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The production of neutrons by secondary processes in the proton bombardment of deuterium Ssu, Yun I. 1955

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THE PRODUCTION OF NEUTRONS BY SECONDARY PROCESSES IN THE PROTON BOMBARDMENT OF DEUTERIUM by Yun I. Ssu 0O0 ' A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in the Department of PHYSICS We accept this thesis as conforming to the standard required from candidates for the degree of MASTER OF SCIENCE Member of the Department of Physics THE UNIVERSITY OF BRITISH COLUMBIA September, 1955 ABSTRACT Several simple and rugged neutron detecting s c i n t i l l a t i o n counters have been b u i l t . The counters • consisted of many layered lucite and zinc, sulfide powder sandwiches placed on the end of Dumont 6292 photomultipliers. One of these counters was used to measure the yield and angular distribution of neutrons produced by the bombardment of heavy ice with 1 .5 Mev protons (below the D(pn)2p threshold). . The angular distribution of the neutrons was found to be somewhat anisotropic and to depend on target thickness, the anisotropy increasing with target thickness. It is proposed that the neutron production i s due to a double process; deuterons after being struck by incident protons collide with further deuterons i n the target producing D(dn)He^ neutrons. This proposal has been confirmed by comparison of the experimental results with calculations for thin and thick targets of the yield and angular distribution of neutrons to be expected from the double process. A further confirmation has been obtained experimentally by observing that the yield of neutrons i s proportional to the square of the D20 concentration in mixed D2O and H2O targets. 35 ACKNOWLEDGEMENTS It is a pleasure to acknowledge the guidance of Dr. J.B. Warren who suggested and kindly supervised the work described herein. The author is indebted to Dr. D.|. James and Dr. K. Erdman for advice and encouragement and to Mr. G.B. Chadwick and Mr. C. Neilson for their help with the experimental part of the work. Thanks are also due to the members of the Van de Graaff team for assistance during the runs, in particular to Mr. J.B. E l l i o t t , and to Dr. G.M. Griffiths for help in the preparation of this thesis. TABLE OF CONTENTS Chapter T i t l e Page I INTRODUCTION 1 II FAST NEUTRON COUNTERS 1 . BF-j Long Counter 5 2 . ZnS-Plastic Sandwich Counter 6 3 . Counter Performance 13 III NEUTRON MEASUREMENTS 1 . Apparatus 15 2 . Measurements 16 (a) Excitation Function for Neutron Production 16 (b) Target Thickness Calibration 17 (c) Thin Target Yield and Angular Distribution 20 (d) Thick Target Yield and Angular Distribution 21 (e) Concentration Run 23 IV CALCULATIONS 1 . Introduction 24 2. Method of Calculation 24 3 . Details of Calculation 26 V DISCUSSION 33 BIBLIOGRAPHY 36 c LIST OF ILLUSTRATIONS Fig . Page T i t l e 1 10 Fast Neutron Counter, 2 18 Neutron Counter Electronics. 3 13 Differential Bias Curve - Ra-Be Neutrons. 4 13 Neutron Counter - Efficiency vs Bias. 5 14 Differential Bias Curve - d on d Neutrons. 5a 14 d-d Neutrons Angular Distribution. 6 15 Apparatus Layout. 7 16 Excitation Function. 8 18 Measurement of DgO Thickness. 9 20 p-d Neutron Angular Distribution - Thin Target. 10 21 p-d Neutron Angular Distribution - Thick Target. 11 23 Concentration Run. 12 24 Target Subdivisions. 13 28 Ratio of p on d Measured to Rutherford Scattering Cross Sections. 1 Chapter I  INTRODUCTION While studying the D(p,jr)Hep reaction Warren and Griffiths found that the angular distribution of flf-radiation from this reaction has the form Sin^e+C, where C i s a small constant equal to 0.0/+6 for 1 Mev protons and 0.025 for 1.75 Mev protons. In 1952 Wilkinson, using the photodisintegration of the deuteron as a polarization analyzer, found that the /-radiation i s predominantly polarized at 90° to the plane containing the direction of the incident protons. The simplest assumption consistent with the angular distribution and the polarization i s that the transition i s electric dipole i n nature. According to direct radiative capture theory, with conservation of the r-component of the angular momentum as a result of no spin-orbit coupling, Blatt and Weisskopf's formula would give an angular distribution of the form s i n 2 6 for capture of a p-wave proton. The small additional isotropic component represented by ! lC n above can be explained by adding a small spin-orbit coupling interaction. Preliminary experiments led Warren and Griffiths to suggest that neutrons accompanied the ^ "-rays from 2 the D(p,^)He^ reaction. . However, the simple lucite and zinc sulfide phosphor combination used by them was not sufficiently sensitive and Boron trifluoride counters were too bulky and /-ray sensitive to study this effect. In order to correctly evaluate C accurately, i t was necessary to study the neutrons further. The objectives of the present research were ( 1 ) to build a highly sensitive neutron detector which must be completely insensitive to /-radiation, ( 2 ) to measure the neutron yield accompanying the D(p,/)He3 reaction and ( 3 ) to explain their origin i f neutrons were actually found. The only previous work on this subject i s described by Jennings et a l ( 1 9 5 0 ) in an unpublished Westinghouse report. They measured the excitation curve of neutron production from a thick D 2 O target, with a Boron trifluoride counter, and suggested.. that the neutrons were due to deuterons in the target being scattered by incident protons and then colliding with other deuterons producing D(d,n)He^ neutrons. These authors made an approximate calculation by considering the target in 5 0 0 kev-thick layers and the result agreed to an order of magnitude with what they found experimentally, assuming the neutrons were emitted isotropically. The direct process D(d,n)2P i s energetically impossible at the energies under consideration and the 3 cross-section of the photodisintegration of the deuteron is too small to account for the observed yield. The