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Time-of-flight neutron spectrometry and the reaction Be⁹ (d,n [gamma]) B¹⁰ Hardy, James Edward 1957

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TIME-OF-FLIGHT NEUTRON SPECTROMETRY AND THE REACTION Be9(a,n {)B 1 0. by JAMES EDWARD HARDY B.A., University of British Columbia, 1955 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 required standard* THE UNIVERSITY OF BRITISH COLUMBIA September, 1957 ABSTRACT The se n s i t i v i t y resolution, and efficiency of a time-of-flight neutron spectrometer developed i n this laboratory (Neilson and James, 1955) have been Improved by the use of a l i q u i d s c i n t i l l a t o r neutron detector and improved electronic techniques. By observation of the D(d,n)He3 reaction, the neutron detec-tion efficiency of the l i q u i d s c i n t i l l a t o r for neutrons i n the energy range 2 to 3»5 mev has been shown to follow the curve where i s the neutron energy i n mev. Investigation of the Be^(d,n / ) B ^ reaction has shown that the /-radiation from the O.72, 2.15, and 3.58 mev levels i n B1^. i s iso-tropic to within 5$ i n the reaction plane while that from the 1.74 mev lev e l i s isotropic to within 15$. Further, the radiation from the O.72, 1.7^, and 3.58 mev levels i s isotropic to within the same precision about the respective r e c o i l axes, while the angular distribution from the 2.15 mev level i s 1 + (0.07 - 0.05) s i n 2 6? , where 9 i s measured from the normal, to the reaction plane. Since energy selection of the ~/ radiation was not performed, i t i s not known which of the three transitions l i s t e d by Ajzenberg and Lauritsen (1955) i s responsible for this anisotropy. The angular distributions of the four neutron groups associated with the B 1 0 levels l i s t e d above, at - 500 kev, indicates that at this energy stripping i s unimportant for the O.72, 1.74 and 2.15 mev levels, in agreement with the work of Pruitt et a l . (1953) at E d = 9^5 kev. The neutron group associated with the 3«58 mev level undoubtedly proceeds via / = 1 stripping, but to obtain the observed position of the peak at this energy from Butler theory, i t is necessary to assign a radius of 13.h lO" 1^ cm to Be^. The observed peak is twice as broad as that predicted by the theory, (undoubtedly a coulomb effect) and there i s an isotropic background roughly one third the peak height, presumed due to compound nucleus formation* In presenting t h i s thesis i n p a r t i a l fulfilment of the requirements f o r an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available f o r reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the Head of my Department or by his representative. It i s understood that copying or publication of t h i s thesis f o r f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of Physics  The University of B r i t i s h Columbia, Vancouver 8, Canada. Date September 10, 1957 ACKNOWLEDGMENTS I would like to thank my supervisors, Dr. J.B. Warren, who suggested this research, and Dr. C.A. Barnes, who aided in the early part of this vork. I am also indebted to the many members of the Van de Graaff group vho helped in operating the generator. Special thanks are due to Dr. Oscar Nydal, who built most of the random and anti-coincidence circuitry which has improved the background rejection of the spectrometer. Finally, I wish to thank the National Research Council for the Bursary and the Imperial Oil Company for the Fellowship which have enabled me to carry out these studies. TABLE OF CONTENTS CHAPTER TITLE PAGE I. DEUTERON STRIPPING THEORY INTRODUCTION 1 1. Geometry 3 2. Nomenclature k 3. Differential Cross Section 5 h* Butler Stripping Theory 7 5. Reduced Widths 12 6. The Butler Approximations 12 7. Stripping "by a Hard Sphere Nucleus lk 8. Spin Polarization in Stripping 15 9« (d ,nY) Angular Correlation in Stripping 17 II. TIME-OF-FLIGHT SPECTROMETER; DESCRIPTION AND CIRCUITS 1. Introduction 19 2. The Spectrometer Circuits 20 3. The Liquid Scintillator Neutron Detector 23 III. THE LIQUID SCJJJTIIIATOR; RESPONSE TO NEUTRONS AND J RADIATION 1. Introduction 25 2. Response to ^- Rays 26 3. Response to Neutrons 26 k. Neutron Detection Efficiency 30 TABLE OF CONTENTS (CONT*D) CHAPTER TITLE PAGE IV. THE REACTION Be9(a,n/)B10. 1. Introduction 33 2. Apparatus 33 3. The K - Ray Distributions 3^ k. Discussion of the Ray Distributions 35 5. The Neutron Distributions 36 6. Discussion of the Neutron Distributions 37 V. FUTURE OF THE T IMS - OF-FLIGHT SPECTROMETER 39 APPENDIX I - NEUTRON DETECTION EFFICIENCY OF A HYDRO CARBON PHOSPHOR UZ APPENDIX II- CALCUIATION OF THE NEUTRON AND RECOIL KINETIC ENERGIES, AND THE RECOIL AXIS, FOR A Nx(d,n )N2 REACTION, WITH APPLICATION TO THE Be9(d,n )B l 0 REACTION. k6 BIBLIOGRAPHY 1*8 ILLUSTRATIONS PLATES SUBJECT FACING PAGE 1 The Liquid Scintillator Neutron Detector 23 2^  The Time-of-Flight Spectrometer 33 FIGURES I- l Stripping Collision Geometry 3 II- l Block Circuit Diagram, Time-of-Flight Neutron Spectrometer 20 II-2 Neutron Detector Circuit 21 II-3 Fast 6BN6 Coincidence Circuits 22 II-1+ Gated Random and Anticoincidence Circuits 22 II- 5 Neutron Collimator and Detector 23 III- l Compton Spectra From Liquid Phosphor NE 202 26 III-2 Liquid Phosphor NE 202 Response to - jf - Radiation 26 III-3 Neutron Spectra From Liquid Phosphor NE 202 26 III- 4 Neutron Detection Efficiency of Liquid Phosphor NE 202 31 IV- 1 The B 1 0 Decay Scheme 31 IV-2 Be 9(d , nY)B 1 0 Reaction. Relative./ - Ray Intensities Around Recoil Axes 35 IV-3 " Be9(d,nV)B10 Reaction. Relative / - Ray Intensities in Reaction Plane 35 IV-4 B ^ d ^ / j B 1 0 and B ^ d ^ n / j C 1 1 Neutron Groups, With Associated Level Energies 36 IV-5 Be9(d,n Y)T$-° Reaction. Neutron Angular Distributions 36 IV-6 Be^(d,ny)B10 Reaction. Neutron Angular Distribution From 3.58 mev. Level in B 1 0. 36 AI-1 Proton Recoil Spectra. Neutron Spectrum: &(E) U3 AI-2 Proton Recoil Spectra* Rectangular Neutron Spectrum k3 Chapter I DEUTERON STRIPPING TREORY INTRODUCTION: The deuteron is a very loosely bound structure. Its binding energy (2.2 mev) is so low compared to the average binding energy (6 to 8 mev) of nucleons in light nuclei! that (d,n) and (d,p) reactions in general have high positive Q values. For this reason, this type of reaction has been, for several decades, an important source of information about the energy levels of light nucleii. Because of its loosely bound structure, the mean distance (2.2 10"^3 cm) -between the proton and the neutron in the deuteron is larger than the range of the nuclear force binding them together. It is this property that gave weight to the idea of "surface reactions" which were introduced by Serber (l9**7) to explain the forward peaked angular distributions of scattered neutrons produced by 190 mev deutrons that had been observed by Helmholtz et a l . (19^7). Earlier, in 1937* Lawrence et a l . had observed that the cross section for the (d,p) reaction was larger at low energies than could be accoun-ted for by assuming that a compound nucleus was formed with subsequent emission of the proton. The coulomb penetrability required of the proton was too large. This discovery led Oppenheimer and Phillips (1935) to postulate the process named after them, in which the neutron is captured while the proton remains outside the range of the nuclear force. More experimental data arrived, beginning in 1950 with the work of Holt and Young (1950) and Burrows et a l . (1950), on the angular distributions - 2 -of scattered neutrons and protons from the (d,n) and (d,p) reactions induced "by medium energy ( l to 30 mev) deuterons in light nucleii. The observed dis-tributions were characterized by sharp peaks either in the direction of the beam or at small angles from i t , which were inexplicable in terms of compound nucleus theory. A great many of these results were explained by Butler (1951) who modified Serber's high energy theory into what is now commonly known as "stripping theory". There remain, however, many neutron and proton angular distributions (three of which are presented herein) which are inexplicable in terms of stripping theory, and are presumed to be due to compound nucleus formation, and possibly to interference between stripping and compound nucleus formation. Since the original papers on the subject, by Butler (l95l)> Bhatia et al. (1952), and Daitch and French (1952), stripping theory has developed into a valuable technique for analyzing the results of the many deuteron in-duced reactions in which only one of the neutron or proton is absorbed, and the other is scattered. It gives the angular distribution of the scattered particles in a simple closed form with only four parameters: the reaction Q, the deuteron kinetic energy, the nuclear radius, and the binding energy of the captured nucleon. Also i t relates, in a generally unambiguous fashion, the distinctive peaks in the differential cross section with the orbital angular momentum of the captured nucleon, and so is a valuable tool in determining nuclear level spins and parities. And thirdly, i t forms a f i r s t approximation upon which to build more detailed and realistic reaction theories. In the following paragraphs we derive the stripping cross section FIGURE I-l STRIPPING COLLISION GEOMETRY - 3 -for a Nj_ (d,n) N2 reaction, and discuss the modifications that have been introduced to refine the theory and to obtain better experimental agreement. 