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

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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 British Columbia, 1966 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 April, 1969 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representa tives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Physics The University of British Columbia Vancouver 8, Canada Date: April, 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 relative yield of the reaction over this range, and the results were normal ized to an absolute measurement made with a deuterium gas target. The reaction is of interest because it 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 intrinsic efficiency of a 5 inch by 4 inch sodium iodide crystal scintillation counter was meas ured by simultaneous alpha particle and gamma ray counting on the 340 Kev resonance of the reaction "^F(p,<*#)^0. The intrinsic efficiency of the de tector was found to be .679 - .03 for the 6.14 Mev gamma rays from this reaction, with the particular 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 ii TABLE OF CONTENTS iiLIST OF TABLES • ' LIST OF FIGURES .« vi 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 , 13.6. Proton Beam 17 CHAPTER IV RELATIVE CROSS SECTION MEASUREMENTS 4.1. Experimental Apparatus • • 19 4.2. Procedure 22 4.3. Data Analysis and Results 2CHAPTER V EFFICIENCY MEASUREMENTS 5.1. Introduction • 30 5.2. Apparatus 31 (a) Target Chamber"i..... •• 31 iii iv (b) Fluorine Targets 33 (c) Alpha Detector Electronics 35 (d) Gamma Detector Electronics ............... 39 5.3. Solid Angle Calculations 3(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 9 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 distribution 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 this experiment 18 V-l Properties of the alpha detector 31 V-2 Alpha detector solid angle 9 V-3 Uncollimated gamma detector geometry 46 V- 4 Crystal efficiencies • 7 VI- 1 Current integrator calibration 54 VI-2 Absolute cross section measurements • • •• 58 LIST GF FIGURES II- l Ratios of coefficients from the angular distribution 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 relative cross section runs 0 IV - 2 Block diagram of the electronic arrangement for the relative 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 yield curve obtained for each detector 27 3 IV - 6 Relative yield for the reaction D(p,tf) He 28 V-1 Fluorine - 19 target chamber 32 V - 2 Alpha particle window 4 19 V - 3 Excitation function for 7F target used for the efficiency measurements 36 V - 4 Block diagram of the electronic arrangement for the crystal efficiency measurements 37 239 V - 5 5.13 Mev Pu alpha particle 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 efficiency 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) He....... 59 vi ACKNOWLEDGEMENTS I wish to express my gratitude to all the members of the Van de Graaff group for their help during the course of this work. Particular thanks go to Dr. G. M. Bailey for his supervision of the experimental part, and to Dr. G. M. Griffiths for his assistance and very helpful suggestions during the writing of this thesis. vii CHAPTER I INTRODUCTION 1.1 General Introduction One key to understanding the properties of nuclei would be to dis 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 theoretical studies have been made to relate details of the force system in a quantitative way to the properties of few nucleon systems, it is important to obtain as much experi mental information as possible about the bound states of nuclei, and particu larly light nuclei, where the many body aspects of the problem do not obscure the specific relations between nuclear structure and characteristics of the internucleon force. Direct radiative capture reactions provide a relatively simple way of determining some of the properties of nuclear bound states and assessing nuclear models through comparing theoretically predicted and experimentally measured cross sections. The simplicity in comparison to other reactions arises because the transition which proceeds directly from a free nucleon state to a bound state is produced by a relatively weak coupling to the electromag netic radiation field 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, in which one nucleon from an incoming complex particle is stripped off the complex and moves directly to a final bound state without forming an intermediate compound state. In this case the interaction between particles occurs through the medium of another particle and involves strong 1. 2" nuclear forces. This makes it much more difficult to extract information about the nuclear forces since a knowledge of the nuclear forces is required to understand the nature of the transition from one nuclear state to another. For the above reason and for further reasons noted below, a study 3 of the direct radiative capture of protons by deuterium to form He should prove useful in understanding the 3 nucleon system. First, this reaction re-3 suits in the formation of He, which is more tightly bound than the deuteron, 3 the only bound two body nucleus. Also He has both singlet and triplet two-nucleon spin configurations while the deuteron has only the triplet configura-3 tion. Thus the structure of He should be more sensitive to the short range components of the nuclear force as well 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 this reaction is of interest is related to astro-3 physics. The reaction D(p,#) He is the second step in the chain of reactions which supplies most of the energy in the hydrogen-burning stage of the smaller main-sequence stars. This chain is 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 is controlled by the first reaction since it occurs by means of the very weak /3-interaction, it is likely that the reaction D(p,2f) He is the first to supply nuclear energy as the star contracts, and it may consequently have consider able effect on the rate at which the star condenses to the main sequence, at least if there is as high a deuterium to hydrogen ratio in the interstellar gas as is found in the earth. 3 In the early stages of stellar 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 probability of occurring since the concentration of hydrogen is much greater than the concentration of deuterium. The latter reaction supplies neutrons to the interstellar gas which are then captured by the heavy elements and thus there may be significant changes in some isotope ratios from the pri mordial ratios depending on the number of neutrons supplied. Clearly the num ber of neutrons available for this process is dependent upon the initial con centration of deuterium and the amount of it that survives long enough to pro duce neutrons. Thus the isotope ratios 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 is removed by this reaction. 