double process suggested by Jennings et a l i s the most promising theory, and as w i l l be seen later i t explains most features of the present experiments, including the fact that the angular distribution i s rather anisotropic. The problem of the neutron yield when a heavy ice target i s bombarded with protons has been attacked in several ways. Fi r s t , an excitation function for neutron production was obtained for protons in the energy range 600 Kev to l.S Mev. . Second, an experimental measurement of the yield and angular distribution of neutrons was made for 1.5 Mev protons and this was compared with the yield and angular distribution results obtained by a calculation based on the double process hypothesis. Finally, a measurement was made of the yield of the neutrons as a function of the concentration of D2O in a mixed heavy water and light water target. If the neutron production i s due to a direct reaction the yield w i l l be directly proportional to the concentration. However, i f a double process i s involved the yield should be proportional to the square of the concentration. This follows from the fact that the number of recoiling deuterons i s proportional to the concentration of deuteron atoms present i n the target, and the chance of a c o l l i s i o n between a recoiling deuteron and a further 4 deuteron i s also proportional to the concentration of deuteron atoms in the target. As suggested by Mr. G. Chadwick, i f the double process mentioned above is the correct one there should be no neutron yield when an ordinary water target i s bombarded by deuterons. However, this suggestion was not tried out experimentally due to the high neutron background that would result from the deuteron beam i n the Van de Graaff generator. 5 Chapter II  FAST NEUTRON COUNTERS 1. B F 3 Enriched Long Counter A B F 3 long counter (Hanson and McKibben 1947, Heiberg 1954) has been used in this investigation. However, since the B F 3 f i l l e d counter i s most efficient for thermal neutrons i t i s necessary to surround the counter with several inches of paraffin i f i t i s used to count fast neutrons. Also i f i t i s to be relatively insensitive to a slow neutron background i t i s necessary to cover the paraffin with cadmium and to surround this with a further paraffin shield on a l l sides except that from which the fast neutrons enter. Consequently the BF^ long counter i s rather bulky and cannot be placed very close to the target. The counter used here was half a meter long and 40 cms. in diameter. Further the long counter i s slightly 2f-ray and slow neutron sensitive, so that when placed close to the target under the Van de Graaff generator the ^-ray and scattered neutron fluxes produce a rather high background count. Therefore a counter with much lower sensitivity to <T-rays and slow neutrons was essential for these experiments. The BF-j counter has, however, proved useful as a mQnitor for 6 d on d angular distribution runs done to check the characteristics of the counter described later. It was also used for the thick target, runs for the p on d experiment where the neutron yield was relatively high, to give an independent check on the identity of the emitted neutrons as well as for the angular distribution measurements. For these experiments an Atomic Instrument Company type 205-B low noise linear preamplifier was . used with the long counter in order to get the best possible signal to noise ratio. The preamplifier output was connected to an Atomic Instrument Company type 204 B linear amplifier followed by a discriminator and scaler. The BF^ counter was operated at 1750V from a stabilized H.T. supply. 2. Zn S-Plastic Fast Neutron Counter Chadwick (1932) f i r s t recognized the existence of the neutron as such, as a result of measurements with a thin window ionization chamber which detected protons which were ejected from a paraffin-xvax plate by the incident neutrons. Since that time several instruments have been employed for neutron detection, which used the same principle with various refinements. A simple extension of Chadwick's method i s that used by Coon and Nobles (1947) who placed a thin hydrogen containing radiator inside a proportional counter. High pressure hydrogen f i l l e d ionization chambers in which the reco i l protons are ejected 7 from the chamber gas itself have also been used (Stafford, 19<+S). With the advent of the scintillation counter, i t has become possible to use solid hydrogen containing crystals to detect neutrons by means of the knock-on protons producing light in the crystal, (Bell, 1948v,Se'gel et al, 1954).. However, such organic phosphors are also /-ray sensitive, which prohibits neutron measurements in the presence of large /-ray fluxes. The jf-raj sensitivity can be considerably reduced by using a very thin layer of an organic phosphor such as Anthra^cene, since the range of an electron is much greater than that of a proton of the same energy. Several tests were made by the author of thin anthraS'cene films, and i t was found that they were not satisfactory for the present experiments, since the neutron detection efficiency is too low when the film is thin enough to have low ^-ray sensitivity. A thin layer of zinc sulphide powder placed on the end of a photomultiplier can also be used to count the recoil protons from a plastic radiator placed in front of the photomultiplier. However, the combination has low efficiency. An improvement in efficiency was obtained by Hornyak (1952) who mixed Zns powder with lucite molding powder and compressed the mixture under heat to form a solid semitransparent button which was used as a neutron detector. With the bias at which a the (Jf'-ray sensitivity i s quite low, the device has a neutron efficiency of 2.5%. The useful size i s limited by the rather poor transparency}. The same idea has been applied by Seagondollar et a l (1954) who mixed the Zns powder with Bio-plastic. Emmerich (1954) placed 0.125 inch sheets of lucite in a Zns-paraffine mixture block to act as light guides; with this arrangement he achieved an efficiency of 3,. 