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The total cross section for fast neutrons of N¹⁴ Kubelka, Werner 1955

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THE TOTAL CROSS SECTION FOR FAST NEUTRONS OF N 1 4 by WERNER KUBELKA 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 Memtie^s T5T the Department of Physics THE UNIVERSITY OF BRITISH COLUMBIA Apr i l , 1955 A B S T R A C T THE TOTAL CROSS SECTION FOR FAST NEUTRONS OF N1Z* The total neutron cross section of N ^ was measured for neutron energies from 3 . 6 to 4 Mev. /A 15-cm.-long liquid Nitrogen c e l l was irradiated with monochromatic neutrons from the D(d,n)He reaction, going i n energy steps of approximately 15 kev. The transmission was measured at each energy, using a propane re c o i l counter for counting the transmitted neutrons. An identical counter was used at 90° for monitoring. The results appear to confirm Stetter and Bothe fs measurements, which were made with a continuous neutron energy distribution. ACKNOWLEDGEMENTS The author wishes to express his thanks to Drs. J.B. Warren and D.B. James, who suggested this project, and encouraged i t with suggestions and patience. Thanks are also due to Dr. James and Mr. Y.I. Ssu, for spending long days and nights with the author at the Van de Graafimachine, when the measurements were taken. CONTENTS INTRODUCTION - i I. THE TRANSMISSION EXPERIMENT 1. Fundamentals - 1 2. D i f f i c u l t i e s and Corrections - 2 II. THEORETICAL CONSIDERATIONS 1. Application of the Breit-Wigner Theory to N 1 4 - 7 2. Yield of Information - 9 III. DETECTORS 1. General - 13 2. "Ideal" Recoil Counters - 13 3. Recoil Gas Counters -.17 4. Counters using Solid Radiators - 19 5. Practical Considerations - 22 6. Recoil S c i n t i l l a t i o n Counters - 24 7. Neutron Reaction Counters - 27 IV. NEUTRON SOURCES - 30 V. EXPERIMENTAL ARRANGEMENT 1. Counters 2. Absorbers 3. Target 4. Geometrical Considerations 5. Energy Control System 6. Electronic System VI. EXPERIMENTAL PROCEDURE 1. Test of the Counters - 43 2. Calibration of the Energy Scale and Measurement of the Target Thickness - 4(5 3. Test of the 'Absorber Dewars - 46 4. Counting Rate and Counting Period - 47 5. Measurement of the Parasitic Neutron Background - 48 6. Measurement of the Cross Section - 49 VII. DISCUSSION OF RESULTS - 52 - 34 - 37 - 38 - 39 - 41 - 42 INTRODUCTION The many p o s s i b l e i n t e r a c t i o n s o f n e u t r o n s w i t h n u c l e i a r e e x p r e s s e d i n t e r m s o f c r o s s s e c t i o n s < 5 ~ s q u a r e cm, f o r t h e v a r i o u s i n t e r a c t i o n s , where cr may be v i s u a l i z e d as an e f f e c t i v e t a r g e t a r e a o f f e r e d by t h e n u c l e u s t o an i n c i d e n t n e u t r o n beam. I f a n e u t r o n p a s s e s n o r m a l l y t h r o u g h a t h i n s h e e t o f m a t e r i a l , a r e a A , t h i c k n e s s t , c o n t a i n i n g N n u c l e i p e r cm , t h e chance o f a c o l l i s i o n w i l l be No o f t a r g e t n u c l e i x <o NtG" A = T ~ s i n c e t h e o v e r l a p p i n g o f n u c l e a r a r e a s i s n e g l i g i b l e . T h u s f o r an i n c i d e n t beam o f n n e u t r o n s p e r c m 3 m o v i n g w i t h a v e l o c i t y v t h e c o l l i s i o n s p e r cm p e r second w i l l be „ _ No o f fearget n u c l e i x G " „ „ . n . v . A n . v . N t . o o r = c o l l i s i o n s p e r c m 5 p e r seonnd ...(1) n . v . N Thus where t h e i n t e r a c t i o n r a t e p e r c m 3 does n o t depend on t h e n e u t r o n e n e r g y , t h e c r o s s s e c t i o n i s i n v e r s e l y p r o p o r t i o n a l t o t h e v e l o c i t y o f the n e u t r o n s . The v a r i e t y o f ways i n w h i c h a n e u t r o n o f an e n e r g y between a few e v . and 20 Mev. may i n t e r a c t w i t h n u c l e i may be c o n v e n i e n t l y g r o u p e d u n d e r f o l l o w i n g p r o c e s s e s . I n t h e f i r s t p l a c e t h e n e u t r o n may be s c a t t e r e d e l a s t i c a l l y w i t h o u t l o s s o f k i n e t i c e n e r g y , as f o r example i n t h e c a s e N 1 ; ^ ( n , n)Nl4. S e c o n d l y t h e n e u t r o n , a f t e r e n t e r i n g t h e n u c l e u s and f o r m i n g - i i -a compound nucleus, may be ejected with a lower energy, the nucleus being l e f t i n an excited state, e.g. N 1 4(n,n» JN14!* This i s ajn inelastic scattering process, in which the surplus energy i s emitted subsequently as a gamma ray. The compound nucleus, i f formed in a state with adequate energy, may break up with the emission of charged particles, such as protons or alpha particles, or an additional neutron, e.g. N^4(n,p)C,<f , N 1 4(n,a)B 1 2, and (n,2n) processes. Again, the neutron may be captured and the surplus energy emitted as a gamma ray, e.g. N-^njfl-jN 1 5, a process obviously favoured at low incident neutron energies. . Finally there i s the fission process, i n which the compound nucleus may break up into two roughly equal fragments. A l l these processes may contribute to the "total cross section" of the nuclei for removal of neutrons from a parallel monokinetic beam. However, a characteristic feature of neutron induced Reactions i s the existence of a well defined total cross section, which i s essentially the sum of the elastic scattering and the reaction cross sections, and i s relatively easy to measure. This i s i n contrast to the situation for charged particles, where the total cross section i s i l l defined, as the Rutherford scattering at low angles becomes large and i s determined by the Coulomb forces far outside the nuclear radius. ' For fast neutrons, 10 to 20 Mev, the total cross section i s around 2TTR2 for a l l nuclei, where R i s the nuclear radius, TfR2 arising from the f i n i t e size of the nucleus - i i i -(R» A.> the de Broglie wavelength of the incident neutron), and IT R 2 from the diffraction or shadow by the nucleus of the neutron waves, i . e . c T c a p t u r e o f a n e u t r o n and 6 - g C a t t e r i n g respectively. For neutrons of energy below a few hundred kev the elastic scattering and capture processes are predominant. Both show very characteristic resonance behaviour at similar energies, the resonance character of the capture process with slow neutrons being especially striking with heavy nuclei and being superimposed on a general y dependance expected from equation (1). In the moderate energy region of a few Mev the formation of the compound nucleus may be followed by a variety of processes such as emission of charged particles, inelastic scattering etc., which are i n competition. The major process in this region i s naturally inelastic scattering, since the re-emission of a neutron i s more probable than that of a charged particle, particularly from high Z nuclei. The general behaviour of the total cross section Q£ w i l l be similar therefore to the cross section for the formation of the compound nucleus, ri s i n g slowly f>Eomlr"R2 at high neutron energies proportionally toir(R + Jc)% at lower energies, with possible resonances superimposed, and the contribution of the elastic scattering cross section from the 'hardsphere' scattering, which i s approximately TTJR2. The presence of resonances i n the neutron cross section i s interpreted as arising from the presence of stationary, quantized, energy levels of the compound nucleus. The width, magnitude and general shape of the resonances may be expressed - i v -by the Breit Wigner formula to a high degree of accuracy, and involves the angular momentum of the excited state. In the present work the total fast neutron cross section of a rather low Z nucleus, N 1 4 :, has been started over the energy region from 3 to 4 Mev, in which the (n,p) and (n,a) processes can compete favourably with the (n,n) processes. The neutron, energy region up to 1.8 Mev has previously been carefully examined and shows several resonances. In this manner one might expect to find resonances arising from levels i n N^ ** at the excitation corresponding to the incident neutron energy, and i f so, to resolve the cross section into i t s component parts to determine which process was contributing. - 1 -I . THE TRANSMISSION EXPERIMENT 1« F u n d a m e n t a l s . C h a r g e d p a r t i c l e s , , b e c a u s e o f t h e i r c h a r g e , have d e f i n i t e r a n g e s , and may t h e r e f o r e be s t o p p e d c o m p l e t e l y by a b s o r b e r s , w h i l e n e u t r o n s and gamma r a y s can be d i m i n i s h e d i n numbers o n l y , b u t n e v e r c o m p l e t e l y s t o p p e d . Thus t h e a b s o r p t i o n o f n e u t r o n s when p a s s i n g t h r o u g h a m a t e r i a l i s c o m p l e t e l y d e t e r m i n e d by t h e chance t h a t e a c h i n d i v i d u a l p a r t i c l e e i t h e r p a s s e s t h r o u g h unharmed, o r i n t e r a c t s w i t h a n u c l e u s o f t h e a b s o r b e r . C o n s i d e r an a r e a o f 1 c m 2 o f an a b s o r b e r o f t h i c k n e s s x , and l e t I • nv be t h e i n t e n s i t y o f t h e i n c i d e n t n e u t r o n s s t r i k i n g t h i s a r e a . I f N i s t h e number o f t a r g e t n u c l e i p e r cm , t h e n t h e number p r e s e n t i n a t h i n l a y e r dx w i l l be Ndx n u c l e i p e r c m 2 . F r o m e q u a t i o n (1) i t can be seen t h a t t h e number o f n e u t r o n s t h a t w i l l i n t e r a c t w i t h s u c h a l a y e r w i l l be nvNdx(5~= I N d x e r A s t h e number o f n e u t r o n s t h a t i n t e r a c t must be e q u a l t o t h e d e c r e a s e o f n e u t r o n i n t e n s i t y , I N d x G " = - d l o r » - Nerdx I n t e g r a t i n g o v e r t h e t h i c k n e s s x o f t h e m a t e r i a l , I _ -Neoc 1 o and s u b s t i t u t i n g I = n v , n _ . Q - N e x = T ( 2 ) n o - 2 -T i s generally referred to as the transmission, coefficient, iince i t represents the fraction of particles transmitted. The measurement of T i s the most direct way of obtaining the total neutron cross section of a substance. It provides us with an absolute value of the cross section for each neutron energy under investigation, and therefore .diminishes the likelihood of additive errors. 