1 . Geometry: Figure I-l shows schematically the various geometrical relation-ships in a deuteron collision with the target nucleus N-j_. Before the collision, R is the position of the centre of mass of the deuteron with respect to that of N^ , while r is the internal position coordinate of the deuteron. After the proton has been captured, forming N 2 with N]_, the position of the neutron relative to the centre of N2 is described by rn«. In these coordinates, the dynamical operators are described as follows: a. Before collision: Let r - r n - r p , 8 - * V? , R . S - R1# Mn + Mp Then Vj£ + V p 2 = 1 / i _ + y 2 r + 1 y 2 S 2MQ 2Mp 2 v *% Mp J 2(Mn + Mp) and 1 « 2 + 1_ (7 R 2 = 1 / 1 + 1_ A r 7 2 2 ^ + Mp) V g M l 1 2 I MQ + Mp Mx )  V R . Let M = Mn + ^  and M1 = MM , M J = Mi M M M l + M Then V £ + It + V j 2 . 7R 2 + ^ ^ 2l\ 2Mp 2 M X 2 J ? 2 M d 1 - k -b. After collision: ^ t1 " ? p - * l > 8 - M A + V P , ? B X - * - S 1. Then + Vp£ = 1 z' 1_ + 1_"\ Vp«2 + 1 |/ S 2MX 2Mp 2 «• M-L Mp J 2 ^ + Mp) ,2 And 1 Jft' 2 + _ i _ V 2= 1 / 1 + 1_ ) rt 2 2(Mj. + Mp) v 2Mn n 2 ^ Mi + Mp 1% ) V n« Let Mp1 = MpM! , Mn1 = ^(Mj + Mp) Mp + Mx Mi_ + M Then Vn£ + Vj£ + V i£ = l y , 2 + l y 2 2MQ 2Mp 2MX 2Mp"^" P 2M&1 n ' 2. Nomenclature: : dynamical variables of a l l nucleons in N .^ kd> n^ : wave vectors of incoming d and outgoing n, in centre of mass coordinates of N^ and Ng respectively. I wave functions of d, N-^ , and Ng, with the n, p, and d spin states given by %1 , > y~p> 6"n, 6"p): Wave function describing the collision. The asymptotic behaviour of ^ in its various channels describes: deuterons incident and scattered neutrons scattered as in N-^  (d n) Ng a l l other energetically possible reactions - 5 -satisfies H? = E J vhere H = H- + H, - n 2 ^  R 2 + H • P = H 2 - i i 2 V n' 2 + N + V. with H d = - i 2 Vr 2 + V and H = H. - n 2 ^ p' 2 + P, where V, N, and 2M1 2 Mp1 D are the n-p, n-N^ and p-N, interaction terms. n ^ d 2 , J i ^ p 2 : "binding energies of the deuteron, and of the proton in Ng. Conservation of energy implies E = E 1 + t^-tii = E 2 + ^ _ , w h e r e H 1 f r = E i T j ? 2M£ 2M1 2^1 ' • 1 31 1 1 il > ^ h - - B a T t e , andE 2 = E l - ^ ! . Thus 54- . a* M ? far- i £ E M£I (1) 3. Differential Cross Section: Following Mott and Massey (l9ty)), let ¥ * ^ "K9^2 ^ (^n) ^ t h e ( n , N a ) fthMme1' 8 1 x 4 -ymg 0 2 I = - y m l 1 y ( R) 1 1 1 ( d * N i ) channel. Then "n2t«2 + E ^ ^ D V m 2 =(N+V)T U y ^ m l r K "ST". ^2 ^ 2 ^ Jm/ 1 J1 r - 6 -or •9 \\w2 So by orthonormality of the T » The Green's function solution is too --ra ,.f . M -p 2 / x T l N + v J i and asymptotically for large r n , Now, in the (d, N,) channel, assuming random spin orientation, ^ has the asymptotic form ^E"^ ^1 i ^ 4 ' R + scattered waves. S"ml 1 J i Thus, the incident deuteron flux in each spin state is nkfl f s o the total Ma incident flux is 0 = 3(2^  + l ) d % . - 7 -Since ^ has the asymptotic form 2 h d rn« -ymg j 2 V in the (n,N2) channel, the scattered neutron flux in the V mg' th spin state is v B,s!^ - (V* * 8 ) * Y m 2 ] The differential reaction cross-section is S (S>,f-) = fig 'n^a , so ( 2 ) 4. Butler Stripping Theory: > In order to obtain the Butler form for the differential cross-section, we make the following simplifying assumptions: a. Coulomb interactions are negligible* h. The neutron does not interact with N]_. That is , we approximate •^mg (Hi i m^ = 0 . c. The reduced reaction widths are independent of relative spin - 8 -orientationso d. The n-p potential V is central - thus neglecting the 3Q; * part of the deuteron ground state - and the wave function is assumed to have the Halthenform: - T l * ^ ) where l^O) ' ^(c^-.e^) e. Consider a sphere of radius ^  about outside of which N and P vanish. We let 3? » 3?d + f , where *d - ^ £ T | T J . e for ,.,>r° and l"p' > r a 0 otherwise. and $' describes the diverging neutron and the captured proton, assuming no n-N2 interaction i.e. (N + V) ty' = 0. This approximation includes (a) and (b) above, and in addition neglects scattering of the deuterons. Under these conditions we have Now 1 has the form: ^ > m ^ * ' " " < H mir|jSn?<jJ,Aim1|jlm,> f ^ i y ) + orthogonal terms containing excited states of N 1 # Where cx^- is the probability amplitude for capture of a proton of orientation 7f in the lm'th subwave and with total angular momentum j = jl * i "fey in the orientation mj^ . in accordance with approximation 3 above, we assume = • Note that to conserve parity, = 0 unless ( - l ) 1 parity N 1 = parity N2. Also, we assume that the proton is captured with either j = + i or j = % - 1 but not botho This is justified by shell model considerations (Blett and 2 - 9 -Weisskopf, 1952, page 768). Since iT satisfies W,) \/>> , with [T ijy^j w e have,by virtue of the orthonormality of the fj] ' and X1 Since the analytical form of P, the p-N interaction, is unknown, this equation cannot yet he solved. But for f*y >To , P = 0, and since the solutions f ^ m are linearly independent, they are identical in the region rJ? fs with the solutions of (Vp " Pp> f £ - 0 which have the simple form (Schiff, 1955) k i ^ * 1i^)^f^r% Thus, for r/>r0 , Substituting (4) into (3) and integrating over the variables of N-^, w e g e t : ;*x , r y > r . Substituting (5) into (2) and using the fact that ^ i i i ^ ^ x l T ^ ^ (-\)h ^ ( ^ i ^ ^ - j - j ^ - M ^ plus the orthonormality of the Chebsth-Gordon coefficients, we find ? F F ^ 7 xi+T ( T ) Now, to evaluate the , we transform to more manageable coordinates: - 10 -Let M'r r (8) But whence Taking the Fourier transform, Let A ^ M be the first integral in (9). (10) We can expand g"4?' ^ = 2 ( > / 2 0 Jg/f iy) ' ' > ^ B i n c e the Y* are orthonormal, L . c£ 7 ( i i ) But since |^  ^  and are spherical Hankel and Bessel functions, they satisfy the identity (cf Schiff, 1955) (f+fW k lfrV jl^ -'J^ V\ H (t iff) rr') , where the Wronskian (12) IK - 11 -And substituting for cj\ and K from (8) into ( l ) , (13) and from (10) and (l3)> I ^ becomes so from (l), rt.^O^MK fc„ awYaMflV * / , 2 | , , , r • , , p Lubnitz (1957) has tabulated the quantity 4^ -(1* ) (15) (16) for j2 = 0, 1, 2, 3, and kf and a wide range of x = qr£ and y = ^ p r 0 . In terms of the experimentally known quantities E d, the laboratory energy of the deuteron beam, the energy release, A, the mass number of N ^ , and 0, the centre of mass scattering angle, we have kl 01+*) fc (17) 4+1 - 1 2 -Reduced Widths: In f i r s t approximation, the reduced width for capture of a proton is given by 7ft < / /?o (V,,)/1 (Blott and Weisskopf, 1952) where is the internal wave function for the captured proton. To avoid discontinuity at the nuclear surface, we must have R^Cn) - o^j ^ 6 ' ^ ^ • Since the reduced width thus appears only as a normalizing factor in the differential cross section, and the predicted curves are not in general a good f i t to experiment at a l l angles, only approximate values of reduced widths can be obtained* ,. Bowcock (1955) has analyzed the situation, and shown how a better J. approximation can be made by expanding £ 2 in Legendre polynomials and comparing the coefficients with those giving best f i t experimentally. More rigorous reduced width derivations, which lead to (18) in first approximation, have been made by several authors, the most useful paper being that of Fujimoto et a l . (1954). From equations (15) to (18), the Butler stripping cross-section ;abes its final form: j. 6. The Butler Approximations: Butler (d,n) stripping describes the reaction of an uncharged - 13 -nucleus, transparent to neutrons, with a deuteron, a reaction in which a proton enters the nucleus without reacting on the neutron, and in which scattering of deuterons is neglected, as is compound nucleus formation* Most of these restrictions have heen examined in the literature* The effect of Coulomb distortion has been investigated by several authors, among them Tobocman (195*0 > Yoccoz (195*0 > and Grant (1955)* In general, the angular distribution is flattened - the stripping peak broadened -the cross-section is decreased, and some spin polarization is produced* The latter subject is discussed below* Yoccoz's analysis is the most straight-forward, and introduces the Coulomb correction as modifications of the external wave functions of the proton and the deuteron in equation (6) . The k percent admixture in the deuteron ground state has been found by Dalitz (1953) to affect only the Fourier transform of the internal deuteron wave function, and not the A ^ m . Thus, the characteristic shape of the angular distributions is unchanged* However, he maintains the assumption that the °^jL^ are independent of m, mi, and 4 • Compound nucleus formation has been taken into account by Grant (1954) and Friedman and Tobocman (l953)> but the analytical forms of the compound nucleus and interference terms are not given in either paper. Since the effect of compound nucleus formation wil l be most significant at resonant energies of d + N^ , several investigations have been made of the behaviour of the stripping peak as the bombarding energy crosses the resonance. (Horowitz, 1956). The only definite conclusion that can be made is that -. Ik -stripping remains Important. 