ray detector of a specified geometry one has only to measure the number of alphas emitted into a known geometry. One can then get the eff i c i e n c y as the r a t i o of the number of gamma rays detected to the number of alphas detected, after suitably correcting f o r the different geometries of the two detectors. 30. » 31 That i s to say, the eff ic iency i s I - -~-—- where S i s the in t r ins ic eff ic iency and N y i s the number of gamma rays detected N a i s the number of alphas detected w<* i s the sol id angle subtended at the source by the alpha counter oJy i s the sol id angle subtended at the source by the gamma detector. 5.2 Apparatus (a) Target Chamber The target chamber used for the eff ic iency measurements (Figure V-l) has been used previously in this laboratory (LE 64) for the same purpose. The or ig inal alpha detector had been destroyed, however, and so this was replaced by one of similar dimensions. The characteristics of the alpha detector (RCA diffused junction detector type C-3-75-0.2) are l i s t ed in Table V-1. TABLE V-1: Properties of the alpha detector Material Res ist iv i ty Diffusion Depth Sensitive Area Operating Voltage Leakage Current (measured) Phosphorus diffused into n-type s i l i con 1000 ohm-cm 0.2 microns ™ 2 20 mm 20 volts 0.43 microamps Resolution (5»13 Mev alphas) 107 kev i to 33 A 25 micro-inch sheet of Grade C (pinhole free) n i c k e l f o i l obtained from the Chromium Corporation of America was placed i n front of the alpha de- tector i n order to reduce the scattered proton f l u x which would otherwise enter the detector at a similar energy to the alphas. This n i c k e l window also r e - duced the energy of the °(z and 0/3 p a r t i c l e s , so that these now appeared i n the same region as the scattered protons. The entrance window to the alpha detector i s shown i n d e t a i l i n Figure V- 2. The target chamber was aligned making use of the angular d i s t r i b u t i o n table on which i t rested, and the gamma detector collimator, which had cross wires mounted on the front and back. These cross-wires were placed i n such a way as to accurately define the centre of the collimator. One then aligned the centre of the beam entrance collimator with the previously mentioned cross- wires; then the angular d i s t r i b u t i o n table was rotated to check that the l i n e j o i n i n g the centre of the entrance window to the alpha counter was i n l i n e with the cross-wires. This ensured that the axis of both detectors passed through the centre of the beam spot on the target. (b) Fluorine Targets The requirements f o r a satisfactory target i s that i t must be t h i n enough to allow the alphas to escape and the protons to pass through without too much degradation of energy, and thick enough to get a reasonable y i e l d . For 340 kev bombarding protons, t h i s means that a thickness of approximately 5 to 10 kev would be s u f f i c i e n t . Following the procedure used by Larson (LA 57) i n t h i s laboratory, the targets were made by evaporating powdered calcium fluoride onto t h i n copper plates. The method i s to put the CaF i n a tantalum boat and pass through t h i s -5 a large current while the apparatus i s under vacuum (approximately 10 mmHg). The vapour then deposits on the copper plates which are placed above the boat. 8 INCHES 4. 16 2 - 5 6 25/u.in JNICKEL \ / \ / 11 5 8 2 7 " 32 Fig. V-2 : Alpha p a r t i c l e window. 35. The stand holding the plates was arranged so that two targets could be made at one time, each at a different distance above the boat. Three pairs of targets were made i n th is fashion, varying each time the amount of C&F^ placed in the boat. Six targets of different thicknesses were thus obtained. The targets were then mounted in the chamber, one at a time, to de- termine the i r thicknesses to 340 kev protons. To ensure that the target was at an angle of 45° to the beam direction a micrometer depth gauge was clamped onto the back of the chamber, and the feeler rod was screwed in unt i l i t just touched the back of the target. The target was then rotated unt i l the rod and i t s ref lect ion i n the target formed a straight l i n e . Since the back of the chamber was 45° to the beam direct ion, the target then was also oriented this way. The excitation function i s shown in Figure V-3 for the target selected. The thickness at half maximum was approximately 7 kev. (c) Alpha Detector Electronics Pulses from the alpha detector were fed into an Ortec Model 101-201 Low Noise Preamplifier-Amplifier combination, and from there into 512 channels of a Nuclear Data Type 160 1024-channel kicksorter. The alpha part ic le pulses were also fed to a