2 . D i f f i c u l t i e s and Corrections. In principle the transmission experiment i s very simple. The absorber i s bombarded with neutrons, and the number of neutrons transmitted i s counted. The cross section i s then calculated from equation ( 2 ) . In practice, however, many d i f f i c u l t i e s have to be overcome before reliable cross section values are obtained. Generally i t i s desired to know the energy dependence of the cross section, and therefore an a r t i f i c i a l neutron source has to be used to obtain monokinetic neutrons. Unfortunately the intensity of a r t i f i c i a l l y produced neutron beams i s not constant with time, thus some reference i s needed to indicate the relative intensity of the beam. This can be done either by measuring the current on to the neutron producing target; or by having a monitor counter, counting either the neutrons emitted at a different angle, or some other particles leaving the target as a byproduct of the neutron producing reaction. If there exists any doubt as to whether the target thickness i s uniform, a monitor counter should be used rather - 3 -than a "current integrator", because with nonuniform thickness a s l i g h t s h i f t i n beam p o s i t i o n might r e s u l t i n a d i f f e r e n t target y i e l d . Using a monitor counter or a current integrator, the transmission c o e f f i c i e n t can be calculated from where r i s the r a t i o of counts over monitor counts with the absorber i n place, and r 0 i s the r a t i o of counts over monitor counts with the absorber removed. Background counts of both scattered neutrons and gamma rays are always present when the neutrons are produced by p a r t i c l e accelerators. By proper se l e c t i o n of the detector i t i s possible to keep the gamma pulses s u f f i c i e n t l y small, so that they may be biased out e l e c t r o n i c a l l y . A large portion of the counts due to scattered neutrons can also be suppressed by means of bias i n g . However there w i l l generally be some amounts of hydrogenous material present to scatter fa s t neutrons into the counter, and these neutrons may have energies comparable to that of the desired neutrons. Ricamo (1951), and Ricamo and Ztinti (1951) showed that these undesired neutrons can be corrected f o r by means of a t h i r d measurement, using an absorber of known transmission c o e f f i c i e n t , T». I f T2 i s the counting r a t i o for the known absorber and r ^ the counting r a t i o f o r the unknown absorber, then the transmission c o e f f i c i e n t f o r the unknown absorber w i l l be T - 1 - (1 - T«) 1° " 11 (4) r o r2 Generally T* i s kept as small as possible so that uncertainties - 4 -in T* do not influence T significantly. If T' can be made small enough to be neglected, equation (4) becomes T = r l " r2 (5) ro - r E In addition to the scattered neutrons, which are more or less continuous in energy distribution, monoenergetic neutrons, which are of other than the desired energy, may come from the source. Such "parasitic" neutrons may be a byproduct of the target reaction, or they may be caused by interaction of the ion beam with some other nucleus which i s present on the target, or in i t s v i c i n i t y . In both cases the energy of the parasitic component w i l l vary with the energy of the ion beam, and therefore with the energy of the neutrons. If the component i f f a i r l y strong, not only erroneous cross section values may be measured, but also resonances may be observed at a wrong place of the energy scale. If the component i s not a byproduct of the target reaction, and i t s energy i s too high to be biased out without sacrificing too much counter efficiency, everything possible should be tried to eliminate i t s source. If this i s not possible^ or i f the component i s a byproduct of the target reaction, then the component must be accounted for, and equation (4) w i l l take the form T = 1 - (1 - TM ro ~ r i ~ p ( 1 ~ t } ,( 6) T . 1 U T J r 0 - r 2 - p ( l - t') l 6 ) where p i s the counting ratio of the parasitic component, and t and tV the corresponding transmissions. The determination of p w i l l depend on i t s origin. If p i s a byproduct of the. target reaction i t should be possible to find i t s strength To follow page 4 V -.».--SOURCE D E T E C T O R . FIG* !• Geometry of the Transmission Experiment - 5 -relative to the desired component i n the literature on that reaction. If p i s originated by some other reaction i t s relative strength may be found by measuring the counting ratio for the same amount of integrator counts, with and without the target in place. The relative energy also may be found either from the literature or by measurement with no target present. t» w i l l generally be available, as an absorber should be chosen for which the transmission coefficient i s known over a wide range of energies, t can be estimated from transmission or cross section values either from the work under investigation or from work done by other authors, depending on the energy range of the parasitic component. Another source of unwanted neutrons i n the detector may be the absorber i t s e l f . Due to i t s f i n i t e size the absorber w i l l scatter some neutrons into the counter. This " i n scattering" may be minimized by keeping both counter and absorber as small as possible i n area. Its effect on the transmission coefficient may be calculated from T Q - T +. (1 - T)G • (7) where T G i s the true, and T the apparent transmission. The geometrical factor G i s given by The solid angles involved here are illustrated on Fig. 1. The problem of the choice of the thickness of the absorber, and therefore the choice of T, was investigated by Rose and Shapiro (1948) and by Ricamo (1951). These authors say the optimal T l i e s between 0.2 and 0.3. Most authors, - 6 -however, prefer T > 0.5, so as to ensure that there i s no multiple scattering i n the absorber. The physical and chemical constitution of the absorber must be carefully chosen. To calculate the cross section from the transmission, the number of nuclei per cm2 must be known, and this depends on the density. Inhomogenity may therefore be a-source of error, especially since only the average density can be measured. I f the absorber i s a chemical compound, other atoms w i l l be present, and their cross section must be corrected for. It i s therefore of advantage to use the absorbers i n liquid form. The use of li q u i d absorbers w i l l also prove of advantage in .another respect. The geometrical form and relative density distribution of the two absorbers should be identical, and the. spacial distribution and relative intensity of source and background should not change during the course of the experiment. Liquid absorbers, i n identical containers, w i l l help to meet these requirements. The s t a t i s t i c a l error of the cross section for the case of equation (5) was calculated by Ricamo (1951), and found to be ^ 17 \ Z / A r l f / A r 2 ( r o - r l } t l f , Q, O- " [lr0 - r i l + I r i - r 2 / + {[ri-r 2)(r 0-r 2 j J J • • • l y J where r 0 , r i and r 2 are the respective s t a t i s t i c a l errors of the counting ratios. - 7 -II. THEORETICAL CONSIDERATIONS 14-1. Application of the Breit-Wigner Theory to N .  The nuclear reactions taking place when neutrons are absorbed by N 1 4 are n + N 1 4 — N 1 5 - ^ C 1 4 + P B 1 1 + a N 1 4 + n The application to nitrogen of the Breit-Wigner theory, as presented by Eeshbachj Peaslee and Weisskopf (1947), Blatt and Weisskopf (1952) and Feld et a l . (1951), i s well illustrated by Hinchley, Stelson and Preston (1952), and by Johnson, Patree and Adair (1951). Considering the reaction a + A — C — ^ B + b bomb.part. target nucleus compound residual outg.part. ang mom.£ spin I nucleus nucleus ang.mom. spin i i n state spin I* spin i 1 ^ ' wave length of spin J 2it^a the maximum value of the cross section at the resonance corresponding to the formation of C i n the state of spin J w i l l be given by . o l S^(a,b) = 4 i r ^ a ( 2 e + l ) g J ^ . . .(10) where-La and I\, are the partial widths for the emission of the particles a and b from the compound nucleus respectively, and jT* i s the total width of the resonance J. gj i s the s t a t i s t i c a l weight factor and i s given by - 8 -A = (2J + 1)  S j (2i f 1)(2I + 1 ) ( 2 ^ + 1) U 1 } This gives for the maximum cross section of the N 1 4(n,n)N 1 4 reaction, i .e. elastic scattering, Sj(n,n) = 4ff* n a | g * * ^] (12) H where r On the other hand from equation (10) for the fact) and (n,p) reactions _ fnfp + 1 nfa Sj(n,p) + S(n,a) = 4*^ 2 S & + 1 r 2 ] ....(15) Using the definitions of ^ = ~ and V = Pn + P A + L~p the expression i n square brackets in equation (13) becomes •i- nip * -Hilct _ in (I?p * Fa * 1 n En \ _ t w - . ^\ r 2 " r v r - ^ J - ^ 1 - ^ and Jfcan be evaluated with the help of equation (13) as ST(n,p) + ST(n,a) 4fr>2 ±(2J + 1) o If there would be a "hard" nucleus, i.e. i f the nucleus could be considered as a perfectly reflecting sphere, there would be only one type of scattering, the "potential" scattering, which i s given by CTp0t = 4T»>!(2£+ l ) s i n 2 c f e (15) where the phase constants, SQ., are given by 8* - x r 1 1 0-^  = x - 2-fi"+ cos" x o 2 - x = IT + cos L 5x J x being x = — (E i s the nuclear radius). This, combined with ?[n - 9 -the cross section due to the (n,n) reaction w i l l give the total elastic scattering as sf (n,n) = Sj (n,n) +(?fOT ............ (16) J t o t . . ^reaction p o t The half widths are not fundamental quantities, but'may-be spl i t up into l a = T a_£ l b £ .