7« Stripping "by a Hard Sphere Nucleus: In the following calculation, we Investigate the modification to the Butler theory produced by assuming that the target nucleus, instead of being transparent to neutrons, is (more realistically) opaque to them. / , • iJ /• oi /or r„' < r, This ls done by evaluating | M + V| ^  ha, > to»TK D ^ f l r r - > r Then < V m , | N'+V| U , > = V Y ^ ^ W W ' Where ^^r\') i s *be wave function for neutrons scattered by a hard sphere, —, p i - - iritis (cf Schiff, 1955* Page 110). The cross section s t i l l has the form of (7), but now 1^ , instead of being given by (lk), is I 8 lf' K J(wWk"rwkHi) A,. ' where K* and q* are defined with Is. replacing ICQ in ( 8 ) , and q is the polar axis for the angles. Comparison with (lk), plus the fact that the radial integral is most significant at the pole k = 1% shows that the angular dis-tribution has the same general shape. The most significant point is that the I ^ m no longer vanish for m 4 Q» Horowitz and Messiah (1953 a) have made a similar calculation, - 15 -assuming zero range for the deuteron potential, and expressing the cross-section for 1 = 0 and 1 in terms of a power series of integrals* After some numerical integration, they find again merely a broadening and slight shift of the distribution, a reduction of the cross-section, and some spin polari-zation (Horowitz and Messiah, 1953 b). 8 . Spin Polarization in Stripping: The polarization of a beam of spin 1 particles is given in terms 2 of its density matrix i by p - S f l l J f (Bethe and Morrison, 1956) and the density matrix j in the case of N-j^dn)^ stripping, assuming that d and are unpolarized, is Explicitly, i f we assume protons with only one value of 1 and one of j are captured' & - **feo *k f ^ ? < ( i « l ^ < « fl WXti, »,b^> where the t refers to whether j = 1 + g or j = 1 - 2 . If this is summed, using the symmetry and orthogonality properties of the Clebsch-Gordon coefficients, (Blatt and Weisskopf, p. 791), we obtain Traced . J^L ^ 0 yV1 components of the polarization: 1>L £m tPL^llff, and for the * - * 4?s 1 • & & £ r fJP***^* f % PUT - 16 -But i f we chose the x coordinate to l i e in the reaction plane (previously Z, the quantization axis, was chosen to l i e in the direction of qj the recoil of N2), i t follows from general symmetry arguments that X'^ - (-0*11 ( c f» Gran** 1955)* and because of this, i t is t r i v i a l to show that Pjj = P z = 0, and In the unmodified Butler theory, we have seen above that l l * T n u s> p y = °> s o n o Polarization is predicted. If one in-cludes hard sphere scattering of neutrons, polarization is predicted. Numerical calculations have been made by Newns (1953) who has used a semi-classical model and obtained typical values for / = 1 }~\ '. p - 0.U j.-i : p-.-o.3i However, i f one considers Butler stripping with Coulomb correc-tions, the opposite sign of P is predicted. (Yoccoz, 195*0 • Grant (1955) has included both Coulomb corrections and attractive well scattering and obtained a smaller net polarization with opposite sign: X This applies to neutrons associated with the fourth level of B 1 0 in the Be^dnB10 reaction. The polarization of protons from the C^dpC1^ reaction (/ = l ) has been measured (Horowitz, 1956) and found to be about -0.6 at Ea k mev and -0.5 at Ed 11*9 mev. - 17 -From these results, several conclusions become apparent: 1. Even though the sign of the polarization depends upon vhether the captured particle has j = JL + | or j = / - | , the question of which sign goes with which spin is unanswered - the answer depending upon which modification of the Butler theory most closely f i t s reality. 2. The magnitude of the polarization measured in the C ^ d p j c 1 ^ case is larger than predicted by any simple modification of the Butler theory. This means that one must look for other types of interaction - for example, spin orbit coupling In the transfer of the neutron from d to N2.. Apparently, no one has yet investigated this possibility - possibly because of the difficulty in obtaining the 1^ rs in workable form. Cheston (195^) has considered spin orbit interaction in the scattering of the protons in Cl2 ( d p j c 1 ^ at Ed 3*29 mev. He predicts negative values for Py with [P^!^ , which is less than half the measured value. 9. (d,nY) Angular Correlation in Stripping: The (d,nV) correlation in unmodified Butler stripping has been investigated by Satchelor and Spiers (1952), Biedenharn et a l . (1952), and Gallaher and Cheston (1952). They show that, as one would expect, the distribution is the same as that produced by a plane wave of protons ( C p ) in the recoil direction, which is fixed by observation of the neutron and conservation of linear momentum. Thus, the standard two stage (n,"/) theory (A.P. French, 1950) applies, and makes the following predictions about the ray intensity: - 18 -a* No Y dependence - i.e. no anisotropy perpendicular to the recoil axis - unless there is a mixture of multipoles. b. Conservation of parity requires symmetry about Q = 90° (i.e. 90° from the recoil axis). c. Complexity limitations: If the proton is captured with orbital angular momentum I into a level with spin J 2 , then the multipolarity 2 1 , of the Y ray is limited by L £ min ( I , J 2 ) , (Blatt and Weisskopf, P. 535). Newns (1953) and Horowitz and Messiah (195*0 have investigated the effect of modifications to the Butler theory on the n 1^ angular corre-lation. Newns considers only his semi-classical hard sphere scattering of the neutrons, and for / =» 1, j = 3/2 he shows there is no (n , Y ) correla-tion in the reaction plane, but there is correlation in the plane through the recoil axis perpendicular to the reaction plane. Horowitz and Messiah, (195*0 using their hard sphere neutron scattering model, show that the Y ray axis of symmetry changes from the recoil axis to the ^  axis (perpendicular to reaction plane). It is thus apparent that no reliable prediction of (n,Y) correlations on the stripping model can be made at present. Apparently no one has investigated the effect of Coulomb forces. - 19 CHAPTER II. TIME-OP-FLIGHT NEUTRON SPECTROMETER; DESCRIPTION AND CIRCUITS 1. Introduction: The development of this type of spectrometer has been described by Neilson (1955) and Neilson and James (1955)* Basically i t consists of two detectors whose outputs are fed into a fast coincidence circuit ("time sorter") which transforms the time difference between the two detector pulses into output pulse amplitude. The present use of the spectrometer is the observation of (d^ n ~jf) reactions. In this type of reaction, the incident deuteron is stripped of its proton by the target nucleus, forming a residual nucleus in an excited state, and the freed neutron escapes. The lifetime of the excited state is short («• 10""9 sec), and the / -detector is placed close to the reaction chamber. Thus the Y -ray detector pulse serves as a marker to signal the start of the neutron's flight. The neutron detector moves on a horizontal circle centered at the target and one meter in radius, so the neutron detection pulse is delayed by the flight time of the neutron over one meter, which varies inversely as the square root of the neutron kinetic energy, for non-relativistic neutrons, and is about kO 10"*9 seconds for a 3 mev neutron. Since the limiter output signals from both detectors are a stan-dard rectangular shape j 2 volts high by 70 10~9 seconds long, the spectrometer can record a range of neutron flight times of 70 10"9 seconds. After the time Moody Amplifier /De tec to r Limiter 0 8 >JS Delay True Coincidence Time Sor ter n Detector I—J Limiter 70rrj/js Delay Kick Sorter Gated Biased Amplifier Gate Generator Random Coincidence Energy Selecting Side Channel Ant i -Coincidence I8>JS Delay FIGURE L I - I BLOCK CIRCUIT DIAGRAM T I M E - O F - F L I G H T N E U T R O N S P E C T R O M E T E R S ide Channel Coincidence Side Channel Gate Generator Gated Random Coincidence Energy Selecting Side Channel Random Scaler - 20 -sorter has transformed the flight time spectrum into a pulse amplitude spectrum, the signal is amplified, gated