6$ for 4 Mev neutrons at a bias level where the efficiency for radium forays was of the order of 10"^. The efficiency of these devices can be improved somewhat by the addition of fissionable elements such as Uranium and Thorium compounds. For the experiments described below i t was necessary to have a y-ray insensitive counter with as high a neutron efficiency as possible. Several attempts were made to incorporate Zns powder in a solid plastic material. Lucite chips were dissolved in acetic acid or i n .eth^ll acetate and Zns powder was mixed i n . However, the method was not successful, because when the plastic solution was too dilute the Zns poxvder settled out before hardening took place, and when the solution was less dilute i t was d i f f i c u l t to introduce the Zns without also introducing air bubbles which destroyed the transparency1 A compromise method has been developed using a large number of thin layers of Zns powder sandwiched between thin lucite plates, 9 the whole assembly forming a rectangular block, from which the light produced in the Zns powder escapes through the plates into the photomultiplier. Zinc sulfide activated with silver has a very high light conversion efficiency ranging from 20 to 2&*#. The emission spectrum i s between 4000 and 6000 Angstroms with peaks at 4500 and 5200 Angstroms. The multiple crystalline powders are opaque for thicknesses greater than about 25 m e - ji cm2. Grave and Dyson (1949) found that with 5 Mevc<-particles the counting rate remains constant from 10 to 22 mg/cm2 and beyond this thickness the counting rate f a l l s rapidly. For these thicknesses the response to /•-radiation and high energy electrons i s relatively small and the /"-ray pulses can be biased out electronically. Layers of equal thickness of Patterson D and R p A 33-Z-20 A ZnS phosphors were placed on the end of a photomultiplier with a lucite plate in front, and were tested with neutrons from a Ra-Be source. It was found that the R C A 33-Z-20 A powder gave about 30$ more counts above the selected bias level and so this phosphor has been used throughout the following work. The preliminary work was. performed with an R C A 5&*19 photomultiplier. This tube has a cathode sensitivity of about 40 /ua. per lumen with a minimum limit of 20 /ua per lumen. Its semi-transparent photocathode i s deposited on the inner surface of the top of the tube Left Figure a. ZnS powder - thin layer b. Lucite light guide Right Figure a* ZnS - Lucite sandwich b. MgO powder c. Photomuitiplier d. Light cover e. Magnetic shield 10 for good light collection. The spectral response extends from about 3000 to 65OO angstroms with a maximum at about 5000 angstroms which overlaps well with the emission spectrum of Zns. The f i n a l runs were made using a Dumont 6292 photomuitiplier which has a spectral response from about 3100 to 6750 anstroms, with maximum sensitivity at about 47^0 angstroms. The cathode sensitivity, between 40 and 60 Afdi per lumen, i s greater than that of the E C A 56*19 and also i t has f l a t photocathode which fa c i l i t a t e s the mounting of the phosphor. Fig. 1 shows the construction and the mounting of the ZnS-plastic multiple sandwich. Thin lucite plates were dipped in ethyl formate and while s t i l l wet a weighed quantity of ZnS powder was sprinkled on evenly through a fine mesh nylon cloth. Then the plates were stuck together under pressure u n t i l dry. The block was polished on a face perpendicular to the plane of the plates. And this face was stuck to the photomuitiplier with DOW-Corning 200 silicone o i l which has a viscosity of 10^ centistokes. Tests were made to determine the optimum thickness of the Zng between the lucite plates. For thicknesses greater than 12 mg/cm2 the V-ray sensitivity becomes appreciable and thicknesses less than 10 mg/cm2 gave a 11 satisfactory neutron response. Several thicknesses of lucite plates were also tried and i t was found that for Ra-Be neutrons the efficiency decreased for thicknesses greater than 0.125 inch. The optimum thickness depends of course on the neutron energy. The ranges of protons in lucite as calculated from their air ranges (Bethe and Livingstone 1937) are shown -below: Ep Mev Range in air (cm) Range in lucite (mm) 1 2.3 ..025 2 7 .1 .073 4 23..0 .25 6 4 6 . 7 ..51 3 77.2 .6*5 10 110 1.2 The maximum thickness that can be used satisfactorily depends on the height of the block required, that i s on the desirable total efficiency since, for a given height, i f the plates are too thin, light i s not transmitted from the top of the block to the photomultiplier. A check was made on the transmission of light down the block by preparing a Zns plastic sandwich with 0.125 inch thick lucite plates 5 inches long. This was placed endwise on the photomultiplier, a Ra-Be neutron source was placed 25 cm away to one side and the counting rate was observed, as a function FAST NEUTRON COUNTER ELECTRONICS 0.5M O 5M O.SM j ^ ^ y ^ . S M .0.5M 0.5 M Ir 6J6 »I0M IM lOOpt 0 5 i 3 * 4= 8 pf H T / \ ,IOOK 7 O.Lif 1| © O U T P U T >3K WW-Dumont 6 2 9 2 preamplifier P.mJ pr e-amp i near amp |H.T. power supply H.A. power supply b i a sed amp c. r. o, scaler puIse he i ght analyzer F i g . 2 12 of the length, which was altered by cutting sections from the end of the sandwich remote from the photo-multiplier. It was found that there was l i t t l e change in counting rate u n t i l the length was reduced below 3 inches and the counting rate became roughly proportional to the length for a length less than 1.5 inches. Of the sandwich assemblies which were made for testing, details of two which had useful characteristics are given below: sandwich (1) Sandwich (2) lucite thickness -^L _^ IL length 1 cm 2 cm width 4 . 2 cm 4 . 