(17) Where the T are the penetration probabilities. They are defined as number of successful attempts to escape ip(a) _ through channel a •' number of attempts to escape where a represents the reaction channels (a£) and (b£*) respectively. In principle these probabilities can be calculated for neutrons and charged particles. The D's lack such a clear cut definition and cannot yet be computed. They are interpreted, i n approximation, as the spacing between the states which can be formed by an incoming particle with a definite angular momentum and spin. 2. Yield of Information. a) Energy levels. The energy states of the compound nucleus consist of two groups. The lower group, that of the "bound levels", extends from the ground state to an energy E g ^ , where E m^ „ i s the smallest of a l l separation energies E a of any particle a within the nucleus. The higher group, that of the "virtual levels", extends from E m-j n up, and the emission of particles i s possible only for these levels. E m ^ n then corresponds to - 10 -the ionization energy of an atom, and the virtual levels correspond to the continuum of an atom. By their nature the bound levels therefore can be found only by observing beta or gamma ray transitions, or reactions giving N^ -5 as end product, while the virtual levels may be found by observing the resonances of the total neutron cross section and the different reaction cross sections. For the compound nucleus N 1 5, E m j [ n i s the separation energy of the proton, and i t s value was reported by Ajzenberg and Lauritzen (1952) to be 10.207 Mev. The separation energy of the neutron i s , according to the authors, 10.834, and virtual levels above this energy only can be found by observing resonances i n the total neutron cross section. However, since the separation energies of the proton and the neutron are so close, this w i l l cover most of the virtual levels. b) Angular Momenta. In the case that the reaction cross sections of the (n,p) and (n,a) reactions are also available, equations (14) and (12) may be used to determine the angular momenta of the different states of the compound nucleus N^5. This was done for the lower region (up to En = 2 Mev) by Hinchley et a l . (1952) and Johnson et a l . (1951). Their method may be summarized by the following sequence of operations: i) Calculate the experimental elastic scattering cross section by subtracting6"(n,p) +<5"(n,a) fromCS^ at the different resonances. i i ) Write down the different states that can be formed by neutrons of angular momentum 0,1,2,3.... - 11 -i i i ) For these states calculate ^nfrom equation (14), using the experimental values of(T(n,p) and6~(n,a). Note that there are two values for Which of the two i s to be used can be decided only i n the next step. iv) Substitute l(**and i t s appropriate J-value into equation (IS) and compare the so obtained Sj(n,n) with the S(n,n) obtained from experimental data i n i ) . c) Energy Level Spacing, D. By assigning the angular momentum to a state, the value of ^ ~ i s also fixed from equation (14). Using, from the total cross section determination, the total width r 2 = r m - A 2 . ( i s ) (where£ m i s the measured width and A the resolution width) £n i s found from 1^ =)f*P, and Dj from „n „ _ i?n n The transmission probabilities may be obtained from T n s 2 l ,2 4*8? 1,2 ( 1 9 ) where l v c l 2 = l x 2 ( v 2 | 2 = (9 + 5x 2 + x 4) 2£ |v 3| 2 = ( 2 2 5 + 45x 5 + 6X4 + x 6) 3C IvJI2 -- 12 -21x~2 + 45x~ 4) 2 + (45x~ 3 - 6 X " 1 ) 2 6x""2)2 + (6x~ 3 - 3x~ 2) 2 a wave length of neutron inside the nucleus d) The Present State of Affairs. In the region E n up to 1.8 Mev6~t as well as6""a andCT have been measured by Hinchley et a l . (1952) and by Johnson et a l . (1951), and angular momenta have been assigned to most of the states found. In the region 1.8 to 3.5 Mev a l l three neutron cross sections have been measured, and energy levels have been assigned by Bollman and Zunti (1951) and by Ricamo and Zunti (1951) but reliable absolute cross section values have been reported only f o rG " a . No angular momenta have been assigned. The region up to l n = 9 Mev has been investigated by Stetter and Bothe (1951) with continuous neutron energy distribution only. As i n this case the outgoing particle energies were measured, the levels may be subject to some uncertainty i n the conversion of the number of ion pairs to energy, and for some of the resonances there i s the uncertainty that they may lead to an excited state i n B**. Furthermore, the Q,-values used to compute the neutron energies may induce some additively constant error. - 13 -III. DETECTORS 1. General. For total cross section measurements for fast neutrons the detector i s chosen mainly for i t s ab i l i t y to distinguish between desirable and undesirable counts.. Many of the undesired counts are due to scattered neutrons.and can be corrected for in the way described on page 3 by using a monitor. Many of the undesired counts are due to gamma rays. Others are due to neutrons of a different energy, which are produced on or close to the source. Therefore the detector should be, to a certain extent, a proportional counter, i.e. i t s pulse distribution must be a function of the energy of the incoming neutrons. Furthermore, i t should have a low response to gamma rays, since gamma rays w i l l always be present i n fast neutron work. Many different types of fast neutron detectors have been developed which meet these requirements to a reasonable extent. Some of these were developed for applications similar to the one of cross section measurement, i.e. counting a l l neutrons with energies above a certain bias energy, while others were developed for absolute neutron energy measurements. Since the neutrons themselves do not ionize, a l l these counters detect neutrons by detection of secondary particles, produced either by c o l l i s i o n with neutrons or some form of neutron induced nuclear reaction. 2. "Ideal" Recoil Counters. Counters i n which the secondary particles are produced - 14 -by c o l l i s i o n are the most common i n fast neutron work. Generally, the secondary, or in this case the "r e c o i l " , i s a proton since neutron proton scattering i s isotropic for a large range of neutron energies up to about 10 Mev. Also, the proton recoil energy i s larger than that of any other recoil particle, the dependence of the cross section on energy i s very well known, and the cross section i t s e l f i s very large. The energy of the recoil particle i s given by Segre (:1953) as % = ( M « M 1 ) P | Bncos20 (10) where M i s the mass of the reco i l , 9 the angle under which the recoil i s emitted with respect to the original direction of propagation of the neutron, and E n i s the energy of the incoming neutron. This reduces for protons to the simple form E R = E ncos 29 (11) which gives a maximum recoil energy of E R = E. The maximum energy of the recoil protons w i l l therefore be equal to the energy of the incoming neutrons. The energy distribution of the recoiling protons i s uniform from zero to the maximum energy and can be calculated from (14) N(E R) = 2 £ ? (12) • ^n where N Q = number of neutrons between 0 and 9 + d0 n - number of protons per unit area G " = total cross section for neutron proton scattering. The yield of hydrogen recoil counters was discussed by Baldinger and Ruber (1938), by Barschall and Bethe (1947) and by Rossi and Staub (1949). These authors showed that the distribution i n energy of the neutrons may be found relatively - 15 -simply from the energy d i s t r i b u t i o n of the r e c o i l i n g protons, under the condition that the range of the r e c o i l s be smaller than the dimensions of the chamber. The measurement of the pulse d i s t r i b u t i o n , however, requires a complicated pulse analyser. But since i n the transmission experiment only the number of neutrons above a c e r t a i n energy i s of i n t e r e s t , the gas f i l l e d r e c o i l chamber can be used to an advantage by counting only pulses larger than a given s i z e . I f the energy of the smallest r e c o i l pulse counted i s BR, neutrons with an energy B = B R are the fas t e s t neutrons which s t i l l are "biased out". The f r a c t i o n of r e c o i l s above /WpJdEp E - B -D — = — = l - £~ (13) BR i s then A N / N t E R ) d E R • E n E n The t o t a l number of r e c o i l s produced by neutrons of energy E m i s proportional to the neutron proton scattering cross section, ( E n ) . The y i e l d i s proportional to the f r a c t i o n of r e c o i l s produced, which are of energy greater than B R , and therefore i s proportional to ^ a < T ( E n ) ( l - !-) (14) •^ n provided the range corresponding to the r e c o i l energy B R i s small compared to the dimensions of the chamber. Making use of the fact that the neutron proton cross section v a r i e s approximately 1 as E""2" f o r neutron energies. above 50 kev, the y i e l d i s nearly proportional to 1 oC E ^ l - |-) = B " 2 ( X - x 3) (15) 2 B • n where x = - 16 -Rossi and Staub (1949) showed that i f 1 crs(i) - S'cX? (") i s the cross section of hydrogen, then the constant of proportionality i s given by 1 1 B = tv§B * (17) where £ represents the efficiency of the radiator for neutrons of energy E = B; t i s the thickness of the radiator i n micrograms per cm2, and \) the number of hydrogen atoms per microgram. In general, according to these authors, the yield w i l l then be given by ^ = (E n) F (§) (18) where (E n) = tv6g(E n) i s the efficiency of the radiator and F. i s the integral pulse height distribution, as can be seen from Fig. Sa. The function x - x 3 has a minimum at x 2 = i . or E - 3B. 3 It does not vary more than 85$ from i t s maximum value i n the energy interval 1.57 B < E n< 9.6B (10) As can be seen on Fig. £a the yield of the counter as a function of energy rises sharply and remains constant for a wide range of neutron energies. There.