to remove noise pulses and one half the random "•background" signals, and fed to the thirty channel pulse height analyser* The gating is accomplished by the use of further coinci-dence and anticoincidence circuits, and by pulse size selecting side channels* The side channels make i t possible to have same choice in the Y -ray energies in coincidence with the neutrons* This yields the possibility of investigating the decay scheme of the residual nucleus* The angular distributions and correlation of the neutrons and /-rays are measured by varying the angular positions of the two detectors with respect to each other and to the incident deuteron beam* 2. The Spectrometer Circuits: Figure II - 1, is a block diagram of the spectrometer circuits* Only those parts of the apparatus which are either new or modified w i l l be described here, as the remainder is either standard equipment, or has been described by Neilson and James (1955)* The "true" coincidence circuit leading to the kick sorter has been sketched above, and described in detail by Neilson and James (1955)* The ?random" and "anticoincidence" circuits have been installed in order respectively to measure the background of pulses uncorrelated with each other and to remove from the spectrum reaching the kick sorter a l l coincidence pulses in which the neutron detector pulse preceded the / -detector pulse* Because of the 70 10~9 second delay cable between the neutron detector and the random coincidence circuit, no true events can yield coincidences in 56K + | 75ov +I20V © 220 O h m Cable 2 m / is long. D 330 O h m Cable 35 m/JS l ong . +250 V T L -H E W L E T T -P A C K A R D £ 2 2 -P Ampl i f ie r No. 4 6 0 A To Fast C o i n c ir—^ > 6342 F I G U R E H -2 N E U T R O N D E T E C T O R CIRCUIT - 21 -the latter circuit. Thus, the output from the random coincidence circuit is the number of random events which produced a neutron detector pulse preceding a "Y -detector pulse by 0 to 70 10"9 seconds. The side channel circuits are given by Weilson (1955)* page 72* They are fed by dynode signals from the two detectors and restrict the pulse amplitude ranges In the inputs to the side channel coincidence circuit. Since the dynode detector pulses are roughly proportional in size to the energy loss in the detector, the position settings of the side channels determine the energy range of the neutron and Y " r a y which may trigger the gate generators and record a count on the kick sorter or random scalar. In particular, the side channel minima are set high enough to eliminate photomultiplier noise pulses. The output from the random coincidence gate to the random scalar is that part of the spectrum which produced coincidences both in the random coincidence and in the side channel coincidence circuits, while the Input to the gate controlling the kicksorter input is that part of the spectrum which yielded a side channel coincidence but not a random coincidence. The Y " r a y detector is essentially as described by Neilson and James (1955), the only difference being that the limiter pulse has been lengthened to 70 10"9 seconds. This change has been necessitated by the fact that the neutron flight distance has been lengthened from kO to 50 cm. to a meter. The neutron detector has been completely changed. The mechanical details are given below, and the circuit is shown In Figure II-2. Operation 6AH6 Co.th.FoH. 6JS Flip- Flop 6J6 Anticoinc. 6J6 Flip-Flop 6AK5 Amplifier 5687 Cat h. Foil. + 300V Random , , c H-Coinc. " -3 C h a n n e l 7 5 0 K £ <750K Ga te »Ows b . | K JLAA -^.Scaler 5 0 zS. 4-30PF £4K -40V Clipper 6*AH6 Amp. -I 150V 6 B N 6 C o i n c . "CT FIGURE H - 4 GATED RANDOM AND ANTICOINCIDENCE CIRCUITS - 22 -of the limiter circuit is unchanged, except that this pulse has been lengthened to 70 10"9 seconds too. The major modification is the use of a Hewlett Packard distributed line amplifier with a gain of ten to Increase the sensi-ti v i t y for low energy neutrons. The fast 6BN6 "true" and "random" coincidence circuits are shown in Figure II - 3 . The true circuit has been modified by the addition of an RC integrator after the pulse-stretching EA.50 diode and a pulse transformer as phase inverter in the output, while the random circuit is quite straightfor-ward, with the coincidence output from the 6BN6 stretched by a IN56 diode and cathode followed out by a 1*03B. Figure 11-h. shows the anticoincidence circuit and the gate genera-tor to the kicksorter input, and the random-side channel coincidence circuit and amplifier for the signal to the random pulse scaler. The input from the fast 6BN6 random coincidence circuit is amplified by a 6AH6 and the pulse top clipped by a IM56 diode. The positive-going pulse is cathode-followed out by another 6&H6 to feed (a) a 6J6 flip-flop producing a standard shaped rectangu-lar positive-going pulse on one grid of the anticoincidence 6J6, and (b) via a 1.6 microsecond delay line, one grid of the 6BN6 random-side channel coinci-dence tube. Suppose a (negative) side channel coincidence signal appears on the other grid of the anticoincidence 6J6. If no random coincidence signal appears on the fi r s t grid, the side channel coincidence signal is amplified and passes through the IN58 diode to trigger the 6J6 gate generator flip-flop. However, i f a (positive) random coincidence signal does appear, a net negative signal appears at the anticoincidence 6J6 plates, and is stopped by the IN58 diode. If a signal from the side channel gate appears at the second grid of MORE WAX BELOW MATERIALS K E Y FIGURE II-5 LE A D -WX WAX- \ \ \ WOOD- 7>? SCALE l" = 4" N E U T R O N C O L L I M A T O R a D E T E C T O R - 2 3 -the 6BN6 in coincidence with the signal fed at (b) above, a negative coinci-dence signal, appearing at the 6BN6 plate, is amplified by the two-stage 6AK5 amplifier and cathode followed out to the random scalar by a 6AH6. Amplifier stability is achieved by a small amount of capacitative feed-back. 3. The Liquid Scintillator Neutron Detector: Figure II-5» is a vertical section through the centre of the neutron detector, showing the wax and lead neutron collimator, the shielding, the scintillator in its glass container inside the steel can with aluminum face, the lucite light pipe, the RCA 63h2 photomultiplier, and the cathode follower chassis. Plate I shows the neutron detector out of its shielding, with the Hewlett-Packard distributed amplifier, and the limiter circuit on the left. Plate II shows the experimental arrangement for observation of the reaction, and is dealt with in context, but i t shows the neutron collimator on its trolley, with the fast coincidence circuits above. The trolley is constrained to turn about a bearing post directly beneath the target, thus keeping the target-to-neutron detector distance fixed, and the collimator correctly aligned. The scintillator is 0 .6 liters of NE 202 Liquid Phosphor *, -1 with a decay constant of 2 10 seconds, pulse height 75$ of that of Anthra-cene, and maximum emission at 4300 A*. The light pipe coupling the glass * Made by Nuclear Enterprises Ltd., 1750 Pembina Highway, Winnipeg 9» - 2k -scintillator vessel to the photocathode of the photomultiplier is a solid cone turned from a single block of lucite. The optical transmission of the lucite was measured on a Beckmann Spectrophotometer, and, when corrected for surface reflection, is over 99$ from 3900 A ° to 8000 A ° . The transmission drops to 90$ at 36OO A ° , and to 50$ at 3500 A " . The light pipe was optically and mechanically coupled to the phosphor vessel by means of Dow Corning million centistoke silicone o i l retained in a lucite ring cemented to the light pipe and pressed tightly over the glass. Then the complete unit was smoked with magnesium oxide as a diffuse reflector, and coupled to the photocathode of the photomultiplier with more Dow Corning fluid. The structure above the scintillator vessel is a chamber f i l l e d with inert gas to take up the thermal volume changes of the scintillator and relieve the pressure on the glass vessel. The latter is supported on lucite rings inside the Shelby tubing housing. The face plate is 0.020 inch alumi-num. - 25 -CHAPTER III. THE LIQUID SCIHTTTiTATOR: RESPONSE TO NEUTRONS AND Y - RADIATION 1. Introduction: The time-of-flight neutron spectrometer described by Neilson and James (1955) used a stilbene crystal as neutron detector. While stilbene is an excellent, fast phosphor for this purpose i t is expensive, very d i f f i -cult to prepare in blocks larger than a few centimeters in linear dimensions, and easily cracks under thermal shock. The limitation on size of stilbene crystal blocks made i t necessary to work rather closer to the target (50 cms.) than was desirable from the neutron energy selection point of view with the time resolution-possible (2 10~9 seconds) from the electronics. Either an organic liquid scintillator or a plastic scintillator offer the possibility of much larger area detectors, whose depth and shape can be easily adjusted to suit the requirements of the problem, and from which the light output and pulse rise time are not much inferior to that of stilbene. Consequently^ a neutron counter was constructed using the liquid phosphor NE202. The mechanical details of this detector are given in section three of the previous chapter. In this chapter we discuss the scintillations produced by monoenergetic neutrons and rays in the liquid phosphor. Response curves for - rays from several standard sources are given, and the pulse height versus energy curve is shown. The response to monoenergetic neutrons is determined from observation of the D(d,n)He3 reaction at various 600-500-F I G U R E UI - I C 0 M P T 0 N S P E C T R A F R O M L I Q U I D P H O S P H O R N E 2 0 2 Na 22 R 1 3 7 C s x R d T h o 400-•34 <7 •48 <7 1 0 7 v-COMPTON EDGE (mev) 2 39 300-200-\ Q o\o \ A \ x V \ C O U N T S 100-o.. N ^"0-.o..o-Q, o...o.. Xj..