single channel analyzer and scaler in order to monitor the number of alphas during the run. A block diagram of the electronics (including the gamma detection c i rcu i t ) i s given in Figure V-4. A description of each unit appears in Chapter III. 239 The kicksorter was calibrated with 5.13 Mev alphas from a Pu source which was inserted into the target chamber for this purpose. The spectrum thus obtained i s shown in Figure V-5. Since the energy of the alphas from the reac- t ion is only 1.73 Mev in the laboratory system, the gain of the main amplifier was halved after cal ibrating the kicksorter, so that the alpha spectrum from the 36. Fig. V-3 : Excitation function for F target used for the efficiency measurements 37. KICKSORTER (6) BIAS (JO) SUPPLY ALPHA (||) DETECTOR PRE- (12) AMPLIFIER MAIN (13) AMPLIFIER CxMPLIF (e IER-B 0 S, C. A.-B (8) SCALER (9) SOURCE H.Y P O W E R S U P P L Y (0 G A M M D E T E C A (2) :TOR P U L S E (5) G E N E R A T O R P R E - (4) A M P L I F I E R AMPLIFIER-AJ (8) S. C. A - A (8) S C A L E R (9) POWER (3) S U P P L Y K I C K S O R T E R (7) Fig. V-4 : Block diagram of the electronic arrangement for the c r y s t a l e f f i c i e n c y measurements. 38 500-1 400- \-z o o 30 oH 200H tj.FWHM 2.2% V (107 Kev) lOOH O 370 ~1 1 390 410 430 CHANNEL NUMBER 450 Fig. V-5 : 5.13 Mev Pu alpha p a r t i c l e spectrum, 39. reaction would, be more nearly in the centre of the range. F inal ly the l inear - i t y was checked using the pulser, and this was found to be excellent over the 19 , X16 entire range. A typ ica l alpha spectrum from the F(p,«^) 0 reaction i s shown in Figure V - 6. (d) Gamma Detector Electronics The pulses from the gamma detector were fed into a preamplifier and then direct ly into the ND 120 kicksorter. A single channel analyzer and scaler were also used so that a continuous check could be made on the number of gamma rays being detected and hence on the deterioration of the target. A typ ica l gamma spectrum from the reaction i s shown in Figure V - 7« 5.3 Solid Angle Calculations (a) Alpha Detector The alpha detector i s mounted so that i t detects part ic les at 135° to the incident proton beam and 90° to the target face. The relevant geometry for the calculation of the sol id angle i s displayed in Figures V - 1 and V - 2, and the dimensions shown there are l i s t ed in Table V - 2. Table V - 2: Alpha detector sol id angle Distance Measured Window diameter (2r) Distance A Distance B Target backing t Detector Window to Target Face R = A-B-t Solid Angle (calculated) 3.196 - .001 mm 3.9836 - .001 in .7225 - .0001 in .0115 - .0001 in 3.2496 - .0002 in Method of Measurement Travell ing microscope over 15 diameters Precision depth gauge Precision depth gauge Micrometer -3 (1.18 - .01) x 10 steradians  5.62 Mev 1.46 Mev 40 K \ 3492 Mev J 6.13 Mev \ \ i \ \ \i 6.48 M.ev 210 0 30 60 F i g . V-7 n 1 90 120 CHANNEL NUMBER 150 Typical gamma spectrum from ^E(p,«2f)"^"^0. 180 42 The errors quoted are standard deviations taken over several meas- urements. (b) Gamma Detector The main purpose f o r the measurement of the c r y s t a l e f f i c i e n c i e s was 3 so that the cross section f o r the reaction D (p, K ) He could be determined. I t was decided that c r y s t a l D would be used f o r t h i s purpose, f u l l y collimated as shown i n Figure I I I - 2 . A summary of the dimensions applicable to the calc u l a t i o n of the s o l i d angle has been given i n Table I I I - 1. An error occurred here, however, since an unreported change had been made to the collimator. Approximately 1.1 cm. had been shaved o f f the front end, and t h i s was not known at the time that the measurements were made. Hence the gamma detector was actually set 1.1 cm. closer to the target than i t should have been. Since the cross section measurements were made at the proper distance, i t was necessary to extrapolate the measured c r y s t a l e f f i c i e n c y to what i t would have been at the proper distance by using a computed change of e f f i c i e n c y with distance. This correction was made by redefining the e f f i c i e n c y to be A = S^K where A i s the absolute e f f i c i e n c y defined as the p r o b a b i l i t y of a gamma ray emitted i s o t r o p i c a l l y from the source being absorbed by the c r y s t a l . The computer program DEWF which calculates the absolute e f f i c i e n c y of collimated gamma ray detectors, was used to obtain the t h e o r e t i c a l absolute e f f i c i e n c y of the detector at the two source to c r y s t a l distances of int e r e s t . The correction was then applied i n the following way. F i r s t the absolute e f f i c i e n c y was calculated using the data