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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 B r i t i s h 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 s e n s i t i v i t y resolution, and e f f i c i e n c y of a t i m e - o f - f l i g h t neutron spectrometer developed i n t h i s laboratory (Neilson and James, 1955)  have been Improved by the use o f 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 detect i o n e f f i c i e n c y o f the l i q u i d s c i n t i l l a t o r f o r neutrons i n the energy range 2 t o 3»5 mev has been shown t o follow the curve where  i s the neutron energy i n mev.  Investigation o f the Be^(d,n / ) B ^ reaction has shown that the / - r a d i a t i o n from the O.72,  2.15,  and 3.58 mev l e v e l s i n B ^. i s i s o 1  t r o p i c t o within 5$ i n the reaction plane while that from the 1.74 l e v e l i s i s o t r o p i c t o within 15$. 1.7^,  Further, the r a d i a t i o n from the  mev O.72,  and 3.58 mev l e v e l s i s i s o t r o p i c t o within the same p r e c i s i o n about  the respective r e c o i l axes, while the angular d i s t r i b u t i o n from the mev l e v e l i s 1 + (0.07  - 0.05)  s i n 6? , where 9 2  2.15  i s measured from the  normal, t o the reaction plane. Since energy selection of the ~/ r a d i a t i o n was not performed, i t i s not known which of the three t r a n s i t i o n s l i s t e d by Ajzenberg and Lauritsen (1955) i s responsible f o r t h i s anisotropy.  The angular d i s t r i b u t i o n s of the four neutron groups associated with the B  1 0  l e v e l s l i s t e d above, at  - 500 kev, indicates that at t h i s  energy s t r i p p i n g i s unimportant f o r the O.72,  1.74  and 2.15 mev l e v e l s ,  i n agreement with the work o f P r u i t t et a l . (1953) at E  d  = 9^5 kev.  The neutron group associated with the 3«58 mev l e v e l undoubtedly  proceeds via / = 1 stripping, but to obtain the observed position of the peak at this energy from Butler theory, i t i s necessary to assign a radius of 13.h  l O " ^ cm to Be^. The observed peak i s twice as broad as that 1  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 p r e s e n t i n g the  this thesis in partial fulfilment  requirements f o r an advanced degree at the  of  University  of B r i t i s h Columbia, I agree t h a t the  L i b r a r y s h a l l make  it  study.  f r e e l y available f o r reference  and  I  further  agree t h a t permission f o r e x t e n s i v e copying o f t h i s t h e s i s f o r s c h o l a r l y purposes may  be granted by the  Department o r by h i s r e p r e s e n t a t i v e .  Head o f  my  I t i s understood  t h a t copying or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l gain  s h a l l not  Department o f  be allowed without my  Physics  The U n i v e r s i t y of B r i t i s h Vancouver 8, Canada. Date  September 10,  Columbia,  1957  written  permission.  ACKNOWLEDGMENTS  I would like to thank my supervisors, Dr. J.B. Warren, who suggested this research, and Dr. C.A. Barnes, who aided i n the early part of this vork. I am also indebted to the many members of the Van de Graaff group vho helped i n 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 O i l Company for the Fellowship which have enabled me to carry out these studies.  TABLE OF CONTENTS  CHAPTER I.  II.  TITLE  PAGE  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 i n Stripping  15  9«  ( d , n Y ) Angular Correlation i n Stripping  17  TIME-OF-FLIGHT SPECTROMETER; DESCRIPTION AND CIRCUITS  III.  1.  Introduction  19  2.  The Spectrometer Circuits  20  3.  The Liquid Scintillator Neutron Detector  23  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 IV.  TITLE THE REACTION Be9(a,n/)B . 10  1.  Introduction  33  2.  Apparatus  33  The K - Ray Distributions  3^  3  .  k. Discussion of the  V.  PAGE  35  Ray Distributions  5.  The Neutron Distributions  36  6.  Discussion of the Neutron Distributions  37 39  FUTURE OF THE T IMS - OF-FLIGHT SPECTROMETER  APPENDIX I - NEUTRON DETECTION EFFICIENCY OF A HYDRO CARBON PHOSPHOR APPENDIX II- CALCUIATION OF THE NEUTRON AND RECOIL KINETIC ENERGIES, AND THE RECOIL AXIS, FOR A N (d,n )N REACTION, WITH APPLICATION TO THE Be9(d,n ) B REACTION. x  UZ  2  l 0  BIBLIOGRAPHY  k6 1*8  ILLUSTRATIONS PLATES  SUBJECT  FACING PAGE  1  The Liquid Scintillator Neutron Detector  23  2^  The Time-of-Flight Spectrometer  33  FIGURES 3  I- l  Stripping Collision Geometry  II- l  Block Circuit Diagram, Time-of-Flight Neutron 20  Spectrometer 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 III- 4  Neutron Spectra From Liquid Phosphor NE 202 Neutron Detection Efficiency of Liquid Phosphor  26  202  31  NE  IV- 1  The B  IV-2  Be (d,nY)B  IV-3 IV-4  1 0  9  "  31  Decay Scheme  Be (d,nV)B 9  B^d^/jB  10  10  1 0  Reaction. Relative./ - Ray Intensities Around Recoil Axes  35  Reaction. Relative / - Ray Intensities in Reaction Plane and B ^ d ^ n / j C Neutron Groups,  35  With Associated Level Energies  36  1 1  IV-5  Be9(d,n Y)T$-° Reaction. Neutron Angular Distributions  IV-6  Be^(d,ny)B Reaction. Neutron Angular Distribution  36  10  From 3.58 mev. Level i n B . 1 0  36  AI-1  Proton Recoil Spectra. Neutron Spectrum: &(E)  U3  AI-2  Proton Recoil Spectra*  k3  Rectangular Neutron Spectrum  Chapter I DEUTERON STRIPPING TREORY  INTRODUCTION: The deuteron i s a very loosely bound structure.  Its binding  energy (2.2 mev) i s so low compared to the average binding energy (6 to 8 mev) of nucleons i n light nuclei! that (d,n) and (d,p) reactions i n 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 i t s loosely bound structure, the mean distance (2.2 10"^3 cm) -between the proton and the neutron i n the deuteron i s larger than the range of the nuclear force binding them together. It i s 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, i n 1937* Lawrence et a l . had observed that the cross  section for the (d,p) reaction was larger at low energies than could be accounted 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, i n which the neutron i s captured while the proton remains outside the range of the nuclear force. More experimental data arrived, beginning i n 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 i n light nucleii.  