^NQ^\©..o..o.. o-. X5 \ \ o' v-. 0..0-^ X C~- --0--0-0 . .o o - o o . 20 25 PULSE HEIGHT -r—y/—T— 30 40 10 15 45 50 FIGURE nr.-2 LIQUID PHOSPHOR NE 202 RESPONSE TO 7- RADIATION / o / PULSE HEIGHT 1 0 2 0 3 0 4 0 5 0 COUNTS 300 A 200 100 A \ i ^X \ \ F I G U R E TJT-3 N E U T R O N S P E C T R A F R O M LIQUID P H O S P H O R N E 2 0 2 E N 3-51 MEV • E N 2 0 6 MEV O 22 NA y CALIBRATION X N O I S E \ \ ° X — X — v x__x~x— x _ x ^ s ^ - x - ~ x ^ x ^ x . • — - • — 5 i— 10 —r~ 15 O — O — Q — I — 20 —i— 25 PULSE HEIGHT - 26 -neutron angles. The relative efficiency for various neutron energies i s given, and compared with a simple calculation assuming that only the energy transfer i n elastic scattering from hydrogen atoms in the phosphor contributes to the s c i n t i l l a t i o n pulse. The importance i n knowing the relative neutron efficiency i s that this quantity i s necessary for normalizing (d,n"V) angular distribution curves, as the neutron energy from such neutrons varies some-what with angle for a given bombarding energy. 2. Response to "Y" - Rays: Figure I I I - l shows the predominantly Compton effect spectra from the three standard sources Na 2 2, Cs^-37, and RdTh, with the noise background subtracted, while i n Figure III - 2 the pulse height at the Compton edge i s plotted against Compton energy. It i s apparent from the latter curve that the phosphor response to y - rays i s s t r i c t l y linear i n the range of energies observed. These results were obtained with the sources placed at the focus of the neutron collimator, and with the usual H.T. of 1750 volts on the photomultiplier. 3. Response to Neutrons: The response of the l i q u i d s c i n t i l l a t o r to monoenergetic neutrons of energies from 2 to 3.5 mev has been measured by observing D(d,n)He^ neutrons at neutron angles of 0° to 150° with respect to the deuteron beam. Figure III-3 displays two neutron spectra, compared with the Na 2 2 V - ray spectrum, and also shows the phototube noise, the tube voltage being 1750 volts and the pulse size at the sixth dynode being about 0.5 volts at the - 27 -Compton edge of the 1.28 mev sodium line. The noise curve has heen subtracted from the first three curves as experimentally obtained. The two neutron curves were taken at detector angles of 0° and 135° from the beam direction, for the higher and lower energies respectively. Preliminary calculations of the shape of the proton recoil spectra have been made in connection with the neutron detection efficiency of the phosphor. (See Appendix I). The predicted recoil spectra, given in Figure AI -1 , bear some resemblance to the observed spectra, but the second approximation, which takes account of secon-dary proton collisions, gives a poorer f i t than the fir s t , which assumes at most one proton collision per neutron. The predicted strong forward peaking due to the secondary collisions is not observed. This may be due to several causes: a. Faulty neutron collimatlon. Small angle scattering down the collimator may be increasing the energy width of the neutron groups. b. Poor resolution. The electronic and light collection reso-lution is good, since the Compton spectra are satisfactory. Hence i t must be the scintillation process itself which gives a less uniform light output for recoiling protons than for recoiling electrons. The light output in a neutron pulse is down about a factor of three from that due to a ray of about the same energy. (This is demonstrated in Figure III - 3 . ) , so presumably the scintillation mechanism is less efficient for recoil protons than for recoil Compton electrons. c. Too great a simplification of the geometry in the efficiency calculation. The assumption was made that the neutron, after having made one - 28 -proton collision, s t i l l had a mean distance of 5 cm. (the detector width) to go "before escaping. Because the neutron mean free path is of the order of the scintillator thickness, the first collision could occur with almost equal probability anywhere through the scintillator, and because of the cos^O pattern of n-p scattering in the lab system, most scattered neutrons would remain headed forward, and so could escape after traversing a mean distance of slightly over half the scintillator thickness. This fact would lower the predicted efficiency in fi r s t approximation, and would have an even stronger effect on the second approximation, bringing i t much closer to the first and greatly reducing the predicted amount of forward peaking. Two structures of interest appear consistently on a l l recoil proton spectra. These are: a. A break in the ramp at the high energy end. Sometimes this occurs as a horizontal section between two roughly equal ramps, and at other times as a bulge in the centre of one long ramp. The high energy and low energy curves in Figure III -3 are respective examples of the two types of break. A possible explanation is that the observed spectrum i s a sum of curves due to several processes. The break might be the top of the ramp due to single proton recoils from f u l l energy neutrons, while the observed top of the ramp may be the top of that ramp due to protons recoiling from neutrons which previously lost some energy to a carbon atom. (The carbon/ hydrogen ratio in the phosphor is O.89 atoms per atom.) Rough calculations of second order processes have been carried out, and i t has been found that the second process mentioned above is about a third as probable in the given geometry as a single hydrogen collision followed by escape. However, the - 29 -probability of a fast neutron colliding with a carbon atom and then a proton is about the same as that of hitting two successive protons, and the lack of strong forward peaking in the observed recoil spectra indicates that the latter process does not contribute significantly to the recoil spectrum. b. A steeply rising portion on the low energy end. This has also been observed by Segel et a l . (195*0 iu the recoil proton spectrum from a stilbene crystal, and a similar effect has been seen by Skyrme et a l . (1951) in the recoil proton spectrum from a hydrogen gas counter. The former authors attributed the effect to phototube noise, background, neutrons from C12(d,n)N13 in carbon on the target, and annihilation radiation from the positrons in the K13 6 decay, while the latter authors attributed i t to ^- rays from fluorine and other impurities in the LiF targets they used. (They obtained their neutrons from LiT(p,n)BeT.) in the present experiment, a l l these possibilities were eliminated by a control run with no deuterium in the target. (Details of the gas target used are given in the next section.) The observed spectrum was everywhere within 10$ of the noise spectrum shown in Figure III-3 and which has been subtracted from the other curves there. It is thus apparent that some further cause must be found, associated with the neutrons. Several suggestions have been made: delayed scintillations, scintillations due to neutrons scattered before they entered the scintillator, and scintillations due to recoiling carbon atoms. The first suggestion is discounted by the fact that the resolving time in the pulse height analyzer is over a microsecond, whereas the quoted decay time of the phosphor NE 202 is 2 10"9 seconds, and the mean time between - 30 -collisions of a 3 mev. neutron in a hydrocarbon is of the order of 10 seconds. Hence any likelihood of a delayed scintillation mechanism being observable seems very remote. The effect of externally scattered neutrons is rather difficult to estimate. Because of the thickness of paraffin that surrounded the counter (a minimum of eight inches everywhere except at the unshielded rear where the concrete walls, ten feet away, subtended a solid angle of 0.4 steradians), i t is believed that the only significant flux of scattered neutrons entering the detector was those scattering from the sides of the collimator. And