from the experimental runs. Then the expected experimental value f o r the proper source to c r y s t a l distance was pre- dicted making use of the computer results referred to above. This was done 43. as a d i r e c t r a t i o between the experimental and computed absolute e f f i c i e n c i e s at the two distances. F i n a l l y , the i n t r i n s i c e f f i c i e n c y f o r the proper distance was obtained by dividing the absolute e f f i c i e n c y by the s o l i d angle subtended by the detector at the source. The s o l i d angle i s defined as shown i n Figure I I I - 2. In order to check that a large error was not being introduced by t h i s method due to the e f f i c i e n c y not varying smoothly with distance, the t h e o r e t i - c a l absolute e f f i c i e n c y for several source to c r y s t a l distances was computed and plotted. The re s u l t s are shown i n Figure 7 - S. I t i s seen that the absolute e f f i c i e n c y follows an approximate inverse square behaviour as the distance be- tween the source and c r y s t a l i s varied. This i s the f a m i l i a r r e s u l t for uncol- limated detectors and i t i s of interest to note that the presence of the c o l l i - mator does not cause a r a d i c a l departure from t h i s behaviour. Arrow "A" shows the source to c r y s t a l distance used f o r the e f f i c i e n c y measurements; arrow "B" shows the proper source to c r y s t a l distance, taken from Table I I I - 1 (R = 19.52 cm.). I t was anticipated that the e f f i c i e n c y f o r c r y s t a l M might also be required at some time i n the future, and also for both cr y s t a l s uncollimated at the front face. These measurements were also taken. For the purpose of getting the e f f i c i e n c y with the crystals uncollimated, the relevant geometry i s shown i n Figure V - 9, with the symbols and t h e i r dimen- sions l i s t e d i n Table V - 3« 44. 16-1 CM o z w o LL LL UJ HI h- 3 _J O CO CO < 14- 12H ID- S' 6-J 4 H o DISTANCE FROM SOURCE TO CRYSTAL FACE (cm) 1 1 25 28 0 10 15 20 F i g . V-8 : Relation of absolute e f f i c i e n c y to distance. F i g . V-9 : Uncollimated gamma detector geometry. 46 Table V - 3s Uncollimated gamma detector geometry Symbol Distance R 6.5 i n . L 2.5 i n . $ 21° 63» The s o l i d angle was taken from the source to the middle of the de- tector, and was calculated to be 0.571 steradians. 5-4* Results After c a r e f u l l y checking the alignment of the target-detector system, an excitation function was again run on the target to locate the 340 kev reson- ance, and then a l l the e f f i c i e n c y runs were made at an energy 2 kev higher. The i n i t i a l y i e l d was approximately 4000 gamma counts per minute with from one- half to one microampere current on the target. The target was shi f t e d whenever the number of gamma counts f e l l to 2000 counts per minute. I t was necessary to run at the low beam current i n order to maintain the dead time of the kicks o r t - ers below 2%, The time of the runs was determined by the time required to get approximately 6000 alpha counts, and was t y p i c a l l y around three hours. The number of alpha counts was summed from the minimum i n the spec- trum to the upper edge of the alpha counts (approximately channel 250), and was then corrected for dead time losses i n the kicksorter. No correction was neces- sary f o r the <*x and <*j counts since the energy of these alphas after passing through the n i c k e l window was considerably less than the lowest energy p a r t i c l e s that were counted. The gamma counts were analyzed by the TREAT com- puter program, which gain-shifted a l l the re s u l t s to the same settings as were used i n the absolute cross-section analysis. This program then summed the counts from 3«492 Mev to 6.48 Mev — the same l i m i t s as used for the 47 cross-section measurements — and subtracted the appropriate amount of time dependent room background. These results were f i n a l l y corrected for dead-time losses i n the kicksorter and f o r absorption losses i n the aluminum window and target backing. A small correction, based on the shape of the spectrum, was also applied to allow for the °<z and <j gamma rays which were i n the energy region of in t e r e s t . No beam dependent background was subtracted since a run on a clean target backing showed that the correction would be le s s than 0.3 percent. The absolute e f f i c i e n c i e s were f i n a l l y calculated as A = NK w ? and the i n t r i n s i c e f f i c i e n c i e s as £ = A/W . The i n t r i n s i c e f f i c i e n c y f o r the proper collimated distance was determined i n the way discussed previously. The i n