1.2 Previous Work Previous work on the reaction by Fowler, Lauritsen and Tollestrup (FO 49) indicated that the angular distribution was of the form a + b sin -e-2 where the isotropic part a was small but not zero. The presence of the sin -©• component in the angular distribution led these workers to advance the hypoth esis that the capture was mainly the result of an electric dipole transition 3 of a p-wave proton to the ground S - state of He. Their investigation of the yield at 90^ for various bombarding energies showed that the reaction was non-resonant in 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 electric dipole in the reaction plane. This confirmed the hypothesis of Fowler et. al. that the capture was the result of_an EL transition. Wilkinson also suggested that the small iso tropic component could arise from a small amount of spin-orbit coupling. How ever, Griffiths and Warren (GR 55) found that the energy dependence of the yield was different at 90° from what it was at 0°, and this raised the possib ility that the isotropic component might arise from S-wave capture of the incoming protons. Verde (VE 50) had shown that magnetic dipole transitions could occur between S-states of the continuum and the bound three nucleon S-state as a result of small non-central components in the nuclear force. Further measurement by Griffiths et. al. (GR 63) in the energy range from 25 Kev to 45 Kev confirmed the hypothesis that the yield at 0° followed an en ergy dependence characteristic of incoming S-waves. The ground state of ^He is known to have = and thus can con tain the components (SA 55): 2 2 2 However, Derrick (De 60) has shown that the amplitudes of the P 4 and P components are negligible. The continuum states arising from the un bound p + D system contains the following components which can give rise to electromagnetic transitions to the bound state components: 4s 2>4P \ ^ 7 2 Thus the El radiation is the result of transitions from P to Si p states which gives rise to the main sin •&• part of the angular distribution. The isotropic part arises mainly from Ml radiation, which results from trans-4 2 itions from S to S^ states. Other transitions which could be of some signif icance are the following: E2 (2D - 2S), E1(4P - S>), EL(4F - ^D) and 4 4 E2( S - D). There are also some interference terms. The most important of these is the El(2P - 2S)/E2(2D - 2S) interference. Donnelly (DO 68) has investigated the effects of these transitions and their interferences theoretically. 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 in an empirical way. It is important that his findings be checked experimentally to determine whether this is a useful 5. model for the reaction, and if so, to try to extract some theoretically sig nificant parameters from the data. It is of particular importance to investi gate the cross sections predicted by this semi-empirical theory, since if these do not compare favorably with experiment, it is unlikely that any of the other parameters will be particularly significant. Other work has been done recently in this laboratory to measure the angular distribution 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 II THEORY A brief description of the parameters required for the determination of the cross section is given in this chapter. 2.1 The Angular Distribution 3 The measured angular distribution of the reaction D(p,y) He can be described as a series of Legendre polynomials in the form W( ) = JQB1 PA (cos (2.1-1) where -©-' is measured in the center of mass system. Before the experimental angular distribution can be compared with the theory, it must be corrected for the finite solid angle of the detector. It has been shown by Rose (RO 53) that for an angular distribution of the form (2.1 - l), these corrections are particularly simple. The corrected angular distribution is given by W (•&') * £ A£ Pn (cos (2.1 - 2) where - Bx /Qi • The so-called smoothing factors, QA take into account the smearing of the angular distribution which results from the finite solid angle of the detector. They are given by /Jc , where is obtained from the following integral. " f K&s $)[l-t-MXa)]M^U$ (2.1 - 3) o where A is the half angle of the detector jU is the linear attenuation coefficient X$ is the distance traversed by radiation incident on the crystal at an angle ^ to the axis and P. are the Legendre polynomials of order H. Now the angular distribution given by (2.1 - 2) is essentially the differential cross section , and from this one can determine the expec ted gamma ray yield, Ny (-«•), at a particular angle by integrating over the solid angle subtended by the detector at the source. The expression ob tained from this integration is N, W * NpA/0 £ ji0it A0 [it k ?,Q, + £ P2Q, + £ p^j (2.1 - 4) where A/p = number of incident protons No - number of target atoms per square centimeter £ = efficiency of the detector Jlfet= solid angle subtended by the detector at the source. Terms for angular momentum 1 greater than three have not been in cluded since it has been shown (DO 67) that the cross section for the Jl = 4 2 2 term, which would arise from an E2 ( D - S) transition is very small com-/2 2 x pared to the main El ( p - S) transition. The form of the angular distribution given in Chapter I implies that the maximum yield is obtained at a laboratory angle of 90° to the incident pro ton beam, and hence from the point of view of the statistical significance of the number of counts obtained, it is best to measure the gamma ray yield at this angle. Now the total cross section is obtained from an integration over all angles of (2.1 - 2), and the result is 0~r = (2.1 - 5) where A0 is given by (2.1 - 4)» Thus the total cross section for a given energy E, 0~T(i) is computed by combining the last two equations to obtain 8. CTT(E) » ND £ADEF [l + th. p, Q, + 4j pz(?2 + ^ PjQl (2.1 - 6) where A/y C^:^» is the gamma ray yield obtained at •& = 90° for a given energy E and the Legendre polynomials , P2 and P^ are evaluated for = 90°. The other parameters are as previously described. The expression (2.1 - 6) shows that before the total cross section can be determined it is necessary to measure the angular distribution in order to obtain the ratio of the coefficients (j-^j , and ^~ j for a given energy E at which the cross section is to be measured. The measurements of the angular distribution has been made at laboratory proton energies of 500 Kev 650 Kev and 800 Kev (BA 69). From a least squares fit of these angular distrib ution measurements, the ratios of the coefficients were determined. The results are listed 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) A1/AQ = -A3/AQ A2/AQ 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 listed 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 Fig. II-l : Ratio of the coefficients from angular distribution measurements. 