-.is, therefore, a threshhold detector of particularly desirable features, in contrast to the reaction counters, whose yield varies in an arbitrary manner above the threshhold. For a certain bias, B, the number of counts observed i s roughly proportional to the number of neutrons with energies greater than approximately 1.5B. This convenient relation i s due to the simple dependence of the hydrogen cross section on energy. - 17 -5. Recoil Gas Counters. Although for use as threshhold detector the exact knowledge of the expected pulse height distribution of a counter i s of no direct interest, i t provides the only really good check upon whether the counter i s behaving properly. In an ideal counter a l l recoils would be produced and stopped inside the sensitive volume. In the transmission experiment however, a compromise must be found between good geometry and counter behaviour, and the counter diameter w i l l therefore have to be kept small. Also because guard rings have to be placed around the ends of the wire in order to have a well defined sensitive volume, some recoils': w i l l always be produced outside the sensitive volume; and there will.always be some neutrons which penetrate sufficiently far into the sensitive volume to produce recoils that leave the volume. Rossi and Staub (1949) calculated the differential and integral pulse height distributions taking into consideration the fact that the counter diameter i s smaller than the range of the recoils (wall effect) and the fact that not a l l recoils are produced or stopped in the sensitive volume (end effect). These distributions are given as function of pulse height, P (in mev), divided by the energy of the incoming neutrons, E n. The differential distribution i s P RQ P R Q 2 P R D P f'^> - 1 + f L + i t M <5£> + b 2 N ( 1 9 ) and the integral distribution , ( L , . , ! _ ! . , + & * B ,L.) + 2aT £ - , „ . | 8 „ j E n E n Q, E n ab E n b E n - 18 -The distributions apply only i f the maximum range, RQ, of the recoils i s smaller than the length "a" of the counter. "b" i s the diameter of the counter. The functions L, M, N, Q,, S and T were calculated by Rossi and Staub (1949) and may be found i n their book tabulated for values of P_ from zero to one. Skyrme, Tunnicliffe and Ward (1952) also calculated the differential pulse height distribution, considering wall and end effects. They obtained the following formula t t x , - 1 + » a S l t » a « a . S a i s a (81) b dx Q, dx ab dx P where x = |r^. However, this distribution applies only i f the range of the recoil i s smaller than the length and the diameter of the sensitive volume. These conditions can hardly be met in a transmission experiment with fast neutrons, while Rossi and Staub's conditions are easier to satisfy, since a small counter diameter i s permitted. The functions Ig and I 3 and their derivatives were calculated by Skyrme, Tunnicliffe and Ward (1952) and are tabulated in their paper for values of x from zero to one and neutron energies of 0.25, 0.50 and 1 Mev. In order to estimate the influence of the wall and end effects on gas counter i n use as threshhold counters, the yield as a function of energy was calculated from equation (18), using Rossi and Staub's (1949) integral pulse height distribution (equation 20) and their tables for the functions Q,, S and T. The range was assumed to be proportional to E. Fig. 2b shov/s R l the yield for a counter of such dimensions that —2. = i and a & r-i- <= 4, for a neutron energy of E = 5B. For Fig. 2c the - 19 -dimensions are — = 0.9 and ^ — = 7.2 for E = 5B. Fig. 2a was already mentioned above, as representing an "ideal" counter, i.e. a o and ^ o = 0. Thus when the maximum range of the a b recoils becomes close to the counter length (case c), there i s a large reduction i n yield at the higher energies, which i s presumably due to the end effects. This causes the straight part of the curve to be steeper, and the energy dependence of the yield w i l l , therefore, be greater. With a counter length which i s twice the range (case b), there i s no such decrease in yield for high energies, the shape of the curve being practically the same as for the "ideal" counter. The reduction i n yield i s distributed evenly and i s presumably mainly due to wall effect. Thus the size of the diameter, which i s the important component in counter design for transmission experiments, does not considerably affect the shape of the response, but only the overall yield. On the other hand, the length of the counter, which has l i t t l e bearing on the transmission experiment, affects considerably the shape of the response. 4. Counters using Solid Radiators. While i n the above discussions i t was assumed that the recoils are produced by the gas f i l l i n g of the counter, the recoils may also be produced by a solid hydrogenous "radiator" mounted close to or inside the counter. In such a case "ideal" counter behaviour can be obtained only with i n f i n i t e l y thin radiators. These are impractical since the efficiency i s proportional to the thickness of the radiator. Finite radiator thicknesses w i l l give a reasonably practical yield, while s t i l l - 20 -preserving the flatness of the "ideal" yield-energy response, or even improving i t . The d i f f e r e n t i a l and integral pulse height distributions r t for solid radiator counters were calculated by Rossi and Staub ( 1 9 4 9 ) . The integral distribution i s given by - A* (hk] d (22) 1 I" E 3/2 p 3/2-1 2 where X - RQ I (|H - (frO J when X < t and X = t otherwise. If R'(E) i s the range i n the material of the radiator then R Q i s assumed to be R*(E) = R&E3/2. The integration of equation (22) was performed by these authors, and the results are shown in t the form of graphs i n their book for different values of ^7 < 1. "o The differential distributions are also shown, as calculated by these authors by differentiating the integral distributions. For 1 there i s always x ^ t, and F(fr-) may readily be integrat Ko -^ n . f 4 [ i . ( P . ) ] ( 2 3 ) From equation ( 1 8 ) then the yield for "thick" radiators w i l l be ^ ^ B ^ [ x - ^ ) 3 / 2 ] 2 (W) i f R* i s assumed to be proportional to E 3 / 2 . The factor g i s given by \ = R'(B)v6bB- 1 / 2 ( 2 5) and represents the average number of recoils per incident neutron of energy E n = B. Since equation (22) as i t stands, does not give any direct information on the dependence on the range of the integral To follow page 20 - 21 -distribution, the yield for "thin" radiators was estimated the following way. From Rossi and Staub's curves of the integral distributions as functions of P__ curves were plotted for F(^—) En E n t Q as a function of -~ for different values of E—. Then, assigning Ro E n nominal thicknesses of =..0.1; 0.25; and 0.75; to the point Ro E n = Bi the effective thicknesses were calculated for different E n neutron energies — 4 4 from one to 10, assuming the range to be B 3/2 B proportional to E n . Using these values, F ( f i - ) could be read . n off the curves of F(lr-) vs. — for each desired neutron energy. n^" RQ Thus, values for F('|L) as a function of neutron energy were obtaine< E n for three different nominal thicknesses. Inserting these into equation (18) the yield as a function of neutron energy was obtained for three different radiator thicknesses. These are graphically represented on Fig. 3b, c, and d. Fig. 3a represents the yield of a thick radiator, calculated from equation (23). As i n equation (23) the yield i s independent of the-radiator thickness, the one curve w i l l demonstrate the behaviour of a i l thick radiators. Fig. 3 illustrates the continuous transition of the energy response of solid radiator counters from the thin to the thick case. Curves d and c show close resemblance to the ideal curve, and due to the increase of the yield with radiator thickness, they indicate even less energy dependence than- that of the ideal counter. As the radiator becomes thicker, however, the response approaches more that of a thick radiator, and the energy dependence of the yield increases. The overall yield increases - 22 -with the thickness of the thin radiator. Thus there i s low yield i n the region of f l a t response and high yield i n the region of steep response. It must be noted, however, that these considerations are made for counters with no* wall and end effects. Since these effects tend to decrease the yield more for the higher energies, i t might be possible, by proper choice of counter dimensions, to obtain f l a t t e r response for thicker radiators and therefore for higher yields. 5. Practical Considerations. In the transmission experiment, as i n most experiments, high counter yield makes i t possible to obtain better st a t i s t i c s i n shorter time. Since, i n order to obtain a good energy resolution, i t must be tried to keep the target as thin as humanly possible, since i t must be tried to keep the points of measurement as close as possible, and since the elimination of background requires three measurements for each point, the experiment w i l l tend to be rather lengthy. It i s therefore specially desirable to raise the counter yield as much as possible. Equation (17) shows that this can be done by keeping the bias energy as low as background and parasitic components w i l l permit. For gas counters the yield can be improved further by increasing the factor t by increasing the gas pressure, and using a gas of high hydrogen content, l i k e a heavy hydrocarbon. This w i l l at the same time reduce the range and consequently the wall and end effects, and therefore w i l l result i n a better response. For solid radiator counters the yield could be improved by increasing the radiator thickness, but only at the expense of the flatness - £3 -o f t h e r e s p o n s e . A l t h o u g h i n t h i s t y p e o f e x p e r i m e n t t h e r e s u l t s a r e i n d e p e n d e n t o f t h e a b s o l u t e y i e l d o f each o f t h e two c o u n t e r s , t h e r a t i o o f t h e y i e l d s o f t h e two c o u n t e r s must s t a y c o n s t a n t d u r i n g t h e whole t i m e o f measurement f o r each p o i n t . F l a t y i e l d t o energy r e s p o n s e i s t h e r e f o r e an i m p o r t a n t c h a r a c t e r i s t i c , s i n c e o t h e r w i s e an i n v o l u n t a r y change i n b i a s , o r s u p p l y v o l t a g e , w o u l d change t h e c o u n t i n g r a t e o f one c o u n t e r w i t h r e s p e c t t o t h e o t h e r . One c o u l d t r y t o r e d u c e t h i s danger by i n c r e a s i n g t h e y i e l d and t h e r e f o r e r e d u c i n g t h e c o u n t i n g t i m e . B u t g e n e r a l l y a system w i l l have n e a r l y t h e same s t a b i l i t y o v e r f i v e m i n u t e s as o v e r h a l f an h o u r , and i t i s t h e r e f o r e t o be p r e f e r r e d n o t t o s a c r i f i c e f l a t n e s s i n r e s p o n s e f o r s h o r t e r c o u n t i n g t i m e . On t h e o t h e r hand i t would be unwise t o t r y t o a c h i e v e optimum r e s p o n s e by means o f c o m p l i c a t e d c o n s t r u c t i o n o f t h e c o u n t e r A w e l l d e f i n e d and p r e f e r a b l y r o u n d c o u n t i n g a r e a i s i m p o r t a n t as i t s i m p l i f i e s t h e e s t i m a t i o n o f g e o m e t r i c a l e f f e c t s . The a r e a s h o u l d be s m a l l , b u t w i l l have t o be a compromise between y i e l d , r e s p o n s e and g e o m e t r i c a l c o n s i d e r a t i o n s . G e n e r a l l y i t w i l l be f o u n d t h a t s i m p l i c i t y i n c o n s t r u c t i o n i s e a s i e r o b t a i n e d w i t h a gas c o u n t e r t h a n h a v i n g a s o l i d r a d i a t o r . S i n c e t h e d e p t h o f t h e c o u n t i n g volume does n o t a f f e c t t h e g e o m e t r i c a l c o r r e c t i o n s t h e c o u n t e r s h o u l d be made s u f f i c i e n t l y l o