t r i n s i c e f f i c i e n c y f o r the uncollimated crystals was calculated using the s o l i d angle shown i n Figure V - 9« The results of the four measurements are l i s t e d i n Table V - 4* The calculated error i s less than 3 percent on a l l the measurements. Table V - 4: Crystal e f f i c i e n c i e s Collimated c r y s t a l s : - Absolute E f f i c i e n c y Detector Experiment Proper Distance D .00838 .00743 M .00864 .00769 I n t r i n s i c E f f i c i e n c y Experiment Proper Distance .704 .679 .730 .702 Uncollimated c r y s t a l s : - Detector D M Absolute E f f i c i e n c y .0218 .0218 I n t r i n s i c E f f i c i e n c y .482 .482 CHAPTER VI GAS TARGET AND ABSOLUTE CROSS SECTION 6.1 Introduction The main sources of uncertainty associated with the measurement of an absolute cross section are the lack of precision i n the knowledge of the number of nuc l e i i n the target and the number of p a r t i c l e s incident on the target. The l a t t e r i s determined by integrating the charge collected by the target, and the former requires a knowledge of the target thickness. I t was o r i g i n a l l y hoped that the deuterated polyethylene target thickness could be found accurately by measuring the energy loss of alpha par- t i c l e s passing through i t . These alphas were to originate from a source depos- i t e d onto the target backing before the polyethylene was poured on. However, d r i f t s i n the electronics made i t impossible to measure accurately enough the location of the alpha peak (and hence the alpha energy) before and after putting on the polyethylene layer, so t h i s method was discarded.. A second p o s s i b i l i t y f o r determining the target thickness was to rt measure the neutron y i e l d from the D(d,n) He reaction. However, t h i s method was also discarded since i t required knowing accurately the e f f i c i e n c y of the neutron counter, and i t was expected that a large correction would be required for the beam dependent background for t h i s e f f i c i e n c y measurement since the accelerator had just been used with a deuterium beam for some time. F i n a l l y a decision was made to use a gas target, where the number of n u c l e i involved can be determined knowing the pressure of the gas and the length of the active volume. The following section describes the target used, and the method of determining the required parameters. * 48. 49 6.2 The Gas Target One of the problems encountered i n measuring the gas pressure involves l o c a l heating effects r e s u l t i n g from the passage of the incident beam through the gas. This heating causes the gas i n the active volume to expand s l i g h t l y , thus reducing the density i n the region of the beam. To minimize the correc- t i o n required f o r t h i s effect the brass backstop of the target was made very large i n the hope that the conduction would be great enough to maintain a constant temperature throughout the c e l l . The temperature of the backstop was monitored with a copper-constantin thermocouple which was inserted into a hole d r i l l e d i n t o the stop. No appreciable difference could be detected between the stop temperature and room temperature with the beam on the target. A f i r s t attempt to measure the effect of l o c a l heating by passing beams through the gas; c e l l with varying currents had also f a i l e d because of a slow carbon buildup on the f o i l while the runs were taking place. This carbon buildup produced an energy loss i n the incident beam with an error larger than the effect being studied. However, the effect has been measured previously i n t h i s way (RO 6 l ) using deuterium gas but at a higher pressure. After making the appropriate allowances for the different pressure, i t was found that, with the beam current used for the cross section measurements, the gas i n the beam path was 0.8$ less dense than that i n the remainder of the target chamber, the pressure of which was measured with a manometer. The entrance window to the gas target was a 30 micro-inch n i c k e l f o i l obtained from the Chromium Corporation of America. This f o i l thickness was chosen as a compromise among the following factors: the strength required to withstand the gas pressure, a minimum energy loss and straggling of the beam i n passing through the f o i l , and a maximum allowable beam current. The energy loss was measured by noting the s h i f t of the 992 kev resonance of the 27 28 A I ( P , rr S i reaction with the f o i l i n place, and then correcting f o r the 50 stopping cross section difference between this energy and 780 kev and 800 kev, the energies at which the absolute cross section