10 Table II - 2: Smoothing Factors. T. 2 ^3 .9884 .9655 .9317 Thus the cross section can now be determined, in principle, if the gamma ray yield is measured at 90° to the incident proton beam in an accurately known geometry. But before the description of this measurement, attention will first be focussed on the apparatus used in the experiment, followed by a dis cussion of the measurement of a series of relative cross-sections, and finally the determination of the gamma detector efficiency, which is required for the computation of the absolute cross section. CHAPTER III EXPERIMENTAL APPARATUS 3.1 Target Chamber The target chamber used for most of the angular distribution runs and for the measurement of the relative cross sections was developed in this labora tory by the author in conjunction with G.M. Bailey and M.A. Olivo. The target consisted of a rotating copper disk covered by a thin layer of deuterated* poly ethylene, (C2 D^)n» The polyethylene was obtained in 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 six inches in diameter. In order to reduce the gamma ray absorption through the walls of the chamber, the l/8 inch wall thickness was machined to a thickness of .040 inch in the region over which gamma rays from the reaction could enter the detector. The target chamber was mounted on an angular distribution table. A lucite insulating disk was attached to the bottom of the chamber, so that the chamber would be isolated electrically from the table. Figure III - 1. shows the chamber and the means of locating it 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 lucite insulating ring was placed on the top of the chamber, and the assembly containing the target disk and the motor which rotated it was placed on top of the lucite. 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 will be described in a later section. 11. 12 Fig. III-l : The rotating target chamber. 3.2 Targets The method of making the targets was as follows. First the deuterated polyethylene was dissolved in xylene by boiling the mixture gently for 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 ring. A smaller 0-ring surrounding the cen tral part of the disk limited the deposit to a band about 3 cm. wide. The xylene was then allowed to evaporate slowly at room temperature in a dust free atmosphere, leaving behind a fairly uniform layer of polyethylene. Note: A superior method of making the targets has since been found and a brief description of this technique follows. The tar get is machined out of l/U inch thick brass leaving two rings of brass to contain the xylene instead of using G-rings for this purpose. The target thickness after machining was ap proximately 0.066 inches. The disk is then preheated to a temperature at which xylene will boil and the mixture of xylene and polyethylene is then poured into the container and is allowed to boil until all the xylene has evaporated. The disk is finally removed from the heat and is allowed to cool. This method of preparing the target has three distinct advan tages. First, the deposited layer of polyethylene is smoother and hence more uniform than was obtained before. Second, there are no losses of the xylene solution through spaces which form erly occurred between the 0-ring and the disk, and this 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. foil 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 identical 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 this 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, called the D detector during the angular distribution runs, was placed inside a heavy lead shielding, the dimensions of which are shown in Figure III - 2., and listed in Table III - 1. This detector was also shielded by an 8 inch diameter lead collar with a 1 5/8 inch thick wall which fitted over the photomultiplier. Mounted in front of the detector was a lead collimator which limited the acceptance angle for gamma rays coming from the source. This collimator was not used during the relative cross section runs, however; instead a l/8 inch thick flat lead sheet was placed in front of the detector to reduce the intensity of low energy gamma rays. The other crystal called the M detector, was placed inside a cylin drical collar with a l/4 inch thick wall, and was shielded in front by a l/l6 inch thick lead sheet. The back of this detector was shielded by a l/8 inch thick lead covering which extended over and hence gave further protection to the sides of the crystal. Fig. III-3 : A schematic diagram of the detector assembly. The dimensions are given in Table III-l. 16 Table III - 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 in the experiment is discussed in some detail in the section to which a particular configuration is relevant. Cir cuit diagrams of the photomultipliers and preamplifiers for the detectors have previously been presented (0L 68). A complete list of the electronics used during the experiment is given in Table III - 2. The numbers in parentheses in the block diagrams refer to the numeral order in Table III - 2. 3*5 Data Analysis Several computer programs were written for the U.B.C. IBM 7044 com puter to assist in the analysis of the data. The rather complex analysis pro cedure was required in order to separate from the gamma ray spectra background radiations falling in the same energy range as the D(p,y)-%e gamma rays. The main contributions to this 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 list of the computer programs, with a brief description of each, is given in the Appendix. 17. 3.6 Proton Beam The proton beam was obtained from the U.B.C. Van de Graaff accelerator. This machine is capable of delivering a beam of approximately 20 microamps on target for the energy range covered during this experiment. 18. TABLE IH- 2 : List 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 Differential 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 all energies with this' target would have required a very long time. Thus it was decided to determine the relative yield 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 effectively determining the absolute cross section over the entire energy range explored. The target was prepared as discussed in the previous chapter, and its thickness was estimated to be approximately 2 50 micrograms per cm corresponding to an energy loss of 14 kev for 800 kev in cident protons. The rotating disk was set at an angle of 45° to the incoming beam as shown in Figure IV - 1. Also shown in this figure are the two detectors placed at 90° to the incoming beam, which were shielded in the manner discussed in the last chapter. The distance from the target centre to the crystal face was 4g inches. The rotating disk was electrically connected to the rest of the tar get chamber so that electrons which were ejected from the target by secondary emission caused by the incoming protons would not cause an error in the measure ment of the current, since these emitted electrons would eventually reach the chamber walls. There would also be some protons scattered off the target to the walls and this electrical 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 for leakage current at the completion of the run. A block diagram of the electronics used is shown in Figure IV - 2. 