4 cm number of layers 50 23 thickness of Zns 7 mg/cm2 7 mg/cm2 Sandwich number one with the thiner plates had an efficiency 1^ times that of number two• However, due to i t s smaller height i t gave fewer counts for a given source strength than number two. Due to the light loss in the thin plates i t was not desirable in this case to make the plates any higher. Sandwich number two was used for the measurements described below. After the sandwich assembly was polished and stuck to the photomultiplier with DC 200 silicone o i l i t was covered with MgO powder produced by burning magnesium ribbon close to the surfaces. Finally a I50 F i g . 3 DIFFERENTIAL BIAS CURVE (2) i 50 mg RaBe mixed source ii one mc RaTh in contact 5 0 0 f 4 0 0 3 0 O 2 0 0 I 0 0 1.55 3-10 4 . 6 5 IOO 5 0 L n ii I o 5 2 0 2 5 pulse height 3 O 3 5 4 0 F i g . , 3 F i g . 4 i I I I * 1 1 1 1 • * • • * • » 20 30 40 50 60 70 80 bias 13 brass light shield was placed over the phosphor and the photomuitiplier and a magnetic shield put in position as shown in figure 1 )• The arrangement of the preamplifier and the subsequent electronics are shown in Fig. 2 . The photomuitiplier was operated at 1250 volts from a well-sfc&bilized powder pack. The signal output after passing through the preamplifier cathode follower was amplified by a Northern Electric type 1444 linear amplifier. The pulses were f i n a l l y passed via a biased amplifier to a scaler and to the 30 channel "Canadian Marconi" kicksorter. Counter performance Fig. 3 shows a bias curve for the fast neutron multiple sandwich counter when a 50 mg Ra-Be source was placed 25 cms from the sandwich. Also shown i s the spectrum produced by a one millicurie RaTh y^ -ray source i n contact with the counter. A comparison between the neutron and gamma ray sensitivities was made using Ra-Be and Co sources of known strengths. The results as a function of discrimination bias are shown in Fig. 4.* It i s clearly apparent that a reasonable neutron efficiency can be obtained at bias levels for which the gamma-ray sensitivity and the counter background are very low indeed. F i g . 5 ^ DIFFERENTIAL BIAS CURVE (I) ( i. monoenergetic d d neutrons 2 0 0 ii. one mc C 0 6 O in contact F i g . 5a ' ' ' 1 — 1 r - l 30 60 90 120 150 180 angle lab system 14 Fig. 5 shows the spectrum obtained with d on d neutrons produced by the U.B.C. 50 Kevaccelerator. For a bias at which the counter had negligible response to RaTh gamma rays the efficiency for 4*3 Mev d on d neutrons (produced by the U.B.C. Van de Graaff generator) was 0 .77#» Under these conditions only four counts were recorded when the counter was placed 40 cms. from a flourine target which was bombarded for 8" minutes with 650 millicoulombs of protons covering the 6*73 fluorine resonance. The cosmic ray and local background under these conditions i s only five or six counts per hour. The angular distribution of the d on d neutrons, produced by bombai^aing a thin D2O target with one Mev deuterons, was measured and the experimental results were compared with the angular distribution which was calculated from results given by Hunter and Richards (1947).* These workers measured the d on d neutron angular distribution at several energies with a BF^ counter and from their results have given an expression for the angular distribution as a function of deuteron energy. The measured and calculated values are shown i n Fig. 5 a . The agreement between the two sets of data i s very satisfactory indicating that the efficiency of the multiple-sandwich for neutrons from two to four Mev is quite independent of neutron energy. 15 a. proton, beam b. mass two beam c. magnet box (size not i n proportion) d. pumping outlet e. paraffin shield f• glass tube g. bellows h« beam stabilizing s l i t s i # quartz focussing plate j . tungsten stops k. window 1. lucite insulating disc m. l i q u i d air trap n. l i q u i d a i r o. gold target backing p. degree circ l e q. fast neutron counter r . rotating arm s. nickel tube t. 50 cc bulb u. Hg manometer Chapter III  NEUTRON MEASUREMENTS 1. Apparatus The target was supported on a copper plate suspended from the bottom of a liquid a i r trap. Heavy water vapor was frozen on a gold plate 1.5 mm thick, which was screwed to the copper plate. The gold plate was thoroughly cleaned as follows. After successive rinses of concentrated sulfuric acid and sodium hydroxide solution the plate was washed with d i s t i l l e d water and pure alcohol and ele c t r i c a l l y etched in potassium cynide solution for eight hours u n t i l crystal structure was apparent on the surface. Finally i t was rinsed with d i s t i l l e d water and baked for a few hours at 100°C. Measured volumes of D2O vapor from the dispenser could be admitted to the target chamber via a small hole in a nickel tube facing the target. The target chamber was supported on a stand provided with a degree ci r c l e for measuring the angular position of the neutron counter which was mounted on a rotatable arm as shown i n Fig. 6. Prior to f i n a l assembly the target chamber and i t s vacuum connections were baked to F i S . 7 20 c o X3 O V-o> •4— if) O) Q. jQ E o O u 0> CL >» c o c hl-5 A corrected EXCITATION FUNCTION o calculated o measured by ZnS counter (absolute scale) A measured by BF 3 counter for background (arbitrary scale) A i b iOOO 150P proton energy (kev) 2000 16 remove a l l traces of water and organic vapors which could have formed a contaminating deposit when the target was cold. On the backside of the copper target mounting plate there was a thin CaF2 target evaporated on a tungsten backing. This was used to measure target thicknesses as described below. • The target and the liquid a i r trap were insulated from the outer target chamber and maintained at a potential of + 3 0 0 volts with respect to the rest of the apparatus i n order to suppress the secondary electron emission. Tungsten stops were used to define the beam hitting the target. The integrated current f a l l i n g on the target was measured by an electronic integrator (Edwards 1951). 