were measured* The f o i l th ick - ness was found in th is way to be 127 kev at 780 kev incident proton energy. The maximum allowable beam current for 780 kev incident protons i s approximately 0.8 microampere according to curves published in the I960 Nuclear Data Tables (Part 3, P« 124); the runs were made at a current of 0.5 micro- amperes. The length of the gas c e l l was determined by f i r s t measuring with a t rave l l ing microscope the distance between the f o i l holder and the backstop. Now the gas in the c e l l causes the f o i l to depress s l ight ly , and this depression was measured by noting the different focussing locations of the travel l ing microscope when focussed on the edge of the holder compared to when i t was focussed on the point where the beam passed through the f o i l . The length was determined to be 1.019 - .002 cm. The average energy of the proton beam in the gas ce l l can be determined by subtracting from the incident beam energy the energy loss as the beam passes through the f o i l , and one-half the energy loss of the beam as i t passes through the gas. This la t ter quantity was determined by the computer program ENL0TA, which subdivides the gas ce l l length into several elements of length, and then computes the energy loss in each small sub-length. In this way, the variation in the stopping cross section of the gas with energy i s allowed for . For 800 kev and 780 kev incident proton energies, the average energy in the gas ce l l was found to be 663 kev and 643 kev respectively. The gas pressure was measured with a U-tube manometer f i l l e d with mercury. Provision was made to evacuate both arms of the tube and then, by closing a glass tap, one of these could be isolated from the main system prior to f i l l i n g ; the gas c e l l . This enabled the pressure in the c e l l to be read direct ly as the difference in the leve l of mercury in the two arms. After f i l l i n g the c e l l , a 51 glass tap on the other arm was also closed to prevent any mercury contamination i n the system. Other features of the target include an all - b r a s s construction except fo r a l u c i t e window on one side through which the beam could be viewed h i t t i n g the backstop, and an aluminum window on the other side through which the gamma rays passed on t h e i r way to the detector. The collimators were made of platinum with a view to reducing the contaminant background radiation, especially that a r i s i n g from ^F(p,<*0"^0, since previous tests had indicated that platinum had the least contaminating material. For t h i s same purpose, a piece of platinum was attached to the face of the backstop where the beam h i t i t . A diagram of the target with the n i c k e l f o i l holder, collimators and electron suppression assembly and gas f i l l i n g device i s shown i n Figure VI - 1. 6.3 Current Integration The other problem associated with measuring the cross section was an accurate determination of the charge delivered to the gas target by the beam. The f i r s t point of concern here i s the ejection of secondary electrons from the backstop, which would res u l t i n an effective increase i n the positive charge measured. To overcome t h i s d i f f i c u l t y , a pos i t i v e bias was put on the backstop to prevent the electrons from escaping. This introduces a second problem, however, which results from the i o n i z a t i o n of the gas as the beam passes through i t . I f the backstop i s p o s i t i v e l y biased and the rest of the target assembly, including the n i c k e l f o i l , i s unbiased, then the negative ions w i l l d r i f t to the backstop and the po s i t i v e ions to the f o i l and chamber wal l s . This w i l l r e s u l t i n a decrease i n the amount of p o s i t i v e charge measured. Hence the f o i l , target chamber and backstop must a l l be at the same p o t e n t i a l . In t h i s experi- ment, +90 v o l t s was used. i 52. T O P U M P Fig. VI-1 : The gas target assembly. 