19. Fig. TV-1 : Detector target configuration for the relative cross section runs. 21. H. V. POWER SUPPLY (0 DETECTOR'W (2) SOURCE DETECTOR"M" (2) PULSE (5) GENERATOR PRE- (4) AMPLIFIER MAIN (14) AMPLIFIER KICKSORTER (6) POWER SUPPLY (3) AMPLIF U "IER-B 3) S. C.A.-B (8) SCALER (9) PRE-AMPLI (4) FIER AMPLIFIER-A (8) S. C.A.-A (8) SCALER (9) KICKSORTER (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 linearity 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 all in the analysis of the data. 4.2 Procedure It was known that the target would decay appreciably during the runs so it was necessary to constantly remeasure the yield at one particular energy so that the yield at other energies could be normalized to this. These norm alization 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. All the runs were taken for an integrated charge of from 6000 to 22,500 microcoulombs. The data was analyzed by the method discussed in the next section. 4.3 Data Analysis and Results Rather than add together the data collected by the two detectors and determine the relative yield from this, it was decided to analyze the results separately, thereby determining a relative yield curve for each detector. These two yield curves were then blended together to obtain the relative yield at the various energies. The two sets of data are referred to as the M crystal and D crystal results. The spectra were first 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 this, one could determine the number of gamma 23. • 3 rays in the spectrum which originated from the D(p,tf) He reaction. A typical output of the NAILS program is shown in Figure IV - 3, which gives the ratio of the number of counts in a preselected range of the spectrum introduced by various components as listed (M5.224 gives D(p,tf) He component^, F19MHI gives 19F(p,°a)l60, C135M gives 13C(p,tf)14N, NBGSM gives neutron background, and 15 12 M4.439 gives N(p,°0Q C ). The curve shows the total spectrum fitted to the data. The spectrum represented in this figure is for a proton bombarding energy of 1100 kev. From the relative intensities listed, it is clear that a considerable amount of the spectrum arose from gamma rays originating from the other reactions, and from the neutron background which arose partly from D on D knock-on reactions in the target and partly from D on D reactions in the magnet box. 3 The number of gamma rays from the D(p,2f) He reaction was corrected for dead time losses in the kicksorter, and for absorption of gamma rays by the target backing, this latter correction being applied only in the case of the D crystal results. Now it was necessary to normalize all the results to a given target thickness since the target was decaying while the runs were in progress. In order to monitor this decay, several repetition runs were made at a proton energy of 800 kev. The results of these runs are shown in Figure IV - 4. The yields shown were those obtained from the analysis as described so far. The error bars indicate the statistical uncertainty resulting from the number of counts. A small correction was added to allow for errors in the computer •pro gram NAILS (part of the output of this program was an estimate of the error). The fourth run was omitted as being inconsistent with the rest. Probably the beam spot shifted during this run. It is seen that the M crystal yield is 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 800-f 600 ~1 30 "~1 60 T 90 120 150 ACCUMULATED CHARGE CxlOOO MICROCOULOMBS) 180 Fig. IV-4 : Target decay from the 800 kev runs. The circles refer to the M crystal. The crosses refer to the D crystal. 26. the D crystal yield. This is the result of the more scanty shielding of the M crystal, and of the absorption of gamma rays by the target backing which affec ted only the D crystal. The results of the normalization runs were fed into the computer pro gram POLY-D, which fitted each curve separately as the sum of two exponentials. The yield per unit charge for each of the relative cross section runs was then determined and the counts obtained for each run were multiplied by the appro priate amount to allow for the target decay. A small correction was also applied to allow for the efficiency change of the detectors with the changing energy of the gamma ray. The result of this normalization procedure was to obtain relative cross section curves, one for the D crystal and one for the M crystal. These curves are shown in Figure IV - 5» The error bars indicate partly the statistical error resulting from the number of counts. This was typically 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. First, each set of results was fitted with a cubic least squares curve. The D curve was then multiplied by a constant factor to give the best fit with the M curve. This analysis was done with the computer program CSFIT. A small correc tion was then applied to allow for the change of the angular distribution with energy. The resultant relative cross section curve is shown in Figure IV - 6. The errors arise from two sources. First, there is the error out lined above for the results from each crystal. Added to this is a 1 percent error for the blending procedure done by CSFIT. The total error then is • 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 0.7 0.8 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) Fig. IV-6 : Relative yield for the reaction D(p,tf) He. 29. approximately 6 percent. With this section of the work completed, it now remained only to fix the location of the curve by measuring the absolute cross section. Before this could be done, however, it was necessary to determine the crystal efficiency, which is the subject of the next chapter. CHAPTER V EFFICIENCY MEASUREMENTS 5.1 Introduction It was necessary to determine an accurate detection efficiency of the scintillation counters for gamma rays before the absolute cross section could be obtained. The reaction "^F(p,«y)"^0 was utilized for this purpose. 19 In this 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 this nucleus. These latter states are the 6.06 Mev state (<Xrr)> which decays by electron pair emission to the ground state, the 6.14 Mev state (°0 the 6.91 Mev state and the 7«12 Mev state (<*j) which all decay by gamma ray emission to the ground state. It has been shown (FR 50) that for the 340 kev resonance where the present measurements were made, the ratio of is 0.024. It 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 particles emitted was in close agreement with the number of gamma rays, and that the angular distribution of both reaction products was isotropic. Devons and Hiney (DE 49) had previously shown that the gamma rays were isotropic. The foregoing discussion implies that to determine the efficiency 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 efficiency as the ratio of the number of gamma rays detected to the number of alphas detected, after suitably correcting for the different geometries of the two detectors. 