The observed dis-  tributions were characterized by sharp peaks either i n the direction of the beam or at small angles from i t , which were inexplicable i n 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 i s now commonly known as "stripping theory". There remain, however, many neutron and proton angular distributions (three of which are presented herein) which are inexplicable i n 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 a l . (1952), and Daitch and French (1952), stripping theory has developed into a valuable technique for analyzing the results of the many deuteron i n duced reactions i n which only one of the neutron or proton i s absorbed, and the other i s scattered. I t gives the angular distribution of the scattered particles i n 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, i n a generally unambiguous fashion, the distinctive peaks i n the differential cross section with the orbital angular momentum of the captured nucleon, and so i s a valuable tool i n 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 r e a l i s t i c 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 N is described 2  by r «. n  In these coordinates, the dynamical operators are described as follows: a. Before collision: Let r - r - r n  ,8  p  -  * V? Mn  Then  Vp  Vj£ + 2MQ  and  1  2 ^  «  2  V  g  Let M = M + ^  +  1_ M  (7  l  R  2 1  2  IM  ,  1  Q  V £ + It 2l\  2Mp  + Vj 2M  2  X  .  1  + Mp  MJ  2 R  2J?  +  ^ 2M  + 1_  A  x  )  M  = Mi M M  7  y  2(Mn + Mp)  M Then  1#  1  + r  = 1 / 2  and M = MM  n  . S - R  Mp  = 1 /i _ + y 2 v *% Mp J  2  2Mp  + Mp)  +  ,R  ^ 1 d  l  +  M  r7 V  2 S  2  R.  - k -  b. After collision:  ^  t  "  1  Then 2M  X  And  1  ?  p - * l >  1  Jft' v  = MpM! Mp + M  2  2M  ,?  1  + Mp)  2 ^  1  - S . ,2  1  |/ S  + 1_ )rt2  2 ^ Mi + Mp  n  n  - *  X B  +  2  + _i_ V 2= 1 /  1% )  n«  V  , Mn = ^(Mj + Mp) Mi_ + M 1  x  Then Vn£ + V j £ + V i £ 2MQ  A + V P  M  + Vp£ = 1 z' 1_ + 1_"\ Vp« 2Mp 2 «• M-L Mp J  2(Mj. + Mp)  Let Mp  -  8  2Mp  =  2M  X  l 2Mp"^"  y ,  2  P  +  l  y  2M 1 &  2  n  '  2. Nomenclature: : dynamical variables of a l l nucleons in N^. d> ^n  k  :  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" , 6"p): Wave function describing the collision. n  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  -  satisfies H?  = EJ  5 -  vhere H = =  with H  d  -i Vr + V 2M  =  2  and H  2  = H.  1  H- + H,  -n ^ R  H  2  2  - i i V n'  2  - n ^p' 2 Mp 2  2  2  + H •P  + N + V.  2  + P, where V, N, and  1  D are the n-p, n-N^ and p-N, interaction terms.  n^d ,  Ji^p  2  : "binding energies of the deuteron, and of the  2  proton i n Ng. Conservation of energy implies  E  = E  1  t^-tii  +  2M£ ^  h  54-  3.  2  far-  M ?  E  2M1  andE =  - - B a T t e ,  =  E  ^_,  2 +  2^1 Thus  fr= iT ? E  whereH1  '  •  1  31  9  i£E  I Then  = -y l m  ^  2  (1)  M£I  ^  (  ^  n)  t  h  e  ( n , N a )  fthMme1  '  8 1 x 4  2  ( )  1 y  R  "n t« 2  2  "ST".  ( * i ) channel.  1 1 1  d  E^^ V D  +  1  . a*  Following Mott and Massey (l9ty)), l e t  * ^"K ^ -ymg 0  1  - ^ ! .  l  Differential Cross Section:  ¥  j  ^2  m  ^2^  2  N  =(N+V)T U y ^ l m  Jm/  1  J  rK r  1  il >  - 6 -  or  •9 \\ 2 w  So by orthonormality of the  T  »  The Green's function solution i s  too --ra  ,. . f  M  -p 2 / x T l N + v  J  and asymptotically for large r  n  ,  Now, i n the (d, N,) channel, assuming random spin orientation, ^ asymptotic form  ^E"^^  1  S" l m  1  i ^4  '  R  +  Ji  Ma  0 = d  3(2^  has the  scattered waves.  Thus, the incident deuteron flux i n each spin state i s nkfl  incident flux i s  i  + l) %  .  f  s o  the total  - 7 -  Since ^  has the asymptotic form  2  in the (n,N )  h  d  r« n  -ymg  j  V 2  2  channel, the scattered neutron flux i n the V mg' th spin state i s  v ,s!^ - ( V * * ) * 8  B  Y m 2  ]  The differential reaction cross-section i s  S (S>,f-)  = fig 'n^a , so  ( 2 )  4. Butler Stripping Theory: >  In order to obtain the Butler form for the differential crosssection, we make the following simplifying assumptions: a.  Coulomb interactions are negligible*  h.  The neutron does not interact with N]_. That i s , we approximate  ^•mg (Hi c.  i  m^  = 0.  The reduced reaction widths are independent of relative spin  - 8 -  orientationso The n-p potential V i s central - thus neglecting the 3Q * part of  d.  ;  the deuteron ground state - and the  wave function i s assumed to have the  - T l * ^ )  Halthenform: e.  Consider a sphere of radius ^  P vanish. We l e t 3?  *d  - ^ £  » 3?d + f  T |  0  T  J.  l^O)  where  about  '  ^(c^-.e^)  outside of which N and  , where  ,.,>° and r  for  e  l"p' > r  a  otherwise.  and $' describes the diverging neutron and the captured proton, assuming no n-N  2  i.e. (N + V) ty' = 0.  interaction  This approximation includes (a) and  (b) above, and i n addition neglects scattering of the deuterons.  Under these  conditions we have  Now  has the form:  1  ^ >  m  ^ * ' " " < H  f^iy)  mir|jSn?<jJ,Aim |j m,> 1  l  + orthogonal terms containing excited states of N Where cx^7f  1#  i s the probability amplitude for capture of a proton of orientation  i n the lm'th subwave and with t o t a l angular momentum j = jl *  orientation mj^.  i  "fey  i n the  i n accordance with approximation 3 above, we assume  Note that to conserve parity,  = 0  unless ( - l ) parity N 1  Also, we assume that the proton i s captured with either j = % - 1 but not botho 2  1  =  = parity N . 2  +  i  or j =  This i s justified by shell model considerations (Blett and  •  - 9 -  Weisskopf, 1952, page 768). Since [T ijy^j  w  e  iT  W,)  satisfies  \/>>  , with fj] ' and X  have,by virtue of the orthonormality of the  1  Since the analytical form of P, the p-N interaction, i s unknown, this equation cannot yet he solved.  But for f*y >To , P = 0, and since the solutions f ^  are linearly independent, they are identical i n the region r ? f with the J  ( V p " Pp> f £  solutions of  ki^*  1i^)^f^r%  Substituting (4)  - 0  which have the simple form (Schiff, 1955)  Thus, for  into (3)  ;  s  r/>r , 0  and integrating over the variables of N-^,  w  e  g e  t:  *x,ry>r.  Substituting (5) into (2) and using the fact that ^iii^^xlT^  ^ (-\)  h  ^ ( ^ i ^ ^ - j - j ^ - M ^  plus the orthonormality  of the Chebsth-Gordon coefficients, we find  ?FF^7 Now, to evaluate the  xi+T  (T)  , we transform to more manageable coordinates:  m  - 10 -  Let  M'r  (8)  r  whence  But  Taking the Fourier transform,  (10) Let A ^ be the f i r s t integral i n (9). M  We can expand the  Y*  g"?' ^ = 2 4  ( > /  0  2  Jg/f iy)  '' > ^  are orthonormal, L  .  