n g t o make end e f f e c t s n e g l i g i b l e . T h i s a t t h e same t i m e g i v e s t h e c o u n t e r a more d i r e c t i o n a l r e s p o n s e , and t h e r e f o r e h e l p s t o r e d u c e t h e b a c k g r o u n d c o u n t i n g r a t e . % - 24 -6. Recoil S c i n t i l l a t i o n Counters. While gamma ray s c i n t i l l a t i o n counters have made rapid advances i n recent years and are widely used,, neutron s c i n t i l l a t i o n counters are s t i l l i n the early development stage. Although the experience gained i n photomuitiplier and electronic techniques i s certainly of great help to the development of neutron counter, the development of sci n t i l l a t o r s for neutrons has to go on a completely independent l i n e , because in most fast neutron work a high gamma ray sensitivity of the counter i s undesirable. Most of the considerations of the previous sections w i l l apply equally to recoil s c i n t i l l a t i o n counters. If the sci n t i l l a t o r and the radiator are either the same substance, or form an isotropic mixture, one should expect a counter behaviour similar to that of a hydrogenous gas counter. If the s c i n t i l l a t o r and the radiator l i e i n different layers one should expect behaviour similar to that of solid radiator counters. Matters can become by far more complicated, however, i f the light output of the arrangement i s not proportional to the energy of the recoil protons. Unfortunately, i n many practical cases this w i l l occur. Anthracene as a s c i n t i l l a t o r for neutron counting has been used since 1947 (Collins, 1948; Moon, 1948; Deutsch; Marshall and Coltman, 1947; Mailman, 1947; Huber et a l . 1949). Its high light output, short pulses, and high proton content make i t appear most suitable. Since the pulse height i s nearly proportional to the recoi l energy (Krebs, 1953), and - 25 -since, due to the high stopping power of anthracene-, one can avoid practically a l l wall and end effects, the response of anthracene counters should be very similar to that, of "ideal" gas counters. However, in spite of a l l these favorable features anthracene counters are unsuitable for most fast neutron work because of their extremely high gamma ray sensitivity. Similarly several organic solutions which have been investigated by Keeping and Lovberg (1952) for application as neutron scin t i l l a t o r s show too high a gamma ray sensitivity to be practical. Furthermore, insufficient information on the energy response of such solutions i s available, so that their suitability for threshhold counters cannot be predicted. In contrast to the organic s c i n t i l l a t o r s , zinc sulfide shows extremely low sensitivity for gamma: rays. Consequently the more recent investigations for heavy particle detection concentrate more on this s c i n t i l l a t o r . Because ZnS i s an opaque powder i t s light output increases with s c i n t i l l a t o r thickness only to a certain point. Its output then decreases with further increase in thickness, as.the light absorption of the s c i n t i l l a t o r becomes comparable to the output. The pulse height distribution for ZnS recoil counters consequently w i l l be completely different from the recoil energy distribution and i t w i l l be d i f f i c u l t to predict the response of such a counter. The^simplest case to consider would be that of an isotropic mixture of zinc sulfide with a transparent hydrogenous material. Here, as a rough guess, pulses can be expected only from those recoils that were formed so close to the photocathode - 26 -that not a l l the light which was originated by them could be absorbed. This should result in a response similar to that of the thick solid radiator, where only those recoils can be counted which are formed so close to the edge as to be able to leave the radiator. One could therefore expect to obtain similar response for these two cases. Hornyak (1952).developed such a counter by molding ZnS powder uniformly into Lucite. His yield energy response i s very similar to that of thick solid radiators. For a fixed bias the yield increases nearly linearly with the neutron energy. While such a response i s not very suitable for transmission experiments the counter shows otherwise very desirable features. The counting volume can easily be adapted to the needs of the experiment. The yield i s very high (up to 8%), and over a wide range of ZnS densities i t does not vary with weight of ZnS per gram of Lucite, so that i t should be relatively easy to construct counter and monitor with the same characteristics. Gamma counts are so low that 17 mev gammas can be completely biased out when counting 0.5 mev neutrons, without having to sacrifice a considerable amount of.the yield. For the case that the radiator and the Zinc sulfide are in two separate layers the situation i s more complicated. For monoenergetic neutrons the recoils leave the radiator at different angles, and therefore effectively encounter different s c i n t i l l a t o r thicknesses. In addition, at each angle there are recoils of various energies, depending on the depth of their point of origin i n the radiator. Thus the pulse distribution of such counters w i l l be determined by the . - 27 -dependence of the light output of ZnS on the neutron energy and the thickness of the ZnS layer as well as by the recoil energy distribution. However, for very thin radiators combined with thin layers of ZnS, one might expect these effects to be relatively small, and i t might be possible to obtain a counter behaviour similar to that of thin solid radiator counters. Several methods have been developed to provide uniform ZnS screens for alpha particle and proton detection (Caldwell and Armstrong, 1952; Graves et a l . 1952). In one of these, the screen i s mounted on Lucite backing and therefore should be practical for neutron counting. The others probably could be easily adapted for neutron counting by adding a hydrogenous radiator, e.g. paraffin or Lucite. Unless the s c i n t i l l a t o r and the radiator are kept relatively thin, however, i t i s d i f f i c u l t to determine the type of response which may be expected from such counters. 7. Neutron Reaction Counters. Although recoil counters are predominantly employed i n fast neutron work, counters producing secondary particles by means of a nuclear reaction have been tried; i t was found that they have a few advantages over the recoil method. It seems, however, that these advantages are outweighed by one great disadvantage, namely the irregularity of the yield energy response. The main advantage of the reaction.counter i s that i t s pulse height i s proportional to the energy of the incoming neutron. This means that the number of pulses of size P w i l l To follow page 27 UJ ^IG. 4 > Yield - Energy Dependance of an Ideal • Reaction Neutron Counter. - 28 -be given by N(P) a No(En) (E n) (26) where N 0(E n) i s the number of neutrons of energy En and6"(En) i s the total reaction cross section. If wev. could find a reaction which had a cross section which i s independent of the neutron energy we would have the perfect threshhold detector, the yield energy response for fixed bias being as shown on Fig. 4. In practice, the response w i l l take the shape of the variations of the reaction cross section with energy. The following reactions are most commonly tried for neutron reaction counters: L i 6 + n He 4 + H 3 B 1 0 + n -->Li 7 + a N 1 4 + n - * C 1 4 + p 11 —> B + a Of these the B 1 0(na) reaction i s used much more than any of the others. It has a very large cross section and i s also known to obey the ^ law i n the low energy region, (E n< 500 ev.). It therefore provides a very suitable counter for thermal neutrons or for flux measurements where no bias i s required; since then the neutrons can be slowed down to thermal velocities before entering the chamber. For higher energies a l l the above reactions are reported to have resonances. Furthermore the complication enters that the material used has to be employed generally as some chemical compound, and therefore i t must be counted with possible resonances i n the other nuclei that are present. As mentioned, the boron reaction i s the most commonly - 29 -used, the boron being chiefly in the fluoride form. The applicability of such counters for fast neutron work was studied by James (1953), and by James et a l . (1955), by investigating the pulse height distributions at different neutron energies of two BF3 counters of different isotopic content of B 1 0. The results showed several resonances, most of which were assigned to B1® reactions. The conclusion was reached that BFg gas i s not suitable for neutron spectroscopy. For use as a threshhold detector in transmission experiments the BF3 counter i s unsuitable, since there a simple dependence of the yield on energy i s desired. At the University of Br i t i s h Columbia, Flack and Warren investigated the Ne 2 0(n,a)0 1 6 reaction, which yields a single a-group up to neutron energies of approximately 3 Mev, and only two a-groups for neutron energies from 3 to 5.5 Mev. The cross section, while adequte, fluctuates rather more than desirable for a fast neutron counter. The introduction of neutron reaction s c i n t i l l a t i o n counters so far has not solved t h i 3 problem. Although already several different counters, and many different s c i n t i l l a t i n g materials, have been tried (Schenck, 1952), they a l l concentrate around the Boron and the Lithium reaction, and are specifically designed for slow neutron work. No indication can be obtained from these investigations as to whether such counters would be suitable for fast neutron work. - 30 -IV. NEUTRON SOURCES In recent years the i n t e r e s t i n cross section measurements has been concentrated as much on the v a r i a t i o n of the cross section with energy, as on i t s actual value. I f the transmission experiment i s to be employed a source of monokinetie; neutrons i s therefore needed, and t h i s source must be capable of de l i v e r i n g mono-kinetic neutrons over a whole range of energies. The energy spread of such a source then w i l l determine the energy resolution of the experiment. Since i t generally w i l l be attempted to f i n d resonances i n the energy dependence of the cross section, the energy resolution should be smaller than the width of