2. Measurements The measurements can be divided into five parts which w i l l be described separately. (a) Excitation function for neutron production The 0° neutron yield from a thick D2O ice target has been measured for proton bombarding energies of 1500, 1200, 1000, 300 and 6 0 0 Kev. using the BF^ long counter and the ZnS lucite sandwich fast neutron counter described above. The results obtained are shown in Fig. 7; i t can be seen that the neutron yield increases rapidly with increasing proton energy. Also shown, by the open circles, are points representing the neutron yield as calculated from the theory for the double 17 process described below. The yield as measured by the BF^ long counter i s indicated by triangles; the vertical scale of this curve i s arbitary since i t was d i f f i c u l t to define the solid angle, when the front of the counter was only one third of the counter length from the target. The 1500 Kev points have had 15 percent background subtracted. The background presumably arose due to the sensitivity of the B F 3 counter to the low-energy degraded neutrons i n i t i a l l y produced by the mass-two beam in the magnet box. The background was measured by interrupting the proton beam by the quartz plate as described in detail i n section "d". It i s worth noting that the background i n the Zns plastic sandwich counter was negligible during the excitation function runs. (b) Target thickness calibration In order to measure the absolute yield of neutrons from a thin target i t was necessary to know the number of deuterons per square cm. on the target. This was determined in the following manner. The target was rotated to expose the CaFg to the proton beam and an excitation curve was obtained for the 373 Kev resonance of the F1^(p,c^,0/) reaction by observing the /T-rays In a Nal s c i n t i l l a t i o n counter. Then the target was turned to face the nickel tube from the D2O vapour dispenser and after the target was cooled F i g . 8 40000r-30000k in • • — c o 20000 CO E C 10000 MEASUREMENT OF D 2 0 THICKNESS 8 6 0 8 9 0 9 2 0 proton energy kev 18 with liquid air, a standard quantity of vapor, hereafter called one scoop, was admitted to the target chamber where i t froze on top of the CaF 2. Finally the CaF2 was turned back to face the proton beam and a second excitation curve was obtained for the 873 Kev resonance. In this case the resonance occurs for proton energies higher than 873 Kev. by an amount equal to the loss of proton energy in passing through the D20 ice layer as shown in Fig. 8. From the measured shift in resonance energy and from a knowledge of the stopping power of ice for protons, the thickness of the ice layer can be obtained. The stopping power of heavy ice has been carefully measured for protons in the range 18 to 540 Kev by Wenzel and Whaling (1952). In this energy range the agreement with Bethe's theory i s good and so some confidence can be placed in values of the stopping power calculated by Hirschfelder and Magee (1948) using the same theory but for higher proton energies. Therefore once the shift in resonance energy E has been measured the target thickness /±x can be calculated. For a target consisting of one standardized scoop of D20 vapor, the shift in the 873 Kev nesonance was found to be 28.3i5 Kev as shown in Fig. £. From the values of versus AX obtained from the above theory, and tabulated by Gri f f i t h s (1953) i t can 19 be shown that a A E of 23.3 Kev for protons of 390 Kev corresponds to a target thickness of 1.13x10"*^ cm. In this way a calibration of the target thickness per scoop was obtained. In subsequent work i t has been assumed that a target l a i d down under exactly the same conditions as the calibration target had the same thickness per scoop. Also i t has been assumed that for targets thicker than one scoop the thickness was proportional to the number of scoops. In order to make thick targets both valves of the dispenser were opened for seven minutes and the neutron yield under proton bombardment was measured. Then the valves were opened for a further seven minutes and the neutron yield was measured again. This process was repeated three times, u n t i l there was no further increase i n neutron y i e l d . Finally the valves were opened for a further four minutes to make absolutely certain that the target was "thick", i . e . at the particular bombarding energy a l l incident-protons and scattered deuterons were stopped i n the ice layer. F i g . 9 pd ANGULAR DISTRIBUTION (thin target) O calculated^ , . O measured > absolute scale 20 (c) Thin target yield and angular distribution A thin target consisting of three scoops of D20 vapor was set at 45° to the incident beam and was bombarded with 1.5 Mev protons. The reaction was monitored with a Nal s c i n t i l l a t i o n counter set at 90° to the incident proton beam in order to count the gamma rays from the D(p,y)He3 process, and the neutron yield was measured with the fast neutron s c i n t i l l a t i o n counter as a function of the angle of the counter with respect to the incident beam direction. Measurements of the incident beam current, the number of neutron counts and the number of gamma ray counts, were made with the fast neutron counter at 0°, 45°, 90°, and 150°. The results after taking into account the efficiency and solid angle of the neutron counter are given in the table below. The errors quoted are s t a t i s t i c a l errors only. No correction has been made for neutron absorption by the target backing. The counter was placed 3.3 cms. from the target. Also shown in the table are figures for the yield on the basis of the double process obtained from calculations given below. Fig. 9 shows the results graphically. Neutron yield per steradian per millicoulomb of proton beam Detector position 0° 45° 90° 135° 150° measured 42200 33300 27900 25500 ±5-7$ ±5.7$ calculated 51700 33200 19100 24500 F i g . 