since to enter the detector these neutrons could undergo only small angle scattering their energy loss would not be sufficient to account for the observed effect. The maximum fractional energy loss of a neutron to a carbon atom in a single collision is I48/169, or about 28$ (U.S.A.E.C.D. 3645, page 75)• It would appear that i f one takes account of the shorter track, with its higher ionization density, and consequently less efficient light output associated with a carbon recoil, as compared with that of a recoil proton of the same energy, that this phenomenon might well account for the observed rise in the scintillation spectrum at low pulse heights. This conclusion is in disagreement with that reached by Skyrme et a l . k. Neutron Detection Efficiency: The detection efficiency of the liquid scintillator for fast neutrons, defined as the number of scintillations observed per neutron passing through the scintillator, has been measured for neutron energies 0-45 0-40 0-35 4 0-30 A 0-25 A 0-20^ A B S O L U T E E F F I C I E N C Y F I G U R E HI - 4 N E U T R O N D E T E C T I O N E F F I C I E N C Y O F L I Q U I D P H O S P H O R N E 2 0 2 £ O B S < E > = O I 4 6 + N £ ^ G G . c X C2(E,D £,(EJ) ° v " x ' T H1 X . . ^ >>o ^ O B S B(E) — 2 —t— 3 T N E U T R O N E N E R G Y , E , M E V - 31 -from 2 to 3.5 mev. by measuring the differential cross-section for the D(d,n)He^ reaction and comparing with the known cross-section, as given by Hunter and Richards (19A9). The D(d,n)He3 reaction was observed by bombarding a target of deuterium gas at 20.4 cmHg pressure with 0.5 ^amps of 500 kev. deuterons. The gas target window was a nickel f o i l * 6250 A° thick (120 kev wide for 620 kev deuterons) and Q.k7 cm. in diameter. The beam passed through 2*3 cm. of deuterium and then was collected inside a copper Faraday cage. The walls of the gas target were 0.030 inch brass. Previous attempts at observing the reaction using heavy ice targets were unsatisfactory due to interference by the $73 kev. ~f - ray in O1? caused by O1^ (d^JO 1? in the oxygen in the water. The absolute neutron detection efficiency at = 2.07 mev. (°n = 135°) was obtained by two methods: As calculated from the target thickness and beam current, the efficiency was found to be 29 - 2$, while, as a check, the neutron flux was measured with a standard BF3 counter, which gave a value of 32 - 2#. A mean value of 30 - 2$ has been taken. The neutron detection efficiency of the liquid phosphor is plotted in Figure III -4 , and compared with the calculated efficiencies in f i r s t and second approximations as obtained from equations 7 and 8 of Appendix I. The increase with falling neutron energy is due mostly to the increase in the n,p scattering cross-section. * Obtained from Chromium Corporation of America, Waterbury, Conn. - 32 -It is apparent from the figure that the second approximation (^2) predicts the shape of the efficiency curve in the region above 2 mev better than the first does, but that both curves predict too high an e f f i -ciency. These calculated curves are somewhat arbitrary, since they depend on the bias energy parameter Et>, which cannot be readily measured. It has been chosen as 1.0 mev since the neutron group to the 3*58 mev level in can «)ust be seen at 1.1 mev with the side channel settings in use here. If a larger value of Bb were chosen, the predicted curves would have much the same shape, but would l i e lower. It would be of interest to measure the detector efficiency at a lower energy, say 1.5 mev, to see i f the predicted f a l l off in efficiency below 2 mev, due to the bias energy, actually occurs. Evidence has been obtained of fine structure in the detector efficiency at the energy (3 mev) of a strong resonance in the carbon neutron scattering cross-section. Since the structure is small (under k$>), i t is of l i t t l e importance in the use of the scintillator in the time-of-flight spectrometer, and will not be discussed further here. PLATE I - T H E TIME-OF-FLIGHT S P E C T R O M E T E R - 33 -CHAPTER IV > THE REACTION Be9(d,n Y) B 1 0 1. Introduction: The time-of-flight spectrometer has been used to measure the angular correlations of neutrons and ~^-ra.ys corresponding to the 0.72, l»7k, 2.15, and 3.58 mev levels in B 1 0, with a deuteron bombarding energy of 500 kev. The deuterons were produced in the U.B.C. Van de Graaff gene-rator. Pruit et a l . (1953) have measured the angular distributions of the neutrons for Ea = 9^5 &ev, and Shafroth and Hanna (195*0 have measured the Y - Y cascade coincidences and correlations. Thus the present results complete the experimental information. The observed portion of the B ^ decay scheme is shown in Figure III- l . Y - ray multipolarities are from Shafroth and Hanna while the rest of the assignments are from Ajzenberg and Lauritsen (1955)* 2 . Apparatus: The apparatus for this measurement is shown in Plate II. The neutron detector is not visible, being at the far end of the neutron c o l l i -mator at the right. It swings on a bearing post which supports the hemis-pherical target pot. The fast 6BN6 coincidence circuits are mounted above the collimator, and have had their thermostatting cover removed for the photograph. The Y detector is mounted in position for measurement of FIGURE 32-1 THE B 1 0 DECAY SCHEME - 3h -~i intensity in the plane normal to the recoil axis of the B-10. The target was about 0.1 mgm/cm2 of Be9 evaporated on a 0.020 inch silver backing. Each bombardment was about 5000 coulombs and took about half an hour. Most of the points on the curves given below are averages of two or more bombardments. 3. The "|f-Ray Distributions. Two measurements were made of the Y - rays corresponding to each neutron group. These were: (a) the angular distribution in the plane normal to the recoil direction of the B 1 0, and (b) the angular distribution in the reaction plane. The first set of angular distributions was measured in order to see i f the polarization predictions discussed in Chapter I could be verified, while the second set was run to determine what n, T correlation there was. For these measurements, the direction of the neutron counter was fixed at k5° to the direction of the incident deuteron beam, as this roughly coincided with the maxima in the neutron angular distributions to the l»7k, 2.15, and 3.58 mev. levels. The calculation of the recoil direction for each level, and the neutron and recoil kinetic energies, is given in Appen-dix II. Since the Y - rays from the 2.15 and 3*58 mev levels are each mixtures of three transitions (Figure III-l), and since the Y- ray detector used was a small stilbene crystal whose compton spectrum does not allow one to choose a Y - ray energy range below that of the most energetic R E L A T I V E I N T E N S I T Y - 150 -_ O i - 50 lr 25 O -60 -30 O T^y 30 60 9 0 B 1 0 ENERGY LEVELS • : i i i FIGURE I Z - 2 7 3 58 Mev Be 9(d,n y) B 1 0 REACTION + 2 1 5 Mev • 1 . 7 4 Mev RELATIVE y - RAY INTENSITIES o o 72 Mev AROUND RECOIL AXES T -O-1 4-o 1 T -o-± J _Q_ 1 T 1 T T 1 150 T -7-i T 7 1 -125 -150 T -125 1 R E L A T I V E I N T E N S I T Y -100 O J_--75 -50 T 7" 1 T + 1 T o-T • v-1 .1. 1 T O -J_-I ... T 1 T +~ 1 -T-G 7 1 1JL T 1 .Ii i . L I B ' 0 ENERGY L E V E L S AS IN FIG.TSL-I POSITION OF RECOIL AXIS: FIGURE 1 2 - 3 B e 9 ( d , n 7 ) B 1 0 REACTION RELATIVE X - R A Y INTENSITIES IN REACTION P L A N E - 35 -"Y , the observed Y intensities, normalized against the count in the fixed neutron counter, are not corrected for detector efficiency. Figure IV-2 shows the azimuthal if - ray angular distributions in the planes normal to the recoil directions. The curve through the 2.15 mev level points is 1 + 0.068 s i n 2 6 , while the ^  - rays from the other three levels are closely isotropic. Figure IV-3 shows the / - ray angular distribution in the plane of the reaction. is measured from the direction of the deuteron beam and is positive on the side away from the neutron monitor. Any anisotropy in the three most intense levels is less than 5#> while in the weak transition from the 2.15 nev level, i t is less than 15$. The appropriate recoil axes are noted on the curves. The gap in the points is the position of the neutron monitor. k. Discussion of the Y - ray Distributions: Theoretical analysis is under way to determine whether the observed ~Y - ray distributions are in agreement with the multipolarities in the BlO decay scheme listed by Shafroth and Hanna (195*0 • This work is slightly complicated by the possibility of polarization occurring. The experimental evidence for polarization herein presented is very weak - the 7$ anisotropy about the recoil axis of the radiation from the 2.15 mev level in B 1 0. The problem is being attacked by calculating the angular distributions using standard techniques, and looking for agreement or otherwise with experiment. Be 9 (d ,n r ) B 1 0 By o° -400 O n 45° COUNTS • 200 /> \ 1 ^  o / V A ° - ° - o - o . a . . ° ^ 3.58 / ° o o \>-°' 2.15 1.74 0.72 X B , 0(d,ny) C " 0 V o° 7 0 n 45° -400 COUNTS A -200 0 /\ / V -o-o-cf' ' ' -o-o-o-o-o-o-o-0 ' ° • X o 4.77 4.23 1.90 °^ FIGURE LY -4 Be9(d,ny)B10 AND B 1 0(d,n/) C M N E U T R O N G R O U P S , WITH A S S O C I A T E D L E V E L E N E R G I E S FIGURE ET-5 B e 9 ( d , n r ) B 1 0 REACTION N E U T R O N A N G U L A R DISTRIBUTIONS 3 0 0 R E L A T I V E I N T E N S I T Y \ 0 - 7 2 200 100 1-74 0 3 0 6 0 9 0 120 150 180 FIGURE E T - 6 B<?