30. » 31 That is to say, the efficiency is I - -~-—-where S is the intrinsic efficiency and N y is the number of gamma rays detected N a is the number of alphas detected w<* is the solid angle subtended at the source by the alpha counter oJy is the solid angle subtended at the source by the gamma detector. 5.2 Apparatus (a) Target Chamber The target chamber used for the efficiency measurements (Figure V-l) has been used previously in this laboratory (LE 64) for the same purpose. The original 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 listed in Table V-1. TABLE V-1: Properties of the alpha detector Material Resistivity Diffusion Depth Sensitive Area Operating Voltage Leakage Current (measured) Phosphorus diffused into n-type silicon 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) nickel foil obtained from the Chromium Corporation of America was placed in front of the alpha de tector in order to reduce the scattered proton flux which would otherwise enter the detector at a similar energy to the alphas. This nickel window also re duced the energy of the °(z and 0/3 particles, so that these now appeared in the same region as the scattered protons. The entrance window to the alpha detector is shown in detail in Figure V- 2. The target chamber was aligned making use of the angular distribution table on which it rested, and the gamma detector collimator, which had cross wires mounted on the front and back. These cross-wires were placed in 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 distribution table was rotated to check that the line joining the centre of the entrance window to the alpha counter was in line 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 for a satisfactory target is that it must be thin 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 yield. For 340 kev bombarding protons, this means that a thickness of approximately 5 to 10 kev would be sufficient. Following the procedure used by Larson (LA 57) in this laboratory, the targets were made by evaporating powdered calcium fluoride onto thin copper plates. The method is to put the CaF in a tantalum boat and pass through this -5 a large current while the apparatus is under vacuum (approximately 10 mmHg). The vapour then deposits on the copper plates which are placed above the boat. 8 INCHES 4. 16 2-56 25/u.in JNICKEL \ / \ / 11 5 8 27" 32 Fig. V-2 : Alpha particle 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 in this 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 their 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 until it just touched the back of the target. The target was then rotated until the rod and its reflection in the target formed a straight line. Since the back of the chamber was 45° to the beam direction, the target then was also oriented this way. The excitation function is 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 particle 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 circuit) is 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 is shown in Figure V-5. Since the energy of the alphas from the reac tion is only 1.73 Mev in the laboratory system, the gain of the main amplifier was halved after calibrating 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 POWER SUPPLY (0 GAMM DETEC A (2) :TOR PULSE (5) GENERATOR PRE- (4) AMPLIFIER AMPLIFIER-AJ (8) S. C. A - A (8) SCALER (9) POWER (3) SUPPLY KICKSORTER (7) Fig. V-4 : Block diagram of the electronic arrangement for the crystal efficiency 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 particle spectrum, 39. reaction would, be more nearly in the centre of the range. Finally the linear ity was checked using the pulser, and this was found to be excellent over the 19 , X16 entire range. A typical alpha spectrum from the F(p,«^) 0 reaction is shown in Figure V - 6. (d) Gamma Detector Electronics The pulses from the gamma detector were fed into a preamplifier and then directly 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 typical gamma spectrum from the reaction is shown in Figure V - 7« 5.3 Solid Angle Calculations (a) Alpha Detector The alpha detector is mounted so that it detects particles at 135° to the incident proton beam and 90° to the target face. The relevant geometry for the calculation of the solid angle is displayed in Figures V-1 and V - 2, and the dimensions shown there are listed in Table V - 2. Table V - 2: Alpha detector solid 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 Travelling 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 Fig. 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 for the measurement of the crystal efficiencies was 3 so that the cross section for the reaction D (p, K ) He could be determined. It was decided that crystal D would be used for this purpose, fully collimated as shown in Figure III - 2. A summary of the dimensions applicable to the calculation of the solid angle has been given in Table III - 1. An error occurred here, however, since an unreported change had been made to the collimator. Approximately 1.1 cm. had been shaved off the front end, and this 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 it should have been. Since the cross section measurements were made at the proper distance, it was necessary to extrapolate the measured crystal efficiency to what it would have been at the proper distance by using a computed change of efficiency with distance. This correction was made by redefining the efficiency to be A = S^K where A is the absolute efficiency defined as the probability of a gamma ray emitted isotropically from the source being absorbed by the crystal. The computer program DEWF which calculates the absolute efficiency of collimated gamma ray detectors, was used to obtain the theoretical absolute efficiency of the detector at the two source to crystal distances of interest. The correction was then applied in the following way. First the absolute efficiency was calculated using the data from the experimental runs. Then the expected experimental value for the proper source to crystal distance was pre dicted making use of the computer results referred to above. This was done 43. as a direct ratio between the experimental and computed absolute efficiencies at the two distances. Finally, the intrinsic efficiency for the proper distance was obtained by dividing the absolute efficiency by the solid angle subtended by the detector at the source. The solid angle is defined as shown in Figure III - 2. In order to check that a large error was not being introduced by this method due to the efficiency not varying smoothly with distance, the