these resonances. Natural sources have much too wide an energy spread to be suitable, and e l e c t r o s t a t i c generators w i l l therefore usually be employed i n investigations with neutron energies of a few Mev. Since, when planning a p a r t i c u l a r experiment, generally the properties of the p a r t i c l e accelerator cannot be chosen, the e f f o r t s i n obtaining an optimum source w i l l have to be concentrated on the target. The problem of choice of the target i s extensively discussed by Graves et a l . (1952). The target reactions which are, according to these authors, the most important, are l i s t e d below i n Table I. Along with the reactions and t h e i r values, the neutron energies obtainable from these reactions with an accelerator capable of 1.5 Mev are l i s t e d . This indicates that, except f o r energies below 1 Mev, there i s one reaction common f o r each neutron energy - 31 -Table I t Reactions employed commonly in the production of neutrons Approx. En. Reaction Q,-value with 1.5 Mev Accelerator - 0.26 0 to 1 Mev C 1 2 + d - » N 1 3 + n T 3 + p —» He 3 + n - 0.76 0 to 1 L i 7 + p —>Be 7 + n - 1.65 D 2 + d — » H e 3 + n + 3.28 2 to 5 N 1 4 + d — » 0 1 5 + n +5.1 5 to 7 T 3 + d —*He 4 + n +17.6 13 to 18 region, and consequently the target reaction w i l l be generally chosen by i t s neutron energy region rather than by other considerations. Many accelerators, however, may give higher potentials, and the neutron energy regions of the reactions then may . overlap. As mentioned i n the Introduction, the energy region of 15 N which was to be investigated, i s the one that corresponds to neutron energies above 3.5 Mev, and the D(d,n) reaction was chosen for neutron production. This reaction was investigated by many workers for neutron energies up to 4 Mev. The angular distribution of the neutrons was found by O A p. Humber and Richards (1949) to be A + Bcos Q + Ccos 6 + Dcos 8 but the much simpler distribution of A + Bcos 29 i s reported by Graves- et a l . (1952) to be correct for deutron energies up to approximately 1 Mev. The neutron yield w i l l thus be greatest in the forward direction. "For deutron energies below 400 kev, thick targets produce 2.5 Mevmonoenergetic neutrons at an angle - 32-of 90°, while in the forward direction the neutrons w i l l take the spectral distribution of the neutron beam. These energies however j w i l l be weighed towards the higher waaagej, 3because the yield increases rapidly with the energy. For deuteron energies above 500 kev monochromatic neutrons can be obtained with thin targets only. Such targets are often gas volumes which are seperated from the accelerator tube by an aluminum f o i l . These targets may presentsconsiderable d i f f i c u l t i e s because of large background produced by such f o i l s . While i t is easier to obtain aluminum f o i l that that produces small energy losses, nickel f o i l s give less background. Deuterium ice targets are also employed. Since the heavy ice can be deposited i n such a way that i t faces the beam directly, there w i l l be no stopping of the deuterium beam, and therefore no thin f o i l s to worry about. Por both gas and ice targets there may be considerable neutron background due to deuterons interacting with carbon deposited i n the target area and on the target i t s e l f . This carbon i originates from o i l vapour i n the vacuum system, and can be considerably reduced by using liquid a i r traps. Another serious source of background may be the contamination of deutes-i rium in the target^area and on the target. Neutronsdue to contamination i n the target area w i l l have different angles and therefore different energies, and contamination w i l l take place mostly at the beam defining apertures; i t can be reduced by heating these apertures. Contamination i n the target support w i l l result i n lower energy neutrons, since the beam has to - 33 -pass the target and part of the target support before reaching this deuterium. Background due. to such contamination can be considerably reduced by changing the target support frequently. To follow page 33 - 34 -V. EXPERMENTAL ARRANGEMENT 1. Counters. As was pointed out in chapter I, two counters, preferably of similar behaviour, are necessary for the transmission experiment. It was thus decided to construct two propane proportional counters as illustrated i n Fig. 5. The choice f e l l on a gas radiator counter because i t was f e l t that i n accordance with the discussions of chapter III this type would combine simplicity of construction with good response, even when considerable wall effects are present. Propane was chosen rather than methane or hydrogen, because propane has a higher hydrogen content and a higher stopping power. Furthermore, the relatively high boiling point of propane (-42°C) simplified considerably the purification of the gas. Fig. 2 i n chapter III indicates that for a proton range R0, and counter length 2Reand diameter ^R0 i t may be expected that the wall and end effects s t i l l may permit a reasonably good yield' energy response. Thus, i n order to decide on the dimensions of the counter, the range of 4 Mev protons i n propane (CgHg) was calculated with the help of the curves of proton ranges i n a i r , and of the relative stopping power, which were published by Livingston and Bethe (1937). The range, according to these authors, i s given by Range in Range in Air , 2 7% propane ~ St. Power Rel.to Air •••••••• \ ) of propane The range of 4 Mev protons in air was read from the curves as To follow page 34 glG. 6 ; The Nitrogen Containers, - 35 -R a = 23.1 cm. The relative stopping power of carbon was read as 0.911 and. that of hydrogen as 0.197; that of propane thus was calculated to be 3 (St. PwrJCgHg = 2 x 0.911 + 4 x 0.197 = 2.15 and the range of 4 Mev protons in propane w i l l be *o - irii a 10-7 cm Consequently the counter length was chosen 20 cm, and a diameter of 1" was estimated to be suitable with respect to counter behaviour as well as with respect to geometry (c.f. section 4 of this chapter). The thickness of the tungsten wire anode was chosen 3 thou i n accordance with recommendations by Korff (1947) and by other workers i n this laboratory. The length of the extension of the counter beyond the sensitive volume, the diameter of the guard rings etc. were mainly determined by practical considerations, such as the kind of copper glass seals, glass and brass tubing available etc. The pulse height distribution to be expected from these counters was calculated from equation (19) and i s shown i n Fig. 6. The calculation of the yield energy response has already been discussed and illustrated above (chapter III and Fig. 2). The counting yield can be calculated from equations (18) and (17). t - ^ i r ^ l ) ( 1 8 ) 1 fcB = t v ^ B " 2 (17:;) Assuming a bias energy of 0.5 Mev, for 4 Mev neutrons - 56 -the relative neutron energy w i l l he =— = 8, and therefore, according to Fig. 2 the ratio of yield over radiator efficiency may he expected to be S- - 0.3. The number of hydrogen atoms 2 ^ per cm , t^, w i l l be equal to the number of hydrogen atoms i n 20 cm propane (CgHg) (8)(20) * fr- (8)(20)(6)(10 2 3) g ( 3 . 5 ) 1 0 2 1 f r V m 7 6 (2.24)(103) 7 6 7 6 where A i s Avogadrd'.s number, vm i s the volume] of one mole at atmospheric pressure, and p i s the f i l l i n g pressure of the counter i n cm Hg. G^ > was assumed to be 4.2 barn, using the relation 6~*=&'012r'2 to calculate i t from cross section values for neutron proton scattering published by Adair. This gives a radiator efficiency of (5.5)(10 2 1)(4.2)(1Q- 2 4) = 2.1% £_ 5 0.5 76 and a counter yield * l = 0.3*3 = 0.63% The counters were .thoroughly cleaned with n i t r i c acid, acetone and alcohol, and outgassed while heated at 0.1 micron pressure. This was done for two days, u n t i l i t was found that no increase in pressure occurred in the counters, when they were l e f t closed up for twelve hours. Although i t was stated by the manufacturers to be chemically pure, the propane used for the f i l l i n g of the counters was condensed i n a dry ice alcohol trap i n the vacuum system. This procedure made i t possible to evaporate only part of the propane, so that i t can be assumed that no heavier hydrocarbons were present. Furthermore, a l l air that could have entered the system together with the propane - 37 -could be pumped out completely before f i l l i n g . The pressure was chosen 54.1 cm Hg, which i s sufficiently below atmospheric to enable the glass-blower to seal off the glass seals. This pressure, according to the calculation of above, would give a counter yield of 0.45$. 2. Absorbers. As was discussed in chapter I, best accuracy of the cross section measurements may be obtained when three measurements are taken for each neutron energy: one without absorber, one with a known absorber and one with the unknown absorber. Furthermore i t was argued that i t i s of advantage to use the absorbers i n liquid form. It was therefore decided to take water as known absorber because of i t s low transmission, and three brass Dewars were constructed as illustrated in Fig. 6. Since by using metal containers i t i s easier to make containers of the same shape, i t was f e l t i t would be of advantage to have three containers rather than one. This would avoid time delay, and contamination of the nitrogen, due to r e f i l l i n g with a different absorber between each measurement. It was decided to base the choice of the length of the containers on a transmission of approximately 0X.5, because different writers do not seem to agree whether i t i s better to choose a transmission above or below this value. Furthermore i t was f e l t , since the cross section of N 1 4 had to be estimated, this was the best way to ensure that the actual transmission would be neither too large nor too small. Thus, using a transmission of 0.5, the desired length of the absorbers was To follow page 3 7 /////// 6rAlN LESS s r e e L d-PIS. 8: Target Arrangement, //////i "ft R ASS J > i O - 38 -calculated for equation (2) T => e - N o r x or - log T = - 0.435s&iT = 0.435N&-X where x i s the length of the absorber, Gr'the total cross section 14 \ of N , and N i s the total number of nitrogen atoms per unit volume. N may be expressed as pot N = = (6.02) (10^) (0.808) = 3 . 