(d,nr) B 1 0 REACTION NEUTRON ANGULAR DISTRIBUTION 3-58 MEV L E V E L B U T L E R H = I C U R V E S : • R e = 5 IO" ' 3 CM. • R 0= 13-4 I 0 " , 3 C M . - 36 -5. The Neutron Distributions: Figure IV-h shows the Be9(d,nY)B10 neutron spectrum as observed on the 30 channel analyser* The weak group corresponding to the 1*74 mev level in B 1 0 is not resolved* For comparison, the neutron groups associated with the fi r s t three levels in C^- are given* These were obtained under identical conditions, with the same bombarding energy, 500 kev* Figure IV-5 shows the angular distributions in laboratory coor-dinates of the neutron groups to the 0*72, 1*7**> and 2*15 mev levels in B 1 0, with the Y monitor fixed at 90° to the beam direction. These curves have been corrected for the change la neutron detection efficiency of the neutron detector as the neutron energy changes with angle (Cf. Figure III-U), but have not been corrected for the finite aperture (seven degrees) of the neutrnn detector. In making the correction for neutron detector efficiency, the efficiency for the neutron group to the 1,7k mev level at ©a = 60° ( E Q = 2.9 mev) was arbitrarily chosen to be unity. Making the correction for neutron detector efficiency yields the correct shape for each neutron group, but the relative neutron intensities in different groups are s t i l l unknown since the measured intensities are weighted by the unknown (at present) Y detector efficiencies for the various energy Y - rays by which the various levels decay - and this weighting is complicated for the 2.15 mev level by the various modes of decay. Figure IV-6 shows the angular distribution of the neutron group to the 3.58 mev level in B 1 0. This is the only group which shows a pronounced stripping curve, and is compared with _/ = 1 stripping distributions as - 37 -calculated from the table of Lubnitz (1957). The energy of this neutron group is low. It varies, at Ed = 500 kev, from 900 kev at 150° to 1.3 mev o at 0 . Consequently, to obtain sufficient yield, the bias level on the neutron detector (Et,) was set at roughly half the value used in a l l previous runs. Consequently the relative heights of the 3.58 mev group and the other groups in Figure IV-3 is not significant. Also, the relative e f f i -ciency of the neutron detector at this low energy is not known, and so the experimental curve in Figure IV-6 is not corrected for i t . It is thought that the relative efficiency at this energy wil l not depend strongly on energy as the decreasing effect of the bias will offset the increasing effect of the n,p cross section (i.e., the maximum of £ 2(E,. 5) wil l be at about 1 mev and wil l have much the same shape as the maximum of £2 ( E*l) at 2 mev in Figure III-4.) 6. Discussion of the Neutron Distributions: Several things are apparent from the shapes of the observed neutron distributions associated with the O.72, l.^h, and 2.15 mev. levels. One Is that, because of the lack of symmetry about 90°, a compound nucleus explanation must assume at least two interfering levels in B 1 1 for each neutron group. This appears rather unlikely. Another is that they are not similar to any Butler stripping curves. (However, there may be some / = 1 stripping in the 1.74 and 2.15 mev. groups.) Thus, i t would appear that they are due to a more involved type of surface reaction, complicated by the coulomb repulsion of the proton. The distributions presented in Figures IV-5 are very similar to those obtained by Pruitt et a l . (1953) at Ea - 0.945 mev. The shape - 38 -of the 0*72 mev level Is quite remarkable in that i t resembles an / =1 stripping group in ( ~n - ©n). The neutron group from the 3*58 mev level is clearly an £ = 1 stripping group which has been modified considerably by coulomb and other effects. If one uses a reasonable radius for Be^ (5 I O " 1 ^ cm), the calculated stripping distribution, as obtained from Lubnitz's (1957) table, does not agree with experiment, as is obvious from Figure 17-5. Indeed, the'best f i t " radius as calculated from Lubnitz, is 13»k lO" 1^ cm. i.e. the stripping appears to occur far from the nuclear surface. Comparison of the curves in Figure IV-5 shows that the coulomb broadening and shifting, as predicted by the authors cited in Chapter I, paragraph 6, does actually occur. - 39 -CHAPTER V THE FUTURE OF THE TIME-OF-FLIGBT SPECTROMETER In its present state of development, the spectrometer can produce significant contributions to the knowledge of the level structure of such nucleii as C U , C 1 2, Nlk, 016, F 1 8, F 1 9, and Ne20, by the investigation of (d,n/) reac-tions in the appropriate target nucleii. It is, of course, not restricted to the observation of deuteron induced reactions, but rather can be applied profitably to any reactions resulting in fast neutron, K - ray coincidences, as for example to the energetically favoured and quite interesting reaction Be 9(t,n/ )B^-. Several modifications and improvements can and should be made to improve the operation of the spectrometer. In order of importance, these are: some means of if energy selection, a better method of target positioning and align-ment, especially with respect to the Y detector, use of more distributed line amplifiers to improve the signal/noise ratio, and better side channel energy selection. The major "blind spot" of this spectrometer is its inability to select the transition to be observed. This i s , of course, due to the fact that no fast scintillators have yet been developed which have any significant photoelectric efficiency. Sodium iodide, with its decay time of a hundred times as long as those of organic scintillators, is just too slow. However, there appears to be hope that with the use of newly developed high gain phototubes, as for example the R.C.A. 6810, i t should be possible to build a sodium iodide circuit that would have a sufficiently steeply rising pulse. Successful preliminary experi-ments to this end have already been carried out. - ko -If the use of a sodium iodide Y - detector does prove to be feasible, another modification of the spectrometer circuits will be of interest. If the true coincidence output were passed through a differential analyzer to select a particular neutron group, and then this signal used to gate the y - detector proportional signal, the gate output would obviously contain only those f - rays in coincidence with the particular neutron group. Thus, with this modification, the spectrometer could be used to measure separately the angular distributions of the various radiations by which the selected level of the residual nucleus decays. In the measurement of a Y ~ ray angular distribution pattern, the distance from the target to the *Y detector must be known as a function of detector angle to better than twice the precision desired in the Y angular distribution, because of the inverse square intensity relationship. A few millimeters of target misalignment is sufficient to produce large and mislea-ding angular distribution patterns. Such was the case in the preliminary runs of the experiments described in earlier chapters. Target positioning to the nearest millimeter is not so important in the case of the neutron distributions, where the source-detector distance is a meter instead of a few centimeters. Use of another Hewlett-Packard amplifier in cascade with the one already In use would enable the H.T. on the neutron photomultiplier to be dropped several hundred volts with the same over-all gain and nearly the same pulse rise time, but with a significant decrease in the phototube dark noise. This would be of most use in the detection of neutron groups with energy at or lower than 1 mev. - kl -The side channel circuits now in use are quite non-linear* The gain falls off rather rapidly with increasing pulse size. This, however, is not as injurious to the operation of the spectrometer as the fact that the lower bias settings are not sufficiently stable. Instability here is serious, as, to obtain as high a sensitivity as possible, the lower biases are normally run as far up the noise threshold as random coincidence consi-derations will permit. Because of this, the noise counting rate, which is extremely sensitive to the lower bias setting, is normal ly a considerable percentage of the actual counting rate. This is of most Importance when running Y - ray angular distributions as the noise in the neutron detector, which is then being used, as the monitor, is of the order of f i f t y times as great as that in the - kZ -APPENDIX I CALCULATION OF THE NEUTRON DETECTION EFFICIENCY OF A HYDROCARBON PHOSPHOR We assume that only elastic collisions with hydrogen atoms in the phosphor result in scintl11ation-producing energy transfers and that the carbon acts merely as a moderator. We are here concerned only with the slowing down of fast ( 3 mev.) neutrons, as the energy available for scin-tillations from thermal or nearly thermal neutrons is negligible. 