c£ 7  But since  |^ ^  and  (ii)  are spherical Hankel and Bessel functions, they  satisfy the identity (cf Schiff, 1955)  (f fW k frV jl^ -'J^ \ H (t if r ') +  Bince  l  V  f)  r  , where the Wronskian  IK  (12)  - 11 -  And substituting for cj\  and K  from (8)  into ( l ) ,  (13) and from (10) and (l3)> I ^ becomes  (1*)  so from (l),  rt.^O^MK  fc„  awYaMflV  *  /  , |, , , 2  r  • ,  ,p  (15)  Lubnitz (1957) has tabulated the quantity  4^  -  (16)  for j2 = 0, 1, 2, 3, and k and a wide range of x = qr£ and y = ^ r . f  p  0  In terms of the experimentally known quantities E , the laboratory energy d  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  - 12 -  Reduced Widths: In f i r s t approximation, the reduced width for capture of a proton i s given by 7f < t  where  (Blott and Weisskopf, 1952)  / /?o (V,,)/  1  i s 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 i n the differential cross section, and the predicted curves are not i n 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  i n Legendre polynomials and  comparing the coefficients with those giving best f i t experimentally. More rigorous reduced width derivations, which lead to (18) i n f i r s t 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 i t s f i n a l form:  6.  j.  The Butler Approximations: Butler (d,n) stripping describes the reaction of an uncharged  - 13 -  nucleus, transparent to neutrons, with a  deuteron, a reaction i n which a  proton enters the nucleus without reacting on the neutron, and i n which scattering of deuterons i s neglected, as i s compound nucleus formation* Most of these restrictions have heen examined i n 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 i s flattened - the stripping peak broadened the cross-section i s decreased, and some spin polarization i s produced* latter subject i s discussed below*  The  Yoccoz's analysis i s the most straight-  forward, and introduces the Coulomb correction as modifications of the external wave functions of the proton and the deuteron i n equation (6). The k percent  admixture i n 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 ^ .  Thus, the characteristic shape of  the angular distributions i s unchanged*  However, he maintains the assumption  m  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 i n either paper.  Since  the effect of compound nucleus formation w i l 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 i s 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, i s (more realistically) opaque to them.  /  This l s done by evaluating  Then < V m , | N'V| U , > +  Where ^^r\')  i s  ,  | M + V| ^ ha, >  • iJ  to»TK  VY ^  =  ^  /• oi /or ^ D  W  flr  r  W  >  r  '  *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), i s  I  8  l' K f  J(wWk"rwkHi)  A,.  '  where K* and q* are defined with Is. replacing ICQ i n ( 8 ) , and q i s the polar axis for the angles.  Comparison with (lk), plus the fact that the radial  integral i s most significant at the pole k = 1% shows that the angular distribution has the same general shape. The most significant point i s that the I ^ no longer vanish for m 4 » m  Q  Horowitz and Messiah (1953 a) have made a similar calculation,  r„' <  - 15 -  assuming zero range for the deuteron potential, and expressing the crosssection for 1 = 0 and 1 i n 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 polarization (Horowitz and Messiah, 1953 b ) . 8.  Spin Polarization i n Stripping: The polarization of a beam of spin 1 particles i s given i n terms 2  of i t s density matrix  i  by p - S f l l J f  and the density matrix  j  i n the case of N-j^dn)^ stripping, assuming that  d and  (Bethe and Morrison, 1956)  are unpolarized, i s  Explicitly, i f we assume protons with only one value of 1 and one of j are  ' & - **feo *k f  captured  ^  ?  <  (  i  « l ^ < « fl WXti, »,b^>  where the t refers to whether j = 1 + g or j = 1 - 2 . I f this i s summed, using the symmetry and orthogonality  properties  of the Clebsch-Gordon coefficients, (Blatt and Weisskopf, p. 791), we obtain  Traced  . J^L 1>L £m ^  tPL^llff,  yV components of the polarization: 0  1  * - * 4?s 1 • & &  £  r  fJP***^*  and for the  f % PUT  - 16 -  But i f we chose the x coordinate to l i e i n the reaction plane (previously Z, the quantization axis, was chosen to l i e i n the direction of qj the r e c o i l of N2), i t follows from general symmetry arguments that X'^ - (-0*11  ( » Gran** 1955)* and because of this, i t i s t r i v i a l cf  to show that Pjj = P = 0, and z  In the unmodified Butler theory, we have seen above that ll*  T n u s  > y p  =  °>  s  o n  o  Polarization i s predicted.  I f one i n -  cludes hard sphere scattering of neutrons, polarization i s predicted. Numerical calculations have been made by Newns (1953) who has used a semiclassical model and obtained typical values for / = 1  }~\ '. p - 0.U j.-i  :  p-.-o.3i  However, i f one considers Butler stripping with Coulomb corrections, the opposite sign of P i s 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 Be^dnB  10  1 0  i n the  reaction. The polarization of protons from the C^dpC ^ reaction (/ = l ) 1  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 i s 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 i n the C ^ d p j c ^ 1  case i s 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 d i f f i c u l t y i n obtaining the 1^ s i n workable form. Cheston (195^) has r  considered spin orbit interaction i n the scattering of the protons i n Cl2 ( d p j c ^ at Ed 3*29 mev. He predicts negative values for Py with [ P ^ ! ^  ,  1  which i s less than half the measured value.  9.  (d,nY) Angular The  Correlation i n Stripping:  (d,nV)  correlation i n 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 i s the same as that produced by a plane wave of protons ( C  p  in the r e c o i l direction, which i s 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 i s a mixture of multipoles. b.  Conservation of parity requires symmetry about Q = 90°  ( i . e . 90° from the recoil axis). c.  Complexity limitations:  I f the proton i s captured with  orbital angular momentum I into a level with spin J , then the multipolarity 2  2  1,  of the Y ray i s limited by L £  min ( I , J ) , (Blatt and Weisskopf, 2  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 correlation.  