53. The positive bias on the n i c k e l f o i l has the added benefit that copious numbers of electrons, which would otherwise be ejected from the f o i l , are prevented from escaping. A problem did arise from the fact that the f o i l and the f o i l holder were t i e d to the backstop. I t was necessary that no pro- tons h i t the edges or sides of the holder; otherwise charge i s collected which has not passed through the gas. To prevent t h i s from happening, a collimator system was designed to l i m i t the diameter of the beam to less than 0.1 inch, whereas the width of the f o i l which was exposed to the incident beam was 0.3 inch. A check was made to ensure that the beam was not diverging by in s e r t i n g a quartz backstop into the target chamber. An end-on view of the proton beam was thus available. F i n a l l y , any secondary electrons which might be emitted from the edges of the collimators must be prevented from reaching the f o i l assembly. To t h i s end, a suppressor with a -300 v o l t bias was placed i n the beam l i n e between the collimators and the f o i l holder. The current measured i n the target chamber was fed to an Eldorado Electronics Current Integrator, Model CI - 110, the same as used during the r e l a - t i v e cross section measurements. Very careful c a l i b r a t i o n of the current i n t e - grator was of course required since any error a r i s i n g here would be transmitted d i r e c t l y to the cross-section. The c a l i b r a t i o n was carried out using a Weston Standard C e l l and a Gambrell precision r e s i s t o r . The accuracy of the standard c e l l was checked using two different resistance bridges (Electro S c i e n t i f i c Industries Model 250DE Impedance Bridge and Model 300 Potentiometric Voltmeter-Bridge). The difference between the measured value and the quoted value f o r both the c e l l and the r e s i s - tor was found to be less than the error of the measuring instruments. The error of the combination of standard c e l l and precision r e s i s t o r was taken to be less than two parts i n a thousand. 54 The method of cal ibrating the current integrator was to feed in a current on the current range used during the cross-section runs, and then to compare the charge integrated for this known current and known time to the charge which was expected. A summary of the results of th is cal ibrat ion i s shown in Table V I - 1 . Table V I - 1 . Current integrator cal ibration Known Current 1.0185 - .001 uamps + Known Time 1138.5 - 3.5 sec. Known Charge (Known Current x + Known Time) 1159.6 - 3.5 ucoul Charge Setting on the Current Integrator 1200 ucoul This table shows that the actual integrated charge i s 96.6 i 0.4 percent of the charge indicated by the current integrator and this correction was applied to the f i na l resul ts . 6.4 Experimental Procedure The collimated Nal (T i ) detector (D crystal) was placed at 90° to the incident beam in order to obtain the maximum y ie ld of gamma rays from the reaction. The cross hairs on the collimator, previously described in the sec- t ion on the crystal eff ic iency, were used to ensure that the detector was aim- ing at the centre of the target. The crystal was set at the proper collimated distance from the centre of the target by measuring the distance from the front face of the crystal to a mark in the centre of the outside face of the backstop. The data col lect ion from the detector was accomplished using the same electronic arrangement used for the measurement of the crystal e f f i c ienc ies , except that the ND 160 was used in place of the ND 120. A scaler was again employed so that the number of counts obtained in a given time interval could1' 55 be p e r i o d i c a l l y monitored to ensure that a l l the equipment was performing sat- i s f a c t o r i l y . F i n a l l y , the measurement of the cross section was broken down into f i v e separate runs i n order to reduce the r i s k of l o s i n g a l l the data i f some- thing were to go wrong, such as the f o i l breaking or large d r i f t s occurring i n the electronics, and to average out any small background variations. Each run took approximately 4 hours and was further s p l i t up into two parts, one with deuterium i n the gas c e l l , and the other with hydrogen. In t h i s way the beam dependent background could be accounted f o r by subtracting the hydrogen run d i r e c t l y from the deuterium. This method proved p r a c t i c a l since no large buildup of background occurred during any one p a r t i c u l a r run. A correction was also applied f o r the time dependent background, but t h i s was very small since i t was necessary to take into account only the time difference between a hydro- gen run and a deuterium run. The deuterium was obtained from the Liquid Car- bonic Division of General Dynamics, and had a quoted p u r i t y of 99.7 percent. In order to change the gas i n the c e l l , the c e l l was f i r s t evacuated, then flushed with the new gas and evacuated again before the f i n a l f i l l i n g took place. The runs were made with approximately 150 mm Hg gas pressure i n the c e l l , measured with the manometer previously described. The t o t a l integrated charge was 2400 microcoulombs per run f o r four of the runs and 3600 microcoulombs f o r the other. A correction was then applied to the charge collected to allow f o r the error i n the current integrator, which has been described previously. 