10 pd ANGULAR DISTRIBUTION (thick target) -20 O calculated O measured with ZnS counter I eft ^ absolute scale A measured with BF counter A corrected for background right-* arbitrary scale 0 1 1 45 90 angle lab system — i — 135 21 (d) Thickv.target yield and angular distribution A thick target was l a i d down, and placed perpendicular to the proton beam. The neutron yield was measured at 0°, 4 5 ° , 90°, and 1 2 5 ° , for a proton bombarding energy of 1 .5 Mev. A Nal s c i n t i l l a t i o n counter served as a monitor by counting the D(p,y)He3 gamma rays. The fast neutron counter was placed 10.7 cms., center to center, from the target. . The f i n a l results are given in Fig. 10 and in the table below i n terms of the neutron yield per steradian per millicoulomb of protons obtained after taking into account the neutron counter efficiency and solid angle. Neutron yield per steradian per millicoulomb of proton beam Detector position 0° 45° 90° 125° 135° measured 14.4xl0 6 9 .57*10 6 7..3xl06 6 . 3 2 x l 0 6 +2.8$ ± 3 . 5 $ ±7.2$ ±4.0$ calculated 11.9xl0 6 6.36xl0 6 3.87xl0 6 5.12xl06 The last line indicates the calculated yield. Also shown are the s t a t i s t i c a l counting errors. Since the neutron yield from the thick target was considerably greater than that from the thin target, i t was also possible to use the BF^ counter in these measurements. The front of the BF-^  counter was placed 33..9 cms. from the target at 0°, 4 5 ° , 90° and 1 2 5 ° , and the number of counts observed at each angle i s shown i n the following table. 22 counter position 0° 45° number of neutron 6700 3560 counts number of gamma ray 46100 46300 counts neutron background 1970 counts corrected neutron 4730 counts The angle distribution indicated by the uncorrected BF^ counter results i s much more isotropic than that for the fast neutron counter given above. The BF^ counter i s , however, sensitive to the rather large background of Slow neutrons. A separate background run was made at 0° and 90° with the proton beam interrupted by the quartz focussing plate, with the results shown in the table. The f i n a l line in the table indicates the BF3 counter results at 0° and 90° after correction for the background, and i t i s apparent that the angular distribution obtained in this way i s in rough agreement with the fast neutron counter results as shown in Fig. 10. It was noted that the BFj counter background was greater, the closer the counter was to the magnet box. 90° 125° 5370 9300 44700 47000 3630 1740 F i g . 11 3, 23 (e) C o n c e n t r a t i o n run In order to provide a further test of the double process hypothesis the neutron yield at 0° for 1.5 Mev protons was measured with thick D2O + H2O mixed targets, with percentages of D2O ranging from 100 to 0 percent. The results are shown i n Fig. 11. The gamma-ray yield i s directly proportional to the deuteron concentration i n the target as expected from the fact that the gamma rays arise from the direct D(p,^)He^ process. However, the square root of the neutron yield i s proportional to the deuterium concentration, pr in other words, the neutron yield i s proportional to the square of the deuterium concentration. This experiment strongly supports the hypothesis of the double-process origin of the neutrons, as suggested in the introduction. F i g . 12 (a) proton beam l a i N \ s c a t t e red deu i terons B D s c a t t e r e d d e u t e r o n c o n e s proton b e a m t y p i c a l s e c t i o n l a y e r A c o n e 3 t u b e 2 s e c t i o n 4 24 Chapter IV  CALCULATIONS 1. I n t r o d u c t i o n Calculations have been made1 of the yield, excitation function, and angular distribution, of neutrons from thick and thin targets of D2O ice bombarded with protons, on the assumption that they are caused by the double process suggested above, 1. e. deuterons scattered by incident protons cause subsequent D(d,n)He3 neutrons by co l l i s i o n with further D atoms in the target. 2. O u t l i n e of C a l c u l a t i o n Method In the case of a thick target the calculations follow, the physical processes step by step as follows. The target i s divided into 6 layers perpendicular to the proton beam as shown in F i . 12(a), and in each layer the protons are considered to have a constant energy equal to the mean energy of the actual protons while in the layer. From a knowledge of p-d scattering the energy and the angular distribution of the deuterons scattered from each layer i s calculated. The scattered deuterons from any layer can be divided into overlapping cones symmetrical about the proton beam direction as shown in Fig. 12(b). It was assumed that a l l the deuterons in each cone had an i n i t i a l 25 energy equal to the mean i n i t i a l energy of the deuterons in the cone, this energy being obtained by simple mechanics knowing the angle of the cone and the incident proton energy. Each cone was divided into 12 tubes running out from the apex and equally spaced about the cone axis. The angle between the axis of each tube and the line joining the target and the neutron counter was then obtained by geometrical methods, so that knowing the angular distribution of the neutrons emitted by D(d,n)He3 reaction caused by deuterons travelling down the cone, through the heavy ice, i t was possible to obtain the contribution from each tube in the direction of the detector. As the deuterons travel down each tube they lose energy and so the tubes were divided into sections along their length as shown in Fig. 12(b) and i n each section the deuterons were assumed to have an energy equal to the mean deuteron energy in the section. The table below gives a rough idea of the number of subdivisions used in the calculation. Subdivision Number used Layers 6 (A,B,C,D,E,F) Cones number depends on layer, e.g. 6 for layer A, 3 for layer D and 1 for layer F. Tubes 12 for each cone Tube sections number depends on the particular layer and cone i.e. on deuteron 26 energy, e.g. 6 for layer A cone 1,3 for layer A cone 4 and 3 for layer D cone 1. Actually the total number of sections was 252 for layer A alone and. 672 for a l l 6 layers. Finally from a knowledge of the energy and angular dependence of neutron yield for the D(d,n)He^ reaction i t was possible to calculate the contribution of each section to the neutron yield in the detector direction. After the individual section contributions were calculated, the total neutron yield in the counter direction can be obtained by summing over a l l sections of each tube, over a l l tubes of each cone, over a l l cones of each layer and over a l l layers. The process was repeated for 4 different counter positions namely 0 ° , 4 5 ° , 90° and 135° between the proton beam direction and the counter to target direction, to give the angular distribution shown in Fig. 10 . Further details concerning the cross-section parameters employed in the calculation are given below. 