Newns considers only his semi-classical hard sphere scattering of  the neutrons, and for /  =» 1, j = 3/2 he shows there i s no ( n , Y ) correla-  tion i n the reaction plane, but there i s correlation i n the plane through the r e c o i l 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). I t i s 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 I I . 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 i s the observation of (d^ n ~jf) reactions.  In this type of reaction, the incident deuteron i s stripped  of i t s proton by the target nucleus, forming a residual nucleus i n an excited state, and the freed neutron escapes. The lifetime of the excited state i s short («• 10""9 s e c ) , and the / -detector i s placed close to the reaction chamber. Thus the Y -ray detector pulse serves as a marker to signal the start of the neutron's f l i g h t .  The neutron detector moves on a horizontal circle  centered at the target and one meter i n radius, so the neutron detection pulse i s 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 i s about kO 10"*9 seconds for a 3 mev neutron. Since the limiter output signals from both detectors are a standard 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  Kick Sorter Gated Biased  Moody Amplifier  Amplifier  Gate Generator  /Detector Limiter  Energy Selecting Side Channel AntiCoincidence  0 8 >JS Delay True Coincidence  S ide Channel  Random Coincidence  Time S o r t e r 70rrj/js Delay  Coincidence I8>JS Delay  Side Channel Gate Generator Energy Selecting Side Channel  n Detector I—J Limiter Gated Random Coincidence  FIGURE L I - I BLOCK TIME-OF-FLIGHT  CIRCUIT DIAGRAM NEUTRON  SPECTROMETER  Random Scaler  - 20 -  sorter has transformed the flight time spectrum into a pulse amplitude spectrum, the signal i s amplified, gated to remove noise pulses and one half the random "•background" signals, and fed to the t h i r t y channel pulse height analyser*  The gating i s 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 i n the  Y -ray energies i n 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, i s 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 i s 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 i n detail by Neilson and James (1955)* The ?random" and "anticoincidence" circuits have been installed i n 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 i n 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 i n  56K  +|7  +250 V  5ov  +I20V  ©  220 O h m Cable 2 m/is long.  D  330 O h m C a b l e 35 m/JS l o n g .  H E W L E T T T L -  £22  6342  To F a s t Coinc  PACKARD  -P  ir—^>  Amplifier No. 4 6 0  A  FIGURE  H-2  NEUTRON D E T E C T O R  CIRCUIT  - 21 the latter circuit.  Thus, the output from the random coincidence circuit i s  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 i n 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 i s that part of the spectrum which produced coincidences both i n the random coincidence and in the side channel coincidence circuits, while the Input to the gate controlling the kicksorter input i s that part of the spectrum which yielded a side channel coincidence but not a random coincidence. The  James  (1955),  Y"  r a y  detector i s essentially as described by Neilson and  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 i s shown In Figure II-2.  Operation  6AH6  6JS  Co.th.FoH.  Random  ,,  c  H-  Coinc.  6J6  Flip- Flop  5687 Cat h. Foil.  JLAA  »Ows 50  "  750K£ Clipper  6AK5 Amplifier  6J6 Flip-Flop  Anticoinc.  6*AH6  Amp.  <750K -I 150V 6 B N 6 C o i n c . "CT  -3 C h a n n e l Gate  zS.  4-30PF  FIGURE  £4K  b  .  |  K  -40V  H-4  GATED RANDOM AND ANTICOINCIDENCE  CIRCUITS  + 300V  -^.Scaler  - 22 -  of the limiter circuit i s unchanged, except that this pulse has been lengthened to 70 10"9 seconds too. The major modification i s the use of a Hewlett Packard distributed line amplifier with a gain of ten to Increase the sensit i v i t y for low energy neutrons. The fast 6BN6 "true" and "random" coincidence circuits are shown i n Figure I I - 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 i n the output, while the random circuit i s quite straightforward, 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 generator 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 i s amplified by a 6AH6 and the pulse top clipped by a IM56 diode.  The positive-going pulse i s cathode-followed out by  another 6&H6 to feed (a) a 6J6 flip-flop producing a standard shaped rectangul a r 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 coincidence tube.  Suppose a (negative) side channel coincidence signal appears on  the other grid of the anticoincidence 6J6.  I f no random coincidence signal  appears on the f i r s t grid, the side channel coincidence signal i s amplified and passes through the IN58 diode to trigger the 6J6 gate generator f l i p - f l o p . However, i f a (positive) random coincidence signal does appear, a net negative signal appears at the anticoincidence 6J6 plates, and i s stopped by the IN58 diode.  I f a signal from the side channel gate appears at the second grid of  MORE WAX BELOW MATERIALS K E Y LE A D - W X WAX- \ \ \ WOOD- 7>?  SCALE  FIGURE I I - 5  l" = 4" NEUTRON  COLLIMATOR  a  DETECTOR  -  23  -  the 6BN6 in coincidence with the signal fed at (b) above, a negative coincidence 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 i s 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, i s 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 i n 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 f l u i d . The structure above the scintillator vessel i s a chamber f i l l e d with inert gas to take up the thermal volume changes of the s c i n t i l l a t o r and relieve the pressure on the glass vessel. The latter i s supported on lucite rings inside the Shelby tubing housing. num.  The face plate i s 0.020 inch alumi-  - 25 -  CHAPTER I I I . THE  1.  LIQUID SCIHTTTiTATOR:  RESPONSE TO NEUTRONS  AND Y - RADIATION  Introduction: The time-of-flight neutron spectrometer described by Neilson  and James (1955) used a stilbene crystal as neutron detector. While stilbene i s an excellent, fast phosphor for this purpose i t i s expensive, very d i f f i cult to prepare i n blocks larger than a few centimeters i n 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 i n section three of the previous chapter. In this chapter we discuss the scintillations produced by monoenergetic neutrons and Response curves for  rays i n the liquid phosphor.  - rays from several standard sources are given, and  the pulse height versus energy curve i s shown. The response to monoenergetic neutrons i s determined from observation of the D(d,n)He3 reaction at various  600-  FIGURE  S P E C T R A  C0MPT0N F R O M  Na  500-  LIQUID  22  UI-I  PHOSPHOR  1 3 7 Cs x R  NE202  RdTh  o  400-  •34  •48  <7  COMPTON  1 0 7  <7  2 39  EDGE (mev)  v-  Q  300-  o\o \  \  A  \ x  200-  V \  COUNTS  X5  \  100-  o..  N 10  ^X  o'  \  v-. .. 0  ^"0-.o..o-Q, o...o.. j..^NQ^\©..o..o.. o-. C~X  15  20 PULSE HEIGHT  25  --0--0-0 . .o  -r—y/—T—  30  0  40  o-o  45  o.  50  FIGURE  nr.-2  LIQUID PHOSPHOR RESPONSE  NE 2 0 2  TO 7- RADIATION  /  o  PULSE HEIGHT  / 10  2 0  3 0  4 0  5 0  FIGURE NEUTRON  COUNTS  FROM  300 A  E  SPECTRA  LIQUID P H O S P H O R  3-51 MEV  N  TJT-3  •  E  N  206  22  NA  \  y  CALIBRATION  X  NOISE  200  \ i  \  ^X  100 A  \  \ °  x__x~x— _ x ^ s ^ - x - ~ x ^  X—X—v x  x  i—  5  10  •—  -  •  —  —r~  O —  ^x.  O — Q  15 PULSE HEIGHT  —I—  20  —i—  25  NE202  MEV  O  - 26 -  neutron angles.  The r e l a t i v e e f f i c i e n c y f o r various neutron energies i s  given, and compared with a simple c a l c u l a t i o n assuming that only the energy transfer i n e l a s t i c scattering from hydrogen atoms i n the phosphor contributes t o the s c i n t i l l a t i o n pulse.  The importance i n knowing the r e l a t i v e neutron  e f f i c i e n c y i s that t h i s quantity i s necessary f o r normalizing (d,n"V) angular d i s t r i b u t i o n curves, as the neutron energy from such neutrons varies somewhat with angle f o r a given bombarding energy. 2.  Response to  "Y" - Rays:  Figure I I I - l shows the predominantly Compton e f f e c t spectra from the three standard sources N a , Cs^-37, and RdTh, with the noise background 22  subtracted, while i n Figure I I I - 2 the pulse height at the Compton edge i s p l o t t e d against Compton energy. the phosphor response to y observed.  I t i s apparent from the l a t t e r curve that  - rays i s s t r i c t l y l i n e a r i n the range of energies  These r e s u l t s were obtained with the sources placed at the focus  of the neutron collimator, and with the usual H.T. of 1750  v o l t s 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 t o 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 N a  2 2  V - ray  spectrum, and also shows the phototube noise, the tube voltage being v o l t s and the pulse s i z e at the s i x t h dynode being about 0.5  1750  v o l t s at the  - 27 -  Compton edge of the 1.28 mev sodium l i n e .  The noise curve has heen subtracted  from the f i r s t 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 i n connection with the neutron detection efficiency of the phosphor.  (See Appendix I ) .  The  predicted recoil spectra, given i n Figure A I - 1 , bear some resemblance to the observed spectra, but the second approximation, which takes account of secondary proton collisions, gives a poorer f i t than the f i r s t , which assumes at most one proton collision per neutron. The predicted strong forward peaking due to the secondary collisions i s 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 i s good, since the Compton spectra are satisfactory.  Hence i t must  be the scintillation process i t s e l f which gives a less uniform light output for recoiling protons than for recoiling electrons. The light output i n a neutron pulse i s down about a factor of three from that due to a about the same energy.  ray of  (This i s demonstrated i n Figure I I I - 3 . ) , so presumably  the scintillation mechanism i s less efficient for r e c o i l protons than for recoil Compton electrons. c. Too great a simplification of the geometry i n 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 i s of the order of the scintillator thickness, the f i r s t collision could occur with almost equal probability anywhere through the scintillator, and because of the cos^O pattern of n-p scattering i n 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 i n f i r s t approximation, and would have an even stronger effect on the second approximation, bringing i t much closer to the f i r s t 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 i n 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 i n Figure III-3 are respective examples of the two types of break. A possible explanation i s 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 i n the phosphor i s 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 i s 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 i s about the same as that of hitting two successive protons, and the lack of strong forward peaking i n 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 i u the recoil proton spectrum from a stilbene crystal, and a similar effect has been seen by Skyrme et a l . (1951) i n the recoil proton spectrum from a hydrogen gas counter. The former authors attributed the effect to phototube noise, background, neutrons from C (d,n)N 3 i n carbon on the target, and annihilation radiation from 12  1  the positrons i n the K  13 6 decay, while the latter authors attributed i t  to  ^ - rays from fluorine and other impurities i n the LiF targets they used.  (They obtained their neutrons from LiT(p,n)BeT.) i n 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 i n 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 i s 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 f i r s t suggestion i s discounted by the fact that the resolving time in the pulse height analyzer i s over a microsecond, whereas the quoted decay time of the phosphor NE 202 i s 2 10"9 seconds, and the mean time between  - 30 -  collisions of a 3 mev. neutron i n a hydrocarbon i s of the order of 10 seconds.  Hence any likelihood of a delayed s c i n t i l l a t i o n mechanism being  observable seems very remote. The effect of externally scattered neutrons i s rather d i f f i c u l t 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 i s 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 i s 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 i t s higher ionization density, and consequently less efficient light output associated with a carbon recoil, as compared with that of a r e c o i l proton of the same energy, that this phenomenon might well account for the observed rise i n the scintillation spectrum at low pulse heights. This conclusion is i n 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  HI -  FIGURE NEUTRON OF  4  DETECTION EFFICIENCY  LIQUID  PHOSPHOR  £ O B S < E > = O I 4 6  +  N  £ ^  0-45  0-40  0-35 4  c ABSOLUTE  X  EFFICIENCY  TH  °v" ' x  0-30 A  C  0-25 A  >>o  2(E,D  1  £,(EJ)  X..  ^  (E)  ^ O B SB  0-20^  —2  —— t  3  NEUTRON  T  ENERGY, E , MEV  202  NE  G  G  .  - 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. i n 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 $73 kev. ~f - ray in O ? caused by O ^ (d^JO ? i n the oxygen i n the water. 1  1  1  The absolute neutron detection efficiency at  = 2.07  mev.  (°n = 135°) was obtained by two methods: As calculated from the target thickness and beam current, the efficiency was found to be 29 - 2$, 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 i s plotted i n Figure I I I - 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 f a l l i n g neutron energy i s due mostly to the increase i n the n,p scattering cross-section. *  Obtained from Chromium Corporation of America, Waterbury, Conn.  - 32 -  It i s apparent from the figure that the second approximation (^2)  predicts the shape of the efficiency curve i n the region above 2 mev  better than the f i r s t 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 i n can «)ust be seen at 1.1 mev with the side channel settings i n use here. I f 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 i n efficiency below 2 mev, due to the bias energy, actually occurs. Evidence has been obtained of fine structure i n the detector efficiency at the energy (3 mev) of a strong resonance i n the carbon neutron scattering cross-section.  Since the structure i s small (under k$>), i t i s of  l i t t l e importance i n the use of the scintillator i n the time-of-flight spectrometer, and w i l l not be discussed further here.  P L A T E I - T H E TIME-OF-FLIGHT  SPECTROMETER  - 33 -  CHAPTER IV THE REACTION Be (d,n Y ) B  >  1.  9  1 0  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 i n B , with a deuteron bombarding energy 10  of 500 kev. The deuterons were produced i n the U.B.C. Van de Graaff generator. 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 i s shown i n 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 i s shown i n Plate I I . The  neutron detector i s 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 i s mounted i n position for measurement of  FIGURE 32-1 T H E B DECAY S C H E M E 10  - 3h -  ~i intensity i n the plane normal to the r e c o i l axis of the B- . 10  The target was about 0.1 mgm/cm of Be 2  9  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 i n the plane  normal to the r e c o i l direction of the B , 10  and (b) the angular distribution  in the reaction plane. The f i r s t set of angular distributions was measured in order to see i f the polarization predictions discussed i n 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 i n the neutron angular distributions to the l»7k, 2.15, and 3.58 mev. levels. The calculation of the r e c o i l direction for each level, and the neutron and r e c o i l kinetic energies, i s given i n Appendix I I . Since the  Y - rays from the 2.15 and 3*58 mev levels are each  mixtures of three transitions (Figure I I I - 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  T  T  4-  -O-  -o-  ±  o  1  T  T  30  60  9  FIGURE  IZ-2  T r  25  1  O  -30  -60  B  10  O •  T^y :  i  ENERGY L E V E L S 7  + •  o  3 58 2  1  5  7 o 72  1 . 4  Mev  i  Be (d,n ) B 9  y  Mev Mev Mev  1  1  - 50  l  J _Q_  RELATIVE  10  1 0  i  REACTION  y - RAY INTENSITIES  AROUND RECOIL A X E S  T 7 150  T  1 T  -7-  7"  i  1  T  I  1  1  .1.  T  • v-  ... T  T  7  1  1  .Ii  i .  -125  -150  T 1  T + 1  1  +~ 1  I  L  -125 RELATIVE INTENSITY  -100 O  J_-  T  o-  T O  -J_-  1JL  -TG  -75  -50  B  ' 0 ENERGY L E V E L S  AS IN FIG.TSL-I POSITION RECOIL  OF AXIS:  FIGURE Be (d,n ) B 9  10  7  RELATIVE  X-RAY  12-3 REACTION INTENSITIES  IN REACTION P L A N E  - 35 -  "Y , the observed Y intensities, normalized against the count i n 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 r e c o i l directions.  The curve through the 2.15  mev level points i s 1 + 0.068 s i n 6 , while the ^ - rays from the other three 2  levels are closely isotropic. Figure IV-3 shows the / - ray angular distribution i n the plane of the reaction.  i s measured from the direction of the deuteron beam  and i s positive on the side away from the neutron monitor.  Any anisotropy  in the three most intense levels i s less than 5#> while i n the weak transition from the 2.15 nev level, i t i s less than 15$.  The appropriate recoil axes  are noted on the curves. The gap i n the points i s the position of the neutron monitor. k. Discussion of the Y - ray Distributions: Theoretical analysis i s under way to determine whether the observed ~Y - ray distributions are i n agreement with the multipolarities i n the BlO decay scheme l i s t e d by Shafroth and Hanna (195*0 • This work i s slightly complicated by the possibility of polarization occurring. The experimental evidence for polarization herein presented i s very weak - the 7$ anisotropy about the r e c o i l axis of the radiation from the 2.15 mev level i n B . 10  The  problem i s being attacked by calculating the angular distributions using standard techniques, and looking for agreement or otherwise with experiment.  Be (d,n ) B 9  r  B  y  O  -400  o° 45°  n  COUNTS  • 200  />  \  /  1 ^ o 1  / °-°-o-o.a..°^  V  °  o\>-°'o  2.15 1.74  3.58  A 0.72  X  B (d,ny) C " ,0  0 o° 7 0 45° V  n  -400 COUNTS  A -200  0 /  /\ V ''-o-o-o-o-o-o-o- '  o  4.77 4.23  1.90 ° ^  FIGURE  Be (d,ny)B AND 9  °• X  0  -o-o-cf'  10  NEUTRON  LY-4  B (d,n/) C 10  M  GROUPS, WITH  ASSOCIATED L E V E L ENERGIES  1 0  FIGURE Be (d,n )B 9  1 0  r  NEUTRON ANGULAR  ET-5 REACTION DISTRIBUTIONS  \0-72  300  RELATIVE INTENSITY  200  100  0  1-74  30  60  90  120  150  180  FIGURE E T - 6 B<?(d,n ) B r  1 0  REACTION  NEUTRON A N G U L A R DISTRIBUTION 3-58 M E V L E V E L BUTLER H = I CURVES: •  R= e  • R= 0  5 IO"' 13-4  3  CM.  I0" CM. ,3  - 36 -  5.  The Neutron Distributions: Figure IV-h shows the Be9(d,nY)B  10  neutron spectrum as observed  on the 30 channel analyser* The weak group corresponding to the 1*74 mev level i n B  1 0  i s not resolved*  For comparison, the neutron groups associated  with the f i r s t three levels i n C^- are given* These were obtained under identical conditions, with the same bombarding energy, 500 kev* Figure IV-5 shows the angular distributions i n laboratory coordinates of the neutron groups to the 0*72, 1*7**> and 2*15 mev levels i n B , 10  with the Y monitor fixed at 90° to the beam direction.  