4 6 ( 1 0 2 2 ) W 14 where A i s Avogadrd'cS number, £ the density of liquid nitrogen, and W the atomic weight of nitrogen. Assuming the cross section to be 1.5 barn the absorber length w i l l be x - " p i 0 * 0 ' 5 <xr - 14 cm (1.5)(10- 2 4)(3.46)(10 2 2) The length of the absorbers thus was chosen to be 15 cm, which gives for these absorbers the relationship between transmission and cross section as <S-= l Q g T P P = - 4.44(10" 2 4)logT • (0.435)(3.46)(10^)(15.0) or "o" = - 4.44 log T (barn) This relation was plotted on semi log paper to permit fast conversion of transmission into cross section values (Fig. 7). 3. Target. Since neutrons of energies above 3.5 Mev were•required 2 3 the neutrons were obtained from the D (d,n)He reaction. A heavy ice target was used, as sketched in Fig. 8. The target was deposited i n the following way. The lower tap was opened u n t i l the manometer read 1.2 cm Hg, then the lower tap was To follow page 38 4 — i S f c w — > I T A R G E T ^ " B S O K b e R -20«rn : > COUNTER MQNVT OR ffIG.9: General Arrangement and Geometry of the Experiment. - 39 -closed and the upper opened u n t i l the manometer read zero pressure. The thickness of a target produced by such a system may be estimated. Since 23.4 l i t e r s of D20 at atmospheric pressure would weigh 30 grams, the amount of D 20 contained i n 50 cm3 at 1.3 cm Hg w i l l be (30)(1.2)(50) „ 7 . 1 ( 1 0 - 4 ) gins 0 f DP0 (33.4)(76)(1000) V 1 ^ 2 Assuming about one half of this deposits on the target we obtain for a 4.7 cm2 target a thickness of 7 .6(10" 2 ) mg per cm2. Taking the stopping power of D 20 to be 8(10~ 1 5 ) ev-cm per molecule ( 8 ) ( 1 0 - 1 5 ) ( 6 J ( i b 2 3 ) or — 2 Q 1 s — L - 0.34 mev per mg we find that the stopping power of the target i s (7.6)(10~ 2 )(0.24) = 1 .8(10 - 2 ) mev/cm2 3 = 18 kev/cm 4. Geometrical Considerations. Fig. 9 illustrates the geometry of the experiment. Assuming the solid angles small, we find Lj« m 3.8 = 0.135 20 a^ o - 14 - o.o67 3.5 Substituting these values into equation (7), the geometrical factor i s G = (0.125)(0.067) = 4.7(10"2) 2 0.039 and i f we assume a measured transmission of 0.5, the true - 40 -transmission w i l l then he from equation ( 8 ) T - T 0 + (1 - T) G = 0.5 + 0.5G = 0.523 which gives us an error due to geometry of A - | - T ° ^ T - 4.7(10-2) = 4.7$ This appeared to be below the expected s t a t i s t i c a l errors. To calculate the expected counting rate the expected target yield for 4 Mev neutrons and a solid angle ofW Q = 0.042 in the forward direction must f i r s t be calculated. The target yield i s given by n = n Q tN' where n Q i s the number of incoming deuterons per second. Assuming a beam current of I - 10 microamperes, we have n 0 = I = i O " 5 1 Q = 6.4(1013) charge of an electron l.6(10" 1 9) N1 i s the number of D atoms per mg of target, N» = 2| = 2 6 ^ g 2 5 ) = 6(10 2 2) per gm = 6(10 1 9) per mg and t i s the thickness of the target in mg per cm2. It was found on page 39 that t i s approximately 0.8'.. mg per cm2 for a 20 kev target. In order tq estimate the cross section for neutrons emerging in solid angle from 9 i to 82» we must integrate the differential cross section over that region. As mentioned in chapter IV, the differential cross section for D-D neutrons i s given by 6"= A:+ Bcos 2e + ccos 4e Thus the total cross section for neutrons between the angles 9^  - 41 -and 0 2 w i l l be ^1,2 " / e2. Assuming sine = 6 and cosG = 1, this expression w i l l reduce to The three constants can be estimated for 1 Mev deuterons from curves published by Graves (1952) A » 4 (10~ 2 7)cm 2, B X 1.4(10""27)cm2, C 1.6(10" 2 7)cm 2 and we obtain for the cross section in the forward direction, at a solid angle of CQ0 = 0.04 G" = (4 + 1.4 + 1.8)(10- 2 7)(0.04) = 1.3(10- 2 8)cm 2 The target yield then w i l l be n = (6.4)(10 1 3)(1.3)(10- 2 8)(6)(10 1 9)(5)(10- 2) = 2.5(104) neutrons/sec Assuming a counter yield of 0.45%, as calculated, on page 37, a counting rate i s thus obtained of n' = (2.5)(104)(4.5)(10*"3); =' 110 counts/sec 5..Energy Control System. In order to obtain resonances i n the energy dependence of the cross section the energy resolution must be good, and the energy of the beam must be stable and accurately known. The system used for controlling the beam energy of the U.B.C. = 6.6(103) counts/min To follow page 41 Target Absorber Counter Monitor Pre.->amplifier .Amplifier Soope Scaler Amplifier Scaler FIG. 10; Blookdiagram of the Electronics of the Experiment• - 42 -Van de Graaf generator i s described by Aaronsen (1952). The deuteron energy was maintained to ±3 kev during the runs made for this experiment, using a reverse electron beam control system. The neutron energy may be obtained from 1/2 3Q, = 4E n - Ea - 2cose(2E dE n) ' (29) 6. Electronic System. Fig. 10 i s a block diagram of the electronic system employed i n this experiment. The counter and the monitor pulses were each connected through a head amplifier and a linear amplifier to a scaler. The individual components that were employed are: E.K. Cole Amplifier Unit Type 1049 B, Atomic inst. Linear Amplifier Model 204-B, Lambda Power Supply Model 28, Northern Electr i c Fast Linear Amplifier AEP 1444, Marconi Pulse Height Analyser AEP 516, Dynatron Radio Scaler Type 1009 A. To follow page 42 FIG .11; Pulse Height Distribution of the Propane Recoil Counters: (a) E N « 4.2 Mev; (b)E n*2.9 Mev (o) Background Counts. To follow pag4 42 PIG.12: PuJae Height Distribution of a Propane ' Counter} "background subtracted (E,f 4*2 Mev) - 43 -VI. EXPERIMENTAL PROCEDURE 1. Test of the Counters. The counters were f i r s t tested with a 50 mc Ra-Be source and the proportional region was found to be around 3000 volts. The background counting rate was found to be excessive. This was traced down to break-down on a piece of Bakelite, which was used to support the f i l t e r of the H.T. input. After the Bakelite had been replaced by Lucite, the background without any source in the v i c i n i t y was found to be practically zero for one counter, and of the order of 10 counts per minute for the other. This must presumably have been due to chemical contamination or possibly alpha contaminations from the walls. The counters were then irradiated with 3.9 and 4.2 Mev monochromatic neutrons, and their pulse height distributions were recorded on- an eighteen channel pulse height analyser. Both counters showed the same distribution, although the operating voltage for the same gas amplification was not quite the same. Typical distributions are shown in Fig. 11. The background due to scattered neutrons and gamma rays was measured by inserting 7*5" of paraffin between the target and the counter (Fig. 11c). Fig. 12 shows a typical distribution from which the background was subtracted. This may be compared with the pulse distribution calculated distribution mentioned on page 3S" and shown on Fig. 6. Although the experimental distributions are not quite in agreement with the calculated they are very similar to those obtained experimentally by Skyrme, Tunnicliffe and Ward (1952) - 44 -with t h e i r methane counter. By varying the operating voltage i t was found that the change i n gas amplification was approximately a f a c t o r of two for 200iivolts. The absolute gas a m p l i f i c a t i o n was measured by the following simple test pulse generator. A 1.5 v o l t battery was connected to a r e s i s t o r chain through a mercury switch which was fastened on a pendulum. The pulse height was determined by a voltmeter and the known attenuation of the r e s i s t o r chain, which was connected through a coupling capacitor to the head amplifier. The attenuation was adjusted u n t i l pulses were ohtained of the same height as pulses from 4 Mev r e c o i l protons. For one counter i t was found that the required pulse voltage was 7.34(10 ) v o l t s . Having a coupling capacitor of 10 micro-microfarad, i t may be assumed a charge of Q, - vc = (7.34) (10~ 2) (10" 1 1) - 7.34(10~ 1 3) coulomb produces a pulse equivalent to that of a 4 Mev proton. Since, on the other hand, the Energy l o s s per ion p a i r i s 33 ev, a primary charge of 1.2(10 ) ions per 4 Mev proton:- w i l l be produced, or —14\ Q„0 = 1.9(10 ) coulombs per proton. Thus the gas amplification . w i l l be A - i _ = 7.54(1Q- 1 5) = 39 ^o 1.9 (10-:2:'4) • In a s i m i l a r way i t was found that the gas amplification f o r the other counter was 30. The r a t i o 39 to 30 checks well with the r a t i o of the output voltages of the main amplifier for'the two counters, which was 44 to 34. These gas amplification values are of the same order of magnitude as one would expect from Rossi and Staub's (1949) curves f o r methane. .To follow page 4 4 2000 1000 Z7.6 27.S 28.0 28& 2B>H 2,*.fc MC P R O T O N R E S . FReGU FIG.131 l?19(n,V) 0.873 Mev Resonanoei (a) with no deuterium- target superimposed, (D) with one deuterium target, superimposed* (o) with two deuterium targets superimposed* FIG•14 ; Neutron Energy vs. Proton Resonance Frequency, for the Energy Control System Employed. - 45 -2. Calibration of the Energy Scale and Measurement of the  Target Thickness. To calibrate the energy scale the 0.873 Mev resonance of 19 20 the F (p,)f)Ne was measured. This resonance has been measured accurately by Aaronsen (1952). The present measurement was carried out in a manner similar to that of the latter. A thin fluorine target and a gamma ray s c i n t i l l a t i o n counter, which were available in this laboratory, were used for the measurement. As Fig. 13a ill u s t r a t e s , the resonance was found to be at a proton resonance frequency of 27.79 megacycles per second. Thus the relation between proton energy and proton resonance frequency can be expressed as 873.5 kev = k p (27.79mc)2 or kp = 1.141 kev/mc2 where kp i s the energy calibration constant for protons. Since, with a constant magnetic f i e l d and a constant beam deflection, the beam energy i s inversely proportional to the mass of the ions, the energy calibration constant for d.euterons w i l l be k D = i = 0.571 kev/mc2 From this the deuteron energy was calculated for different frequencies from 31 to 43 mc. Substituting these values into equation (29) of the last chapter, the neutron energies corresponding to the different proton resonance frequencies were obtained and a calibration curve of neutron energy as a function of proton resonance frequency was plotted. This curve i s illustrated in Fig. 14. The energy thus having been calibrated, the target - 46 -thickness of one "scoop" DgO (i.e. 50 c c . DgO at 1.2 cm Hg) was measured th© following way. A one "scoop" DgO garget was superimposed on the fluorine target, and the fluorine resonance was measured again. The resonance was found to he at 27.97 mc (Fig. 13D). Another target was added, and the resonance was found to be at 28.35 mc (Fig. 13c). The energies for these frequencies were calculated with the help of the above k p to be 915 and 930 kev respectively. Thus a target of 50 c c D20 at 1.2 cm Hg was found to be 15 kev thick for protons of 0.8 Mev energy. Assuming that the stopping power for deuterons i s twice that for protons, such a target w i l l have a thickness of 30 Mev for deuterons of 0.8 Mev energy. 