3 . Calculation Details The target was divided into layers each one having approximately ^ of the incident proton energy of 1.5 Mev dissipated in i t . From the known stopping power of heavy ice for protons (Wenzel and whaling 1952, Griffiths 1953) the corresponding thickness in cms. of each layer was obtained. The energy of the protons 27 in each layer was assumed to be constant and equal to the average energy of the protons in the layer. Then the number and the angular distribution of deuterons scattered out of each layer was obtained as follows: The scattering cross-section of deuterons for incident protons has been measured at 1510 Kev and 825 Kev by Bailey et a l (1947) and at 250 Kev by Taschek (1942).. From the angular distribution and cross-section data of these authors angular distribution and cross-section curves were interpolated for the mean proton energies assumed for each layer. Thus, from these curves the number of deuterons scattered from any layer into any. angle could be estimated. Also from the mechanics of the scattering process (Schiff) the energy of the deuterons from any layer at any angle could be obtained. The scattering i s symmetrical about the proton beam direction. Therefore since the problem has to be numerically integrated the scattered deuterons were divided into cones; the angular limits of each cone were defined in terms of approximately equal energy intervals of the scattered deuterons, and i t was assumed that these deuterons a l l have an energy equal to the mean energy of the deuterons in the cone. Since i t would have been d i f f i c u l t to integrate the graphical results concerning the number and angular distribution of scattered deuterons given above over the angles of Fig- 13 O 3 0 6 0 9 0 120 I50 ANGLE CM. 28 each cone, the following procedure was adopted to get the total number of deuterons scattered into each cone. From the above scattering data and from calculated values of Rutherford scattering, the ratio of actual measured scattering to Rutherford scattering at the angles and energies required were plotted as shown in Fig. 1 3 . It should be noted that the measured scattering i s higher than the value obtained from Rutherford scattering alone, the ratio depending on energy gnd angle. Assuming Rutherford scattering and using the analytical expression for the energy and angular dependence of this scattering cross-section the number of deuterons scattered into each cone was obtained by analytical integration between the angular limits of the cone. Then this number was multiplied by the ratio of measured to Rutherford cross-sections for the angle and energy involved in the cone to obtain an approximate value for the actual number scattered into each cone. Now although the cone i s symmetrical about the proton beam direction through the target, the cone i s not symmetrical with-respect to the target to counter direction except when the counter i s at 0 ° . Since an angular distribution was required from the calculations each cone was divided into 12 "tubes™ as shown in Fig. 12b, so that each tube contains of the deuterons i n the particular cone. A l l the deuterons in each tube were assumed to travel down the center of the tube, and for each •frllhff t-.V)fi ancrlp hpt.wpfin t.hi s rli r o f H nn onH -hVio l i n o 29 joining the target to the detector was obtained using the methods of solid geometry. These angles were competed for the counter at four different angles, namely at 0 ° , 4 5 ° , 90° and 1 3 5 ° with respect to the incident beam direction. Finally each tube was divided into sections along i t s length such that the energy loss of the deuteron in traversing each section was approximately equal to the difference between the deuteron energies at the outside and the inside of the particular cone. Assuming the stopping power of heavy ice for deuterons was the same as that for protons of the same velocity the data of Wenzel and whaling (1952) was used to compute the stopping power of heavy ice for deuterons as a function of deuteron energy. From this data the thickness, and hence the number of stationary deuterons in each tube-section of the target, was obtained. From various measurements of the angular distribution of d on d neutrons at different bombarding energies Hunter and Richards (1949) have plotted the coefficients as a function of energy for expressing the angular distribution i n terms of Legendre polynomials. From this data curves were plotted of the d on d neutron yield as a function of angle for the various energies required for this calculation. Thus knowing the angle between the direction of motion of the scattered deuterons in any tube section and the line joining the target to the 30 counter, the number of neutrons produced by the scattered deuterons passing through the particular tube-section and emitted in the direction of the counter could be evaluated. This number was evaluated for each of the tube-sections for the counter in the four different positions specified above. Finally for each of these counter positions the total number of neutrons emitted i n the direction of the counter was obtained by adding the contributions from a l l 672 tube-sections. The results are plotted in Fig. 10 . In order to obtain the calculated 0° excitation function given i n Fig. 7, the neutron yield at 0° for each of the six layers was extracted from the thick target calculation given above. These values are given i n the table below along with the energies of the protons in each layer. 