These curves have  been corrected for the change l a 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 f i n i t e 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 i n 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  i s 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 i n B . 1 0  This i s the only group which shows a pronounced  stripping curve, and i s compared with _/ = 1 stripping distributions as  - 37 -  calculated from the table of Lubnitz (1957). group i s low. o  The energy of this neutron  It varies, at Ed = 500 kev, from 900 kev at 150° to 1.3  mev  at 0 . Consequently, to obtain sufficient yield, the bias level on the neutron detector (Et,) was set at roughly half the value used i n a l l previous runs.  Consequently the relative heights of the 3.58 mev group and the  other groups i n Figure IV-3 i s not significant. Also, the relative e f f i ciency of the neutron detector at this low energy i s not known, and so the experimental curve i n Figure IV-6 i s not corrected for i t . It i s thought that the relative efficiency at this energy w i l l not depend strongly on energy as the decreasing effect of the bias w i l l offset the increasing effect of the n,p cross section (i.e., the maximum of £ ( E , . ) w i l l be at about 2  5  1 mev and w i l l have much the same shape as the maximum of £2 ( * l ) at 2 mev E  i n 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 i n B  1 1  for each  neutron group. This appears rather unlikely. Another i s that they are not similar to any Butler stripping curves. / = 1 stripping i n the 1.74  (However, there may be some  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 i n 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 i n that i t resembles an / stripping group i n ( ~n  =1  - ©n).  The neutron group from the 3*58 mev level i s clearly an £ = 1 stripping group which has been modified considerably by coulomb and other effects.  I f one uses a reasonable radius for Be^ (5 I O " ^ cm), the 1  calculated stripping distribution, as obtained from Lubnitz's (1957) table, does not agree with experiment, as i s obvious from Figure 17-5.  Indeed,  the'best f i t " radius as calculated from Lubnitz, i s 13»k l O " ^ cm. i . e . 1  the stripping appears to occur far from the nuclear surface.  Comparison  of the curves i n Figure IV-5 shows that the coulomb broadening and shifting, as predicted by the authors cited i n Chapter I, paragraph 6, does actually occur.  - 39 -  CHAPTER V THE FUTURE OF THE TIME-OF-FLIGBT SPECTROMETER  In i t s present state of development, the spectrometer can produce significant contributions to the knowledge of the level structure of such nucleii as C , U  C , 12  N, lk  0 , 16  F , F , and Ne , by the investigation of (d,n/) reac18  19  20  tions i n the appropriate target nucleii.  It i s , of course, not restricted to the  observation of deuteron induced reactions, but rather can be applied profitably to any reactions resulting i n fast neutron, K - ray coincidences, as for example to the energetically favoured and quite interesting reaction Be (t,n/ )B^-. 9  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 alignment, 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 i s i t s 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 i t s decay time of a hundred times as long as those of organic scintillators, i s 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. ments to this end have already been carried out.  Successful preliminary experi-  - ko -  If the use of a sodium iodide Y - detector does prove to be feasible, another modification of the spectrometer circuits w i l l 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 i n 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 i n the Y  angular  distribution, because of the inverse square intensity relationship. A few millimeters of target misalignment i s sufficient to produce large and misleading angular distribution patterns.  Such was the case i n the preliminary runs  of the experiments described i n earlier chapters. Target positioning to the nearest millimeter i s not so important i n the case of the neutron distributions, where the source-detector distance i s a meter instead of a few centimeters. Use of another Hewlett-Packard amplifier i n 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 i n 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 i n use are quite non-linear* The gain f a l l s off rather rapidly with increasing pulse size.  This, however,  i s not as injurious to the operation of the spectrometer as the fact that the lower bias settings are not sufficiently stable. Instability here i s 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 considerations w i l l permit.  Because of this, the noise counting rate, which i s  extremely sensitive to the lower bias setting, i s normal l y a considerable percentage of the actual counting rate. This i s of most Importance when running  Y  - ray angular distributions as the noise i n the neutron detector,  which i s then being used, as the monitor, i s 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 i n the phosphor result i n scintl11ation-producing energy transfers and that the carbon acts merely as a moderator. slowing down of fast (  We are here concerned only with the  3 mev.) neutrons, as the energy available for scin-  t i l l a t i o n s from thermal or nearly thermal neutrons i s 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 i s Independent of the neutron's previous history.  Since the scintillator  used was a disc five inches i n 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* ^ per cc.) 2  Thus, i n this approximation  q(E) = 1 - ~°» 7 6 ( ) 2  E  e  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) =  C C +E  , where C = 2.67 mev.  Let P U ^ E Q ) be the probability that a neutron with energy E loses energy E i n exactly n collisions. Then  (1) D  FIGURE PROTON  RECOIL  NEUTRON  0-3  AI-I SPECTRA  SPECTRUM:  R(E^3)>  8(3)  0-2 -  fi - >- L->?