6.5 Other Corrections Factors Reference to equation (2.1 -5 ) and the ensuing discussion shows that the s o l i d angle subtended by the detector and the angular d i s t r i b u t i o n factor 56 4* p i <?i + — f fi 5, - ft must also be determined in order to compute the no 4;, V, cross section. A small correction must also be applied to the detector e f f i c - iency, since th is was measured with 6.14 Mev gamma rays compared to the 5«92 3 Mev gamma rays obtained from the reaction D(p, y ) He at a proton bombarding energy of 643 kev, which was the average proton energy in the gas c e l l . The so l id angle was calculated from the data l i s t ed i n Table III - 1. for Figure III - 2. and was found to be 0.1376 - .0006 steradians. To determine the angular distr ibution factor, use i s made of the data l i s t ed i n Tables II - 1. and II - 2. The Legendre polynomials were c a l - culated for centre of mass angles, and i t i s found that an angle of 90° i n the laboratory frame corresponds to 90.71 degrees i n the centre of mass frame. Thus the angular distr ibution factor was calculated to be 1.4624. In order to determine the eff ic iency change of the detector, use was made of the computer programs LFIT and SHAPE. These programs used in conjunc- t ion with each other produce from known gamma ray shapes at various energies interpolated gamma ray shapes for intermediate energies. Thus the standard shape for the 5»92 Mev gamma rays from the D(p, *) He reaction was found. 3 Consider two gamma rays, the 5*92 Mev D(p,y) He radiation and the 19 16 6.14 Mev F(p,<><y) 0 radiation for which the absolute eff ic iency has been de- termined. Now i f each standard gamma ray spectrum has the same number of counts in the to ta l spectrum and i s plotted for the same energy gain and zero, and we assume that the two gamma rays have approximately the same energy so that the shapes of the two spectra can be considered to be the same, then the rat io between the number of counts in a given energy region of the two spectra w i l l give the relat ive eff ic iency of the detector for the two gamma rays, provided that the upper l imit of the energy region considered i s above the f u l l photopeak, and the lower l imit i s approximately one-half the f u l l energy, or lower. It was found that over the chosen energy region from 3*492 Mev to 57 6 . 4 8 Mev, there were 9 9 1 « 4 counts of the 5*92 Mev radiation and 1 0 0 0 counts of the 6 , 1 4 Mev radiation. Hence the e f f i c i e n c y for the D detector which was found as described i n the l a s t chapter was mult i p l i e d by . 9 9 1 4 to allow for the change i n energy of the gamma ray. Two other corrections, both of which resulted i n a modification to the number of detected gamma rays, were required. The f i r s t of these arose from dead time losses i n the kicksorter,.and resulted i n a factor of 1 . 0 0 3 i n - crease i n the number of gamma rays detected. The second arose from absorption losses through the aluminum window, and required a factor of 1 . 0 0 6 increase. F i n a l l y , the pressure i n the gas c e l l was corrected f o r the density change of mercury with temperature, since the measurements were not made at the standard temperature and pressure. 6 . 6 Results The spectra, which were obtained from the f i v e runs—each consisting of one hydrogen and one deuterium part—were gain-shifted to the same gain and zero by the computer program TREAT, and then were summed over the energy region 3 « 4 9 2 Mev to 6 . 4 8 Mev. The appropriate corrections which have just been described were then applied to these r e s u l t s , and the absolute cross section was calculated f o r each run. The re s u l t s of these calculations are l i s t e d i n Table VI - 2 . The error quoted with each result i s the root mean square error of the quantities which contribute to the cross section. 58. Table VI - 2: Absolute cross section measurement Laboratory Proton Energy Absolute Cross Section 663 kev 2.33 - .10 microbarns 663 kev 2.57 - .11 643 kev 2.35 ± .10 643 kev 2.28 - .10 643 kev 2.42 - .11 The measurements made at 663 kev were converted to the equivalent 643 kev result making use of an approximate expression for the cross section given in the paper by Fowler et a l which has been discussed previously. This expression i s n —20 2 = KE x 10 cm (6.6 - 1) where K = 0.74 - 50% n - 0.72 - 15% and E is the laboratory energy in Mev. It i s found that this conversion gives the f i r s t run a result of 2.28 microbarns and the second a result of 2.51 microbarns. The result of the second run seems inconsistent with the other four, and hence was discarded. No reason for the discrepancy was readily apparent. The result of averaging the other four runs gives the cross section as 2.33 - .07 microbarns, where the error i s the standard deviation of the four runs. Thus the absolute cross section i s effect ively determined for the entire range of values over which the relat ive cross section was measured. Figure VI-2 shows these resul ts , and the results of previous measurements made in this laboratory. The present work gives quite good agreement with the previous results , 59. 