theoreti cal absolute efficiency for several source to crystal distances was computed and plotted. The results are shown in Figure 7 - S. It is seen that the absolute efficiency follows an approximate inverse square behaviour as the distance be tween the source and crystal is varied. This is the familiar result for uncol-limated detectors and it is of interest to note that the presence of the colli mator does not cause a radical departure from this behaviour. Arrow "A" shows the source to crystal distance used for the efficiency measurements; arrow "B" shows the proper source to crystal distance, taken from Table III - 1 (R = 19.52 cm.). It was anticipated that the efficiency for crystal M might also be required at some time in the future, and also for both crystals uncollimated at the front face. These measurements were also taken. For the purpose of getting the efficiency with the crystals uncollimated, the relevant geometry is shown in Figure V - 9, with the symbols and their dimen sions listed in 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 4H o DISTANCE FROM SOURCE TO CRYSTAL FACE (cm) 1 1 25 28 0 10 15 20 Fig. V-8 : Relation of absolute efficiency to distance. Fig. V-9 : Uncollimated gamma detector geometry. 46 Table V - 3s Uncollimated gamma detector geometry Symbol Distance R 6.5 in. L 2.5 in. $ 21° 63» The solid 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 carefully 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 all the efficiency runs were made at an energy 2 kev higher. The initial yield was approximately 4000 gamma counts per minute with from one-half to one microampere current on the target. The target was shifted whenever the number of gamma counts fell to 2000 counts per minute. It was necessary to run at the low beam current in order to maintain the dead time of the kicksort-ers below 2%, The time of the runs was determined by the time required to get approximately 6000 alpha counts, and was typically around three hours. The number of alpha counts was summed from the minimum in the spec trum to the upper edge of the alpha counts (approximately channel 250), and was then corrected for dead time losses in the kicksorter. No correction was neces sary for the <*x and <*j counts since the energy of these alphas after passing through the nickel window was considerably less than the lowest energy particles that were counted. The gamma counts were analyzed by the TREAT com puter program, which gain-shifted all the results to the same settings as were used in the absolute cross-section analysis. This program then summed the counts from 3«492 Mev to 6.48 Mev — the same limits as used for the 47 cross-section measurements — and subtracted the appropriate amount of time dependent room background. These results were finally corrected for dead-time losses in the kicksorter and for absorption losses in 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 in the energy region of interest. No beam dependent background was subtracted since a run on a clean target backing showed that the correction would be less than 0.3 percent. The absolute efficiencies were finally calculated as A = NK w? and the intrinsic efficiencies as £ = A/W . The intrinsic efficiency for the proper collimated distance was determined in the way discussed previously. The intrinsic efficiency for the uncollimated crystals was calculated using the solid angle shown in Figure V - 9« The results of the four measurements are listed in Table V - 4* The calculated error is less than 3 percent on all the measurements. Table V - 4: Crystal efficiencies Collimated crystals:-Absolute Efficiency Detector Experiment Proper Distance D .00838 .00743 M .00864 .00769 Intrinsic Efficiency Experiment Proper Distance .704 .679 .730 .702 Uncollimated crystals:-Detector D M Absolute Efficiency .0218 .0218 Intrinsic Efficiency .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 in the knowledge of the number of nuclei in the target and the number of particles incident on the target. The latter is determined by integrating the charge collected by the target, and the former requires a knowledge of the target thickness. It was originally hoped that the deuterated polyethylene target thickness could be found accurately by measuring the energy loss of alpha par ticles passing through it. These alphas were to originate from a source depos ited onto the target backing before the polyethylene was poured on. However, drifts in the electronics made it 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 this method was discarded.. A second possibility for determining the target thickness was to rt measure the neutron yield from the D(d,n) He reaction. However, this method was also discarded since it required knowing accurately the efficiency of the neutron counter, and it was expected that a large correction would be required for the beam dependent background for this efficiency measurement since the accelerator had just been used with a deuterium beam for some time. Finally a decision was made to use a gas target, where the number of nuclei 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 in measuring the gas pressure involves local heating effects resulting from the passage of the incident beam through the gas. This heating causes the gas in the active volume to expand slightly, thus reducing the density in the region of the beam. To minimize the correc tion required for this effect the brass backstop of the target was made very large in the hope that the conduction would be great enough to maintain a constant temperature throughout the cell. The temperature of the backstop was monitored with a copper-constantin thermocouple which was inserted into a hole drilled into the stop. No appreciable difference could be detected between the stop temperature and room temperature with the beam on the target. A first attempt to measure the effect of local heating by passing beams through the gas; cell with varying currents had also failed because of a slow carbon buildup on the foil while the runs were taking place. This carbon buildup produced an energy loss in the incident beam with an error larger than the effect being studied. However, the effect has been measured previously in this way (RO 6l) using deuterium gas but at a higher pressure. After making the appropriate allowances for the different pressure, it was found that, with the beam current used for the cross section measurements, the gas in the beam path was 0.8$ less dense than that in 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 nickel foil obtained from the Chromium Corporation of America. This foil 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 in passing through the foil, and a maximum allowable beam current. The energy loss was measured by noting the shift of the 992 kev resonance of the 27 28 AI (P, rr Si reaction with the foil in place, and then correcting for 