1. Predicted Recoil Spectra: Let q(E) be the probability that a neutron with energy E cannot escape from the scintillator without colliding with a proton. We assume that q is Independent of the neutron's previous history. Since the scintillator used was a disc five inches in diameter by two inches thick, a mean phosphor dimension of 5 cm. was assumed. The specification of phosphor NE 202 give a hydrogen density of 0,05k atoms per cm. barn. (i.e. 0.05^  lO*2^ per cc.) Thus, in this approximation Using values for o" (E), the n,p scattering cross-section, from Hughes-Harvey (1955)* we obtain a reasonably good f i t to q by q(E) = 1 - e~°»27 6( E) q(E) = C , where C = 2.67 mev. (1) C + E Let P U ^ E Q ) be the probability that a neutron with energy E D loses energy E in exactly n collisions. Then 0-3 0-2 -F I G U R E AI - I P R O T O N R E C O I L S P E C T R A N E U T R O N S P E C T R U M : 8(3) fi LE>?> R(E^ 3)> O- -I - >- - - -• p o - i -2 E N , M E V 6 3 0-3-F I G U R E A I - 2 P R O T O N R E C O I L S P E C T R A R E C T A N G U L A R N E U T R O N S P E C T R U M £ = 0 - 2 E N = 3 M E V 0-2 -0-1-2 E N > M E V - 43 -By induction* Let P N(E,E Q) be the probability that a neutron with energy E 0 will lose energy E In at most n collisions before escape or thermalization. If our assumptions are correct, the shape of P n should approach the observed recoil spectrum as n becomes large* How Figure AI-1 shows the shape of the predicted recoil spectra for a 3 mev neutron group, assuming single hydrogen collisions, and at most two hydrogen collisions, i.e. i t shows Pi(E,3) and P2(E,3). These curves cannot be compared with experiment 6ince they assume that the neutron group is a £ -function in energy. A further calculation has been made of the recoil spectra assuming that the neutron group, instead of being a £-function in energy, is a rectangle centred on EQ, of height ~ - and width £. , where |3 is a variable parameter proportional to the half width of the neutron group. Let S(E,E Q) be the recoil spectrum from this neutron group. Thus ( £ - kk -Also, it form of S, to be a long and cumbersome expression, and will not be given here. but, even in this approximation, the explicit ,>(E,Eo) turns out Numerical calculations of S1(E,3) and S2(E,3) have been made, assuming ji - 0.2, and the curves are shown in Figure AI-2. The abruptness of the curves in Figure AI-2 is due to the angularity of the rectangular input neutron spectrum, and would be rounded off in practice due to the fact that the energy spread of an actual neutron group would approximate a Gaussian more closely than a rectangle* Also, the presence of a roughly equal atomic population of carbon (0.01*8 atoms per cm. barn) in the phosphor will tend to blur the neutron energy distribution before scintillation producing collisions with protons. And since the net effect of the carbon wil l be to lower the centroid of the neutron energy distribution before proton collisions, i t wil l tend to increase the detection efficiency, due to the fact that the n,p scattering cross-section rises strongly with falling neutron energy. 2. Neutron Detection Efficiency: Let £ n(En,Eb) be the scintillation efficiency for a neutron with energy E D. Et,, the bias energy, is the minimum energy (pulse height) that can be detected above noise* - 45 -Since P n(E,E Q) is very similar to S n(E,E Q) for low energies (Compare Figure AI-1 with Figure AI-2) we use P n in calculating the detection efficiency. Then £ ^  (£ 0, £ fc) * ° (£} £.) </£ Note that in the limit ^ — ^ 0 , £ - £ 2 = q(E Q). i.e. any neutron which collides with a proton in the detector is detected. 3. Relative Neutron Detection Efficiency: Since the neutron energy depends on the angle of detection in a neutron producing reaction, i t is necessary to know the relative detection efficiency of the neutron detector. For a given E^ and an arbitrarily chosen reference energy Ey , in the n'th approximation the required function is , x 9(E 0)Er(E 0 - Eb) In particular, R x(E 0,E r) - ^ Comparison with Nielson (1955) and Nielson and Warren (1956) shows that the expression there given omits the factor E r/E Q • - 1+6 -CALCUIATION OF THE NEUTRON AND RECOIL KINETIC ENERGIES, AND THE RECOIL AXIS, FOR A N^d,!. Y)N2 REACTION, WITH APPLICATION TO THE Be9(d,n f)B10 REACTION. We work exclusively In laboratory coordinates. The conservation equations are: 1 1 1 ( 2 % % ) ? = (2M2T2)2 Cos Q2 + (2*1^)5 Cos ^  (l) 1 1 (2M2T2)5 Sin © 2 = (2MnTn)2" Sin © n (2) Q = T n + T 2 - T d ( 3 ) where the T's are kinetic energies and the Q's are angles measured from the direction of the deuteron beam. 1. Neutron Kinetic Energy: Squaring and adding (l) and (2), and substituting for Q 1 from (3), T ^ + Mg) - ^ T ^ T ^ ) 2 Cos © n + T ^ - TdMg - Q ^ ^ 1 M <T> M nna 2 r\ *s \t . m f U ui \ I ^ S O T n a l t t W C O S 0U + . . M n T d d C 0 S K . Q Mg + Td(lfe - Md) *V ————— -f 1 (fc) At 0 n = 90 , T N = QMP + Td(Mg-Ma) mev, Mn + M2 2. Recoil Kinetic Energy: Eliminating T n instead of T2 in ( l ) , (2) and (3) results in - 47 -V*2 -Trns ? C o s e + f MdMfl C o g 2 Q + Q % • T d(lfa - Mg) Mn + Ma 1 2 3. Recoil Axis: (5) Eliminating T n and T 2 from ( l ) , (2) and (3), we find Sin 2 ( V «2> - ^ - s i n ^ , * s * % , vhere«. ^ Note: As Q —*»- ©4 , o{-*-0 , so © + 9 2 If we solve for 0 2 in terms of ©n, the result is 2 S i A g = S l n 2 0 n | l + j | + & - - sin2©,, + 2 Cos ©n C??sin2©n 12—_ **2 + ^ " Vn M2 (6) The correct choice of © 2 is the one corresponding to ©n+ © 2 7T as Q -» °Q 4. Be 9(d , ny)B 1 0 Recoil Axes: so We choose T d = 0.5, ©n = 45 and take \ = 1, Md = 2, Mg = 10, 1 ^ i — ^ and equation (6) becomes Sin2e 2 = 1 + ^ - Q.l£«2.2K- 0.21a2) 2 (1 + o<2) The table below shows the recoil directions for the f i r s t four excited states of B 1 0: B 1 0 Level 3.58 2.15 1.74 0.72 Q (mev) O.78 2.21 2.62 3.64 O.78 0.37 0.32 0.24 Q 2 74° 97° 100? 106 0 BIBLIOGRAPHY Ajzenberg, P. and Lauritsen, T. (1955) Rev. Mod. Phys. 2J , 77. Bethe and Morrison (1956) "Elementary Nuclear Theory", Ch. XVIII. Bhatla et a l . (1952) Phil. Mag. kfr 485. Biedenharn et a l . (1952) Phys. Rev. 88, 517. Blatt and Weisskopf (1952) "Theoretical Nuclear Physics". Bovcock, J.E. (1955) Proc. Phys. Soc. London A, 68, 512. Burrows, H.D. et a l . (1950) Phys. Rev. 80, IO95. Cheston, W.B. (1954) Phys. Rev. $6, 1590. Daitch, P.B. and French, S.B. (1952) Phys. Rev. 8J , 900. Dalitz, R.H. (1953) Proc. Phys. Soc. London A 66, 28. French, AJP. (1950) "Electromagnetic Radiation and Angular Correlations" Mimeographed notes. Friedman, F.L. and Tobocman, W. (1953) Phys. Rev. $2, 93. Fujimoto et a l . (1954) Prog. Th. Phys. Japan JJL, 264. Gallaher, L.J. and Cheston, W.B. (1952) Phys. Rev. 88, 684. Grant, I.P. (1954) Proc. Phys. Soc. London A 6J , 981. Grant, I.P. (1955) Proc. Phys. Soc. London A 68, 244. Helmholtz et a l . (1947) Phys. Rev. 72, 1003• Holt, J.M. and Young, C.J. (1950) Proc. Phys. Soc. London A 63, 833. Horowitz, J. and Messiah, A.M.L. (1953a) J. de Phys. et le Radium, 14, 695. Horowitz, J. and Messiah, A.M.L. (1953b) J. de Phys. et le Radium, 14, 731. Horowitz, J. and Messiah, A.M.L. (1954) J. de Phys. et le Radium, 15_, 142. Horowitz, J. (1956) Physica XXII, 969. Hughes, D.J. and Harvey, J.A. (1955) "Neutron Cross Sections", Brookhaven fiational Laboratory. Hunter, G.T. and Richards, H.T. (1949) Phys. Rev. J6, 1445. Lawrence, E.D. et a l . (1935) Phys. Rev. 48, 493. Lubnitz, CR. (1957) "Numerical Tabulation of Butler-Born Approximation Stripping Cross Sections", University of Michigan. Mott, N.F., and Massey, H.S.W., (1949) "Theory of Atomic Collisions", page 140. Newns, H.C. (1953) Proc. Phys. Soc. London A66, 477. Neilson, G.C. and James, D.B. (1955) Rev. Sci. Inst. 26, 11, 1018. Neilson, G.C. (1955) Ph.D. Thesis, University of British Columbia. Neilson, G.C. and Warren, J.B. (1956) Phys. Rev. 103, 1758. Oppenheimer, J.R. and Phillips, M. (1935) Phys. Rev. 48, 500. Pruitt, J.S. et a l . (1953) Phys. Rev. Q2, 1456. Satchelor, G.R. and Spiers (1952) Prog. Phys. Soc. London A65, 980. Schiff, L.I. (1955) "Quantum Mechanics", pages 77ff. Shafroth and Hanna (195*0 Phys. Rev. 96. Skyrme et a l . (1951) Rev. Sci. Inst. 23^ _ 204. Tobocman, W. (1954) Phys. Rev. §4, 1655. U.S. Atomic Energy Commission D 3645, 1955 "The Reactor Handbook", Volume 1, Physics. Yoccoz, J. (1954) Proc. Phys. Soc. London, A67» 813. 


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