60-i 5.0- 4.0- 3.0- 2.0- I T + 1 T t I.O- 0.3 T 1.2 0.6 0.9 LABORATORY PROTON ENERGY (Mev) 1.5 I 1.8 F i g . VI-2 : The absolute cross section f o r the reaction D(p,y) He. The c i r c l e s are the res u l t s of G r i f f i t h s et. a l . (GR 6l). The crosses are the present measurements. 60 although at higher energies the present r e s u l t s seem to be s l i g h t l y lower. This i s possibly due to an incomplete subtraction of the fluorine contamination i n the e a r l i e r measurements. BIBLIOGRAPHY » BA 69 G.M.Bailey, to be published. CH 50 C.Y.Chao, A.V.Tollestrup, W.A.Fowler and G.C.Lauritsen, Phys. Rev., 22 (1950) 108 DE 49 S.Devons and M.G.N.Hine, Proc. Roy. Soc. (London) 199A (1949) 56. DE 60 G.Derrick, Nucl. Phys. 16 (i960) 405. DO 67 T.W.Donnely, Ph.D. Thesis, University of Br i t i sh Columbia (1967). FO 49 W.A.Fowler, C.C.Lauritsen and A.V.Tollestrup, Phys. Rev., 7j> (1949) 1767. FR 50 J.M.Freeman, Ph i l . Mag. 42 (1950) 1225. GR 55 G.M.Griffiths and J.B.Warren, Proc. Phys. S o c , 68 (1955) 781. GR 61 G.M.Griff iths, E.A.Larson, and L.P.Robertson, Can. J. Phys. 4J) (1962) 402. GR 63 G.M.Griff i ths, M.Lai and C.D.Scarfe, Can. J. Phys., 41 (1963) 724. LA 57 E.A.S. Larson, M.A. Thesis, University of Br i t ish Columbia (1964). LE 64 J.L. Leigh, M.Sc. Thesis, University of Br i t ish Columbia (1964). OL 68 M.A. Ol ivo, Ph. D. Thesis, University of Br i t ish Columbia (1968). RO 53 M.E. Rose, Phys. Rev., 9_1 (1953) 610. RO 61 L.P. Robertson, B.L.White and K.L. Erdman, Rev. Sc i . Inst., 22 (I96l) 1405. VE 50 M. Verde, Helv. Phys., Acta 23, (1950) 453. WI 52 D.H. Wilkinson, Ph i l . Mag., 42 (1952) 659. WO 67 W.Wolfli, R. Bosch, J.Lang, R. Muller, and P. Marmier, Helv. Phys. Acta, 40 (1967) 946. 61 APPENDIX COMPUTER PROGRAMS DEWF" : This program calculates the absolute detection e f f i c i e n c y of s c i n t i l - l a t i o n c r y s t a l s for gamma rays, and the weighting (Q) factors that compensate for the f i n i t e s o l i d angle of the counter, LFIT : The input to t h i s program i s a number of standard gamma ray shapes of various energies. The f u l l peak of each input spectrum appears i n the same channel and has the same number of counts as a l l the other spectra, and a l l spectra have the same gain. The program then does a cubic f i t of the counts versus energy r e l a t i o n for each channel of the input spectra. The output i s a matrix giving the four coefficients from the cubic f i t f o r each channel. SHAPE : The input to t h i s program i s the output from LFIT. The program then determines the number of counts i n each channel f o r a gamma ray of a specified energy. Thus LFIT and SHAPE used i n conjunction interpolate the shape of a specified gamma ray from several given gamma rays. TREAT ; This i s a general purpose program f o r the preliminary treatment of data p r i o r to the detailed analysis done by NAILS. The program can be used to smooth the data, gain-shift i t , and sum the counts between two given energies. Up to eight spectra can be subtracted from or added to the spectrum being treated. NAILS : This program i s used to determine by an i t e r a t i v e least squares pro- cedure the r e l a t i v e amounts of various specified components i n a given spectrum. Included i n the output i s an estimate of the accuracy of the r e s u l t s based on the differences of the intermediate i t e r a t i o n s with 6 3 the f i n a l r e s u l t s . The input to NAILS was usually the output of TREAT. POLY-D : This program corrects f o r the deterioration of deuterated poly- ethylene targets by f i t t i n g the target decay with the sum of two exponentials. CSFIT : This program f i t s both of the r e l a t i v e cross section r e s u l t s of the two detectors with a cubic least squares curve, and then mul t i p l i e s one of these curves by a constant factor to give the best f i t with the other. ENLOTA This program calculates the energy loss of a beam when passing through a gas target. Allowance i s made for the va r i a t i o n of the stopping power of the gas with energy.

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