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 foil thick ness was found in this way to be 127 kev at 780 kev incident proton energy. The maximum allowable beam current for 780 kev incident protons is 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 cell was determined by first measuring with a travelling microscope the distance between the foil holder and the backstop. Now the gas in the cell causes the foil to depress slightly, and this depression was measured by noting the different focussing locations of the travelling microscope when focussed on the edge of the holder compared to when it was focussed on the point where the beam passed through the foil. The length was determined to be 1.019 - .002 cm. The average energy of the proton beam in the gas cell can be determined by subtracting from the incident beam energy the energy loss as the beam passes through the foil, and one-half the energy loss of the beam as it passes through the gas. This latter quantity was determined by the computer program ENL0TA, which subdivides the gas cell 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 is allowed for. For 800 kev and 780 kev incident proton energies, the average energy in the gas cell was found to be 663 kev and 643 kev respectively. The gas pressure was measured with a U-tube manometer filled 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 filling ; the gas cell. This enabled the pressure in the cell to be read directly as the difference in the level of mercury in the two arms. After filling the cell, a 51 glass tap on the other arm was also closed to prevent any mercury contamination in the system. Other features of the target include an all-brass construction except for a lucite window on one side through which the beam could be viewed hitting the backstop, and an aluminum window on the other side through which the gamma rays passed on their way to the detector. The collimators were made of platinum with a view to reducing the contaminant background radiation, especially that arising from ^F(p,<*0"^0, since previous tests had indicated that platinum had the least contaminating material. For this same purpose, a piece of platinum was attached to the face of the backstop where the beam hit it. A diagram of the target with the nickel foil holder, collimators and electron suppression assembly and gas filling device is shown in 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 first point of concern here is the ejection of secondary electrons from the backstop, which would result in an effective increase in the positive charge measured. To overcome this difficulty, a positive bias was put on the backstop to prevent the electrons from escaping. This introduces a second problem, however, which results from the ionization of the gas as the beam passes through it. If the backstop is positively biased and the rest of the target assembly, including the nickel foil, is unbiased, then the negative ions will drift to the backstop and the positive ions to the foil and chamber walls. This will result in a decrease in the amount of positive charge measured. Hence the foil, target chamber and backstop must all be at the same potential. In this experi ment, +90 volts was used. i 52. TO PUMP Fig. VI-1 : The gas target assembly. 53. The positive bias on the nickel foil has the added benefit that copious numbers of electrons, which would otherwise be ejected from the foil, are prevented from escaping. A problem did arise from the fact that the foil and the foil holder were tied to the backstop. It was necessary that no pro tons hit the edges or sides of the holder; otherwise charge is collected which has not passed through the gas. To prevent this from happening, a collimator system was designed to limit the diameter of the beam to less than 0.1 inch, whereas the width of the foil which was exposed to the incident beam was 0.3 inch. A check was made to ensure that the beam was not diverging by inserting a quartz backstop into the target chamber. An end-on view of the proton beam was thus available. Finally, any secondary electrons which might be emitted from the edges of the collimators must be prevented from reaching the foil assembly. To this end, a suppressor with a -300 volt bias was placed in the beam line between the collimators and the foil holder. The current measured in the target chamber was fed to an Eldorado Electronics Current Integrator, Model CI - 110, the same as used during the rela tive cross section measurements. Very careful calibration of the current inte grator was of course required since any error arising here would be transmitted directly to the cross-section. The calibration was carried out using a Weston Standard Cell and a Gambrell precision resistor. The accuracy of the standard cell was checked using two different resistance bridges (Electro Scientific Industries Model 250DE Impedance Bridge and Model 300 Potentiometric Voltmeter-Bridge). The difference between the measured value and the quoted value for both the cell and the resis tor was found to be less than the error of the measuring instruments. The error of the combination of standard cell and precision resistor was taken to be less than two parts in a thousand. 54 The method of calibrating 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 this calibration is shown in Table VI-1. Table VI-1. Current integrator calibration 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 is 96.6 i 0.4 percent of the charge indicated by the current integrator and this correction was applied to the final results. 6.4 Experimental Procedure The collimated Nal (Ti ) detector (D crystal) was placed at 90° to the incident beam in order to obtain the maximum yield of gamma rays from the reaction. The cross hairs on the collimator, previously described in the sec tion on the crystal efficiency, 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 collection from the detector was accomplished using the same electronic arrangement used for the measurement of the crystal efficiencies, 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 periodically monitored to ensure that all the equipment was performing sat isfactorily. Finally, the measurement of the cross section was broken down into five separate runs in order to reduce the risk of losing all the data if some thing were to go wrong, such as the foil breaking or large drifts occurring in the electronics, and to average out any small background variations. Each run took approximately 4 hours and was further split up into two parts, one with deuterium in the gas cell, and the other with hydrogen. In this way the beam dependent background could be accounted for by subtracting the hydrogen run directly from the deuterium. This method proved practical since no large buildup of background occurred during any one particular run. A correction was also applied for the time dependent background, but this was very small since it 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 purity of 99.7 percent. In order to change the gas in the cell, the cell was first evacuated, then flushed with the new gas and evacuated again before the final filling took place. The runs were made with approximately 150 mm Hg gas pressure in the cell, measured with the manometer previously described. The total integrated charge was 2400 microcoulombs per run for four of the runs and 3600 microcoulombs for the other. A correction was then applied to the charge collected to allow for the error in 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 solid angle subtended by the detector and the angular distribution factor 56 4* pi <?