5. Test of the Absorber Dewars. In order to ensure that a l l three absorber Dewars were equivalent, and that their absorptions therefore cancelled, the transmission of each of the three containers was measured. This was done by comparing the counting ratio with the Dewar in place with the counting ratio with the Dewar removed. The transmissions were found to be 0.763, 0.622 and 0.630. Since this i s a relatively low transmission and since one of the Dewars showed quite a discrepancy, the side walls of the Dewars were thinned as far as i t was mechanically possible. This improved the transmissions to values of 0.922, 0.918 and 0.876. It was thus decided to use the Dewar with the slightly different transmission with water as an absorber, so that this discrepancy would not influence the results. - 47 -•4. Counting Rate and Counting Period. It was found that with a 12 kev target the counting rate was of the order of 3000 counts per minute for a 12 microamp. beam. The estimate in the last chapter gave 6600 counts per minute for a 20 kev target and 10 microamps, which would give conditions. Thus the calculated and the measured counting rates were in f a i r agreement. That they are not i n complete agreement was to be expected, since in the estimate a theoretical counter efficiency was used, and since the ion beam i s never Because of the ins t a b i l i t y of the beam i t was decided to control the counting periods for the different measurement by means of a current integrator rather than with a clock. To decide on the most suitable counting period for each of the three different runs on one energy point, i.e. the nitrogen run, the water run and the run with no absorber, preliminary measurements of the counting ratios were made. It. was found that the counting ratios for the different absorbers were roughly: for no absorber r 0 = 0.90, for nitrogen r i - 0.50, and for water r 2 = 0.25. Inserting these into the expression given in chapter I for the s t a t i s t i c a l error (equation 9), we obtain This indicates that the nitrogen run has twice as much influence on the statistics than each of the two other runs. Thus i t was decided to count on the nitrogen runs twice as long as (6600)(12)(12) (20)110) 4700 counts per minute under the above quite constant. I fo follow page 47 - 48 -« on the other ones. 5. Measurement of the Parasitic Neutron Background. Since the D(d,h)He reaction produces only one group of monochromatic neutrons no parasitic neutrons from the target i t s e l f were expected, while i t was assumed there would be some neutrons coming from carbon contamination of the target and deuterium contamination of the target support. As the amount of such contamination would depend on the time that the target had been exposed, the corrections as discussed i n chapter I could not be applied. Thus a l l efforts concentrated towards reducing these neutron components. To be able to distinguish between the two types of background, a thick carbon target was prepared by applying some aquadac to a copper sheet. Then a heavy ice target was bombarded for several hours, while the preliminary runs for the cross section measurement were done. When the target looked nicely dirty, the heavy ice was evaporated and the pulse spectrum of the dirty target support was measured (Fig. 15a). The support was then buffed thoroughly u n t i l a l l the di r t was removed, and was afterwards cleaned thoroughly with carbon tetrachloride. The pulse spectrum of the cleaned target i s shown on Fig. 15b. Then the carbon target was inserted and i t s pulse spectrum measured. (Fig. 15c). A comparison of these three curves seems to indicate that the large background i s due to deuteron contamination i n the target backing support. That the contaminated deuterons give neutron energies of about 400 kev lower than the ice target i s presumably due RUN NO.; I3S*-15Q I U1 - I3S | lo>t»t i 7 | 1-3-0 * 4 t - 103 K 2 - «*2. -L5 -1.0 NEUTROfs/ ENERGY y ?5 V : 3ts (mo y> FIG. 16: The Total £ro»s Section of -N 1 4 at Neutron Energies from 3,6, t o 4 Mev. - 49 -to stopping of the beam by the target support, before i t reaches the deuterium. To ensure that this argument i s right, and to have an estimate of the strength of the background, the following were measured under the same beam conditions: a) ' Dirty heavy ice target, 600 counts per 15 integrator counts. b) The same target support, the heavy ice evaporated, 351 counts per 15 integrator counts. c) A new target support, made from the same sheet of copper as the other, 80 counts per 15 integrator counts. Thus, the background, after long bombardment of the target, was up to 50% of the counting rate, was due to deuterium absorption by the target support, and was approximately 400 kev lower i n energy than the desired neutrons. Since there seemed no way of eliminating this background completely i t was decided to minimize i t by changing the target support after each six points of cross section measurement. 6. Measurement of the Cross Section. The cross section was measured for neutron energies from approximately 3.6 to 4.1 Mev. The results are plotted i n Fig. 16 as a function of energy. To' il l u s t r a t e how these results were achieved, Table II l i s t s the readings of a typical point. The neutron energy and the cross section value were read from curves similar to Figs. 14 and 7 respectively. The s t a t i s t i c a l errors were calculated with the help of equation (9). F i r s t , however, the errors of the individual counting ratios were calculated. If x i s the number of counts on the counter - 50 -Table II Readings of a typical point of measurement Absorber Time Integrator Monitor Counter Counting sec counts counts counts ratio Air 117 25 5507 7090 1.288 = r Q H20 119 25 5646 1465 0.259 = r 2 N 2 107 25 5756 3567 0.620 0.603 N 2 113 25 5652 3315 0.587 Proton resonance frequency: 33.202 mc E n = 3.671 Mev Generating voltmeter: 675 kev Target current: 12 microamps Transmission: T = :?'o2E " £'f S = 0.334 6"= 2.16 barn and y i s the number of counts on the monitor, we obtain for the error of the nitrogen counting ratio in the example of Table II 4 r , = f S J - I i l i - [3964 + 8252 ~U 0 # 4 8 1 = 0 . 0 1 0 2  1 L x l v l J 1 [ (3964)(8252)J Similarly we get for the water counting ratio - [uiisntigs]^  °-261 - °-00876 and with no absorber and to calculate the error i n cross section we find - 51 -A r 2 ( r o " r i } I 2 _r(8.76)(10- 5)(0.467)l U i - r 2 ) l r 0 - r 2 ) J ~ \_ (0.220) (0.687) J and the fractional error then i s F 1507313 T19'2 + S 1 ' 5 + 7'31 * - 0.059 - 5.955 VII. DISCUSSION OF RESULTS Only one resonance has so far been measured i n this energy region by other workers ( c f . chapter II, section 2d). It was reported as being questionable because the measurement was undertaken with continuous neutron energies and therefore may have been caused by a transition into an excited state of B^. Its position was reported at a neutron energy of 3.7 Mev. This would coincide approximately with the small peak i n cross section on Fig. 16. However, although the statistics obtained might justify the assumption that there i s a resonance, the inst a b i l i t y of the points below that energy makes i t rather doubtful. This i n s t a b i l i t y must presumably have been due to some ins t a b i l i t y in the energy control system. It may thus be concluded that the present measurements neither confirm nor deny the resonance reported at 3.7 Mev by Stetter and Bothe (1951). The fact that there appears to be no resonance between 3.7 and 4 Mev, according to Stetter and Bothe, seems confirmed by the present experiment. - 53 -BIBLIOGRAPHY D. Aaronsen, Thesis, 1958, University of B r i t i s h Columbia. Ajzenberg and Lauritzen, 195£, Revs. Mod. Phys., 24, 321. Baldinger and Huber, 1933, Helv. Phys. Acta, 11, 245. Barshall and Bethe, 1947, Rev. Sci. Inst., 18, 147. Bollman and Zunti, 1951, Helv. Phys. Acta,.24, 517. Caldwell and Armstrong, 1952, Rev. Sci. Inst., 23, 508. Collins, 1948, Phys. Rev., 73, 1543. Deutsch, M.I.T. Technical Report No, 3. Feld, Feshbach, Goldberger, Goldstein and Weisskopf, 1951, "Final Report of the Fast Neutron Project" USAEC, Report No. NYO-636-January 31. Feshbach., Peaslee and Weisskopf, 1947, P.R.71, 145. Graves et a l . , Nucl., 1952, 10, 68, December. Graves and Frbman, editors, 1952, "Miscellaneous Physical and Chemical Techniques of the Los Alamos Project", McGraw-Hill. Halliday, 1950, "Introductory Nuclear Physics", Wiley. Hinchley, Stelson and Preston, 1952, P.R.86, 483. Huber et a l . , 1949, Helv. Phys. Acta, 22, 418. Humber and Richards, 1949, Phys. Rev., 7j>, 335A. D.B. James, Thesis, 1953, Cambridge Unitersity. James, Kubelka, Heiberg and Warren, 1955, Can. J. of Phys. "to be published". JF.ohnson, Patree and Adair, 1951, P.R.84, 775. Kallman, 1947, Natur unci Technik, J u l i . Keeping and Lovberg, 1952, Rev. Sci. Inst., 23, 483. Korff, 1947, "Electron and Nuclear Counters", Van Nostrand. Krebs, 1953, Erg. Ex. Naturw. , 27, 379. - 54 -Livingstone and Bethe, 1937, 9, £69. Marshall and Coltman, 1947, Phys. Rev., 72, 5£8. Moon, 1948, Phys. Rev., 73, 1210. Ricamo, 1951, Nuovo Cim., 8, 383. Ricamo and Zunti, 1951, Helv. Phys. Acta, £4, 419. Ricamo and Zunti, 1951, Helv. Phys. Acta, £4, 30£. Rose and Shapiro, 1948, Phys. Rev., 74, 1853. Rossi and Staub, 1949, "Ionization Chambers and Counters", McGraw-Hill. Schenck, 195£,Nucl., 10, 54, August. E. Segre, editor, 1953, "Experimental Nuclear Physics", Vol. Skyrme, T u n n i c l i f f e and Ward, 1952, Rev. S c i . Inst., £3, £04. Ste t t e r and Bothe, 1951, Z. Naturfschg., 6a, 61. 

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