> - -• E  O-  p  -I  o-i-  2  FIGURE PROTON RECTANGULAR £=0-2  E ,MEV N  AI-2  RECOIL  SPECTRA  NEUTRON  SPECTRUM  E =3MEV N  0-3-  0-2 -  0-1-  2  E  N >  MEV  6 3  - 43 -  By induction*  Let P ( E , E ) be the probability that a neutron with energy E N  Q  0  w i l l lose energy E In at most n collisions before escape or thermalization. If our assumptions are correct, the shape of P recoil spectrum as n becomes large*  n  should approach the observed  How  Figure AI-1 shows the shape of the predicted r e c o i l 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 i s a £ -function i n energy. A further calculation has been made of the r e c o i l spectra assuming that the neutron group, instead of being a energy, i s a rectangle centred on EQ, of height where |3  ~-  £-function i n  and width  £.  i s a variable parameter proportional to the half width of the  neutron group.  Let S ( E , E ) be the r e c o i l spectrum from this neutron group. Q  Thus  ( £  ,  - kk -  Also,  but, even i n this approximation, the explicit i t form of S, S,>(E,E ) turns out o  to be a long and cumbersome expression, and w i l l not be given here. Numerical calculations of S (E,3) and S (E,3) have been made, 1  2  assuming ji - 0.2, and the curves are shown i n Figure AI-2. The abruptness of the curves i n Figure AI-2 i s due to the angularity of the rectangular input neutron spectrum, and would be rounded off i n 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) i n the phosphor w i l l tend to blur the neutron energy distribution before scintillation producing collisions with protons. And since the net effect of the carbon w i l l be to lower the centroid of the neutron energy distribution before proton collisions, i t w i l l tend to increase the detection efficiency, due to the fact that the n,p scattering cross-section rises strongly with f a l l i n g neutron energy. 2.  Neutron Detection Efficiency: Let £ (En,Eb) be the scintillation efficiency for a neutron n  with energy E . D  Et,, the bias energy, i s the minimum energy (pulse height)  that can be detected above noise*  - 45 -  Since P (E,E ) i s very similar to S (E,E ) for low energies n  Q  n  (Compare Figure AI-1 with Figure AI-2) we use P efficiency.  Then  £ ^ (£ , £ ) * 0  °  fc  Note that i n the limit ^ — ^ 0 ,  £  - £  Q  n  i n calculating the detection  (£ £.) </£ }  2  =  q(E ). Q  i.e. any neutron which collides with a proton i n the detector i s detected. 3. Relative Neutron Detection Efficiency: Since the neutron energy depends on the angle of detection in a neutron producing reaction, i t i s necessary to know the relative detection efficiency of the neutron detector. For a given E^ and an arbitrarily chosen reference energy Ey , i n the n'th approximation the required function i s  , x In particular, R (E ,E ) x  0  9(E )Er(E 0  0  - Eb)  r  ^  Comparison with Nielson (1955) and Nielson and Warren (1956) shows that the expression there given omits the factor E / E • r  Q  - 1+6 CALCUIATION OF THE NEUTRON AND RECOIL KINETIC ENERGIES, AND THE RECOIL AXIS, FOR A N^d,!. Y)N REACTION, WITH APPLICATION TO THE Be9(d,n f)B  10  2  REACTION.  We work exclusively In laboratory coordinates. The conservation equations are: 1 (2%%)?  1 = (2M T )2 2  1 (2M2T ) Sin © Q  = T  n  + T  2  2  1 = (2M T ) "  5  2  1 Cos Q + (2*1^)5  2  Sin ©  2  2  n  -T  n  Cos ^  (l)  (2)  n  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 ^  - T Mg d  - Q ^ ^  1 SO  T  n  a  l  t t W  M <T> M nna 2 r\ K C O S 0 .+ . n d d M  U  *V  T  M  C 0 S  —————  .  -f  \t m fU ui \ Q*s Mg +. T (lfe - M ) d  I  d  1  (fc) At 0 = 90 , T = QMP + T (Mg-Ma) Mn + M2 n  N  d  mev,  2. Recoil Kinetic Energy: Eliminating T  n  instead of T2 i n ( l ) , (2) and (3) results i n  ^  - 47 -  V*2 -Trns? 3.  C o s  e  +  f MdMfl  C  o  g  2  Q  +  Q %  • T (lfa - Mg) Mn + Ma d  (5)  Recoil Axis: Eliminating T  Sin  (  2  n  and T  «2> - ^ - s i n ^ ,  V  Note: As Q —*»-  ©4 ,  o{-*-0  from ( l ) , (2) and (3), we find  2  *  s  , so © + 9  If we solve for 0  * % , vhere«.  ^  2  i n terms of ©n, the result i s  2  2  S i A g = Sln 0 |l + j |+ & -  -  2  n  C??sin ©  1 2  sin ©,, + 2 Cos ©n 2  **2  +  ^  "  Vn  2  n  M2 1 2 — _  (6) The correct choice of © 4.  Be (d,ny)B 9  10  i s the one corresponding to ©n+ ©  2  7T as Q - » °Q  Recoil Axes:  We choose T  d  = 0.5, © = 45 n  and take \  i — ^ and equation (6) becomes Sin2e =  so ^  2  2  = 1, M  d  = 2, Mg = 10,  1 + ^ - Q.l£«2.2K2 (1 + o< )  0.21a ) 2  2  The table below shows the r e c o i l directions for the f i r s t four excited states of B : 10  B  1 0  3.58 2.15 1.74 0.72  Level  Q (mev) O.78  2.21 2.62  0.37 0.32  3.64  2 74°  Q  O.78  0.24  1  97° 100? 106 0  BIBLIOGRAPHY  Ajzenberg, P. and Lauritsen, T. (1955) Bethe and Morrison (1956) Bhatla et a l . (1952)  Rev. Mod. Phys. 2 J , 77.  "Elementary Nuclear Theory", Ch. XVIII.  P h i l . Mag. kfr 485.  Biedenharn et a l . (1952)  Phys. Rev. 88, 517.  Blatt and Weisskopf (1952) Bovcock, J.E. (1955)  "Theoretical Nuclear Physics".  Proc. Phys. Soc. London A, 68, 512.  Burrows, H.D. et a l . (1950) Cheston, W.B. (1954)  Phys. Rev. 80, IO95.  Phys. Rev. $6, 1590.  Daitch, P.B. and French, S.B. (1952)  Phys. Rev. 8 J , 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) Fujimoto et a l . (1954)  Phys. Rev. $2, 93.  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  Grant, I.P. (1955)  Proc. Phys. Soc. London A 68, 244.  Helmholtz et a l . (1947)  A 6 J , 981.  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 l e Radium, 14, 695. Horowitz, J . and Messiah, A.M.L. (1953b) J . de Phys. et l e Radium, 14, 731. Horowitz, J . and Messiah, A.M.L. (1954)  J . de Phys. et l e 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) Lawrence, E.D. et a l . (1935) Lubnitz, CR. (1957)  Mott, N.F.,  Phys. Rev. J 6 , 1445.  Phys. Rev. 48, 493.  "Numerical Tabulation of Butler-Born Approximation Stripping Cross Sections", University of Michigan.  and Massey, H.S.W., (1949)  "Theory of Atomic Collisions",  page 140. Newns, H.C. (1953)  Proc. Phys. Soc. London A66,  Neilson, G.C. and James, D.B. (1955) Neilson, G.C. (1955)  477.  Rev. S c i . Inst. 26, 11, 1018.  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) Pruitt, J.S. et a l . (1953)  Phys. Rev. 48, 500.  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 Skyrme et a l . (1951) Tobocman, W. (1954)  Phys. Rev.  Rev. S c i . Inst. 23^_ 204. Phys. Rev. §4, 1655.  D 3645, 1955 "The Reactor Handbook", Volume 1, Physics. Proc. Phys. Soc. London, A67» 813.  U.S. Atomic Energy Commission Yoccoz, J . (1954)  96.  

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