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 effic iency, since this 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 cell. The solid angle was calculated from the data listed in Table III - 1. for Figure III - 2. and was found to be 0.1376 - .0006 steradians. To determine the angular distribution factor, use is made of the data listed in Tables II - 1. and II - 2. The Legendre polynomials were cal culated for centre of mass angles, and it is found that an angle of 90° in the laboratory frame corresponds to 90.71 degrees in the centre of mass frame. Thus the angular distribution factor was calculated to be 1.4624. In order to determine the efficiency change of the detector, use was made of the computer programs LFIT and SHAPE. These programs used in conjunc tion 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 efficiency has been de termined. Now if each standard gamma ray spectrum has the same number of counts in the total spectrum and is 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 ratio between the number of counts in a given energy region of the two spectra will give the relative efficiency of the detector for the two gamma rays, provided that the upper limit of the energy region considered is above the full photopeak, and the lower limit is approximately one-half the full energy, or lower. It was found that over the chosen energy region from 3*492 Mev to 57 6.48 Mev, there were 991«4 counts of the 5*92 Mev radiation and 1000 counts of the 6,14 Mev radiation. Hence the efficiency for the D detector which was found as described in the last chapter was multiplied by .9914 to allow for the change in energy of the gamma ray. Two other corrections, both of which resulted in a modification to the number of detected gamma rays, were required. The first of these arose from dead time losses in the kicksorter,.and resulted in a factor of 1.003 in crease in the number of gamma rays detected. The second arose from absorption losses through the aluminum window, and required a factor of 1.006 increase. Finally, the pressure in the gas cell was corrected for 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 five 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«492 Mev to 6.48 Mev. The appropriate corrections which have just been described were then applied to these results, and the absolute cross section was calculated for each run. The results of these calculations are listed in Table VI - 2. The error quoted with each result is 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 al which has been discussed previously. This expression is 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 is found that this conversion gives the first 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 is the standard deviation of the four runs. Thus the absolute cross section is effectively determined for the entire range of values over which the relative cross section was measured. Figure VI-2 shows these results, 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 Fig. VI-2 : The absolute cross section for the reaction D(p,y) He. The circles are the results of Griffiths et. al. (GR 6l). The crosses are the present measurements. 60 although at higher energies the present results seem to be slightly lower. This is possibly due to an incomplete subtraction of the fluorine contamination in the earlier 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 British Columbia (1967). FO 49 W.A.Fowler, C.C.Lauritsen and A.V.Tollestrup, Phys. Rev., 7j> (1949) 1767. FR 50 J.M.Freeman, Phil. Mag. 42 (1950) 1225. GR 55 G.M.Griffiths and J.B.Warren, Proc. Phys. Soc, 68 (1955) 781. GR 61 G.M.Griffiths, E.A.Larson, and L.P.Robertson, Can. J. Phys. 4J) (1962) 402. GR 63 G.M.Griffiths, M.Lai and C.D.Scarfe, Can. J. Phys., 41 (1963) 724. LA 57 E.A.S. Larson, M.A. Thesis, University of British Columbia (1964). LE 64 J.L. Leigh, M.Sc. Thesis, University of British Columbia (1964). OL 68 M.A. Olivo, Ph. D. Thesis, University of British 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. Sci. Inst., 22 (I96l) 1405. VE 50 M. Verde, Helv. Phys., Acta 23, (1950) 453. WI 52 D.H. Wilkinson, Phil. 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 efficiency of scintil lation crystals for gamma rays, and the weighting (Q) factors that compensate for the finite solid angle of the counter, LFIT : The input to this program is a number of standard gamma ray shapes of various energies. The full peak of each input spectrum appears in the same channel and has the same number of counts as all the other spectra, and all spectra have the same gain. The program then does a cubic fit of the counts versus energy relation for each channel of the input spectra. The output is a matrix giving the four coefficients from the cubic fit for each channel. SHAPE : The input to this program is the output from LFIT. The program then determines the number of counts in each channel for a gamma ray of a specified energy. Thus LFIT and SHAPE used in conjunction interpolate the shape of a specified gamma ray from several given gamma rays. TREAT ; This is a general purpose program for the preliminary treatment of data prior to the detailed analysis done by NAILS. The program can be used to smooth the data, gain-shift it, 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 is used to determine by an iterative least squares pro cedure the relative amounts of various specified components in a given spectrum. Included in the output is an estimate of the accuracy of the results based on the differences of the intermediate iterations with 63 the final results. The input to NAILS was usually the output of TREAT. POLY-D : This program corrects for the deterioration of deuterated poly ethylene targets by fitting the target decay with the sum of two exponentials. CSFIT : This program fits both of the relative cross section results of the two detectors with a cubic least squares curve, and then multiplies one of these curves by a constant factor to give the best fit with the other. ENLOTA This program calculates the energy loss of a beam when passing through a gas target. Allowance is made for the variation of the stopping power of the gas with energy. 

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