0° neutron yield. - neutrons per steradian per millicoulomb Layer proton energy Kev A 1500 to 1322 B 1322 to 900 C 900 to 563 D 563 to 338 E 338 to 113 F 113 From this table the thick target yield of neutrons as a function of energy can be easily obtained by adding 0° neutron yield 3.25 x 1 0 6 7.02 x 1 0 6 1.55 x 1 0 6 1.08 x 105 1.08 x 1 0 4 neglected 3 1 the 0° contributions from the bottom of the table to the layer which has an incident proton energy equal to the particular energy at which the total yield i s required. Thus the 0° thick target yield for 900 Kev incident proton energy i s equal to the sum of the contribution from layers F, E, D and C. In this manner the calculated yield points of Fig. 7 were obtained. The calculation for the thin target yield and angular distribution consisted of essentially a repetition of the thick target calculation but for one layer only with the added complication that i t was necessary to take into account the escape of some of the scattered deuterons from the back of the thin ice layer. Since many of the higher energy scattered deuterons escaped from the thin target i t was necessary in this * case to consider the contributions from low energy scattered deuterons more thoroughly than was necessary for the thick target case. The contribution to the neutron yield from the scattered deuterons in energy range from 100 Kev to 15 Kev was obtained by folding the curve representing the number of scattered deuterons as a function of energy, obtained from the Rutherford formula, with the curve representing the D(d,n)He^ neutron yield (Bretscher, et a l 1943), as a function of energy. In this energy range the Rutherford formula i s sufficiently close to the measured scattering cross-section that i t s use 32 should involve only a small error. The contribution from the scattered deuterons of energy less than 15 Kev was neglected. 33 Chapter V  DISCUSSION In the calculations described above a number of approximations have been made concerning the proton energy i n each layer, the deuteron energy in each section, and the angular distribution of the scattered deuterons. Also i t has been assumed that the scattered deuterons travel i n straight lines without further scattering. The latter assumption is reasonably good since for the energy concerned the deuterons lose most of their energy by ionization. In the thin target yield measurement the greatest uncertainty arises from the possible error in the target thickness measurements. Further an error which i s d i f f i c u l t to estimate may have been introduced by the method used to find the tot a l number of deuterons in each cone. However, the method was used in order to make an analytical integration possible. In spite of the approximation involved i t i s f e l t that the calculated results should be correct to considerably better than one order of magnitude and should therefore provide, by comparison with 'the experimental results, a useful test of the hypothesis on which the calculations were made. 34 The fact that the neutron yield i s proportional to the square of the D2O concentration as shown in Fig. 11 provides a strong confirmation of the double process nature of the neutron^yield. However, i t does not provide any informa-tion concerning the nature of the double process. The agreement between the calculated and the experimental yield and angular distribution for both thin and thick targets as shown in Fig. 9. and 1 0 , i s sufficiently good to confirm the postulated nature of the double process.- The hypothesis i s further confirmed by the good agreement between the calculated and the experimental excitation functions shown in Fig. 7 . It may at f i r s t sight seem strange that the anisotropy in neutron yield appears to be greater for the thick target than for the thin one. However, this can be explained by the fact that the major contribution both to the yield and to the anisotropy i s produced by the highest energy scattered deuterons . In the case of the thin target with 1.5 Mev incident protons most of the high energy scattered deuterons escape from the ice layer so that a greater percentage of the neutron yield comes from low energy scattered deuterons for ' which the neutron yield i s nearly isotropic. 35 36 BIBLIOGRAPHY References given in the text by author's name and year of publication are li s t e d alphabetically below: Arnold, W.R., Phillips, J.A., Sawyer, G.A., Stovell, E.J. and Tuck, J.L. (1952),. Phys. Rev. 83, 159. Bailey, C , Blair, J.M., Kratz, H.R., Sherr, R. and Taschek, R.F. (1947). Phys. Rev. 22 , 670. Beiduk, F.M., Pruett, J.R. and Konopinski, E.J. (1950). Phys. Rev. 22, 622. Bell, P.R. (1948). Phys. Rev. 21, 1405. Bennett, W.E., Mandeville, C E . and Richards, H.T. (1946). Phys. Rev. 69_, 418. Bretscher, E., French, A.P. and Seidl, F.G. (1948). Phys. Rev. 21, 815. Chadwick, J. (1932). Proc. Roy. Soc. A136. 692. Coon, J.H. and Nobles, R.A. (1947).. Rev. Sci. Instr. 18, 44* Edwards, M.H. (1951). M.A. Thesis, University of British Columbia. Emmerich, W.S. (1954). Rev. Sci. Instr. 2j>, 69 . Graves, J.D. and Dyson, J.P. (1949). Rev. Sci. Instr. 20, 560. Griffiths, G.M. (1953),. Ph.D. Thesis, University of British Columbia. Hanson, A.O. and McKibben, J.L. (1947). Phys. Rev. 22 , 673. Heiberg, S.A. (1954).. Ph.D. Thesis, University of British Columbia. Hirschfelder, J.O. and Magee, J.L. (1948),. Phys. Rev. 21, 207. 37 Hornyak, W.F. (1952). . Rev. Sci. Instr. 2J,, 2 6 4 . Hunter, G.T. and Richards, H.T. (1949).. Phys. Rev. 2£> 1445-Jennings, B., Sun, K.H. and Leiter, H.A. (1950) . Phys. Rev. 8jD,' 109. Livingston, M.S. and Bethe, H.A. (1937) . Rev. Mod. Phys. £ , 268. Manning, H.P., Huntoon, R.D., Myers, F.E. and Young, V.J. (1942) . Phys. Rev. 6 l , 3 7 1 . Neilson, C. (1955).. Ph.D. Thesis, University of British Columbia. Richards, B.B. (1937).. Phys. Rev. j>l, 810 . Seagondollar, L.W., Esch, K.A. and Cartwright, L.M. (1954) . Rev. Sci. Instr. 2£, 689. Segel, R.E., Swartz, CD. and Owen, G.E. (1954) . Rev. Sci. Instr. 2£, 140,. Schiff, L.I. (.1949). "Quantum Mechanics", McGraw-Hill Book Co. Taschek, R.F. (1942) . Phys. Rev. 6 1 , 1 3 . Wenzel, W. and Whaling, W. (1952) . Phys. Rev. 82, 499. 


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