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The scattering of polarized neutrons and the gamma rays from the reactions B[10](d,p8) B[11] and B[10](d,n8)… Sample, John Thomas 1955

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THE SCATTERING OF POLARIZED NEUTRONS AND THE GAMMA RAYS FROM THE REACTIONS B^Cd.p'OB AND B ^ ^ n O C 11  1 1  by JOHN THOMAS SAMPLE  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in the Department of PHYSICS  We accept this thesis as conforming to the standard required from candidates for the degree of DOCTOR OF PHILOSOPHY.  Members of the Department of Physics THE UNIVERSITY OF BRITISH COLUMBIA July, 1955  ABSTRACT  Detailed calculations have been carried out which indicate that the small-angle scattering of fast neutrons by lead depends on the polarization, or spin orientation, of the neutrons. When the scattering of neutrons whose spin vectors point upward i s observed i n the horizontal plane, more neutrons should be found scattered to the right than to the left.  For completely polarized 3.1 Mev neutrons, the theory predicts a  maximum "right to left" intensity ratio of 14.5*1 at a scattering angle of 0.5°, the ratio decreasing to 1.6:1 at 5°, and approaching unity rapidly as the scattering angle increases. An attempt to detect this effect with neutrons from the reaction D(d,n)He3 failed because the degree of neutron collimation attainable, while satisfactory for most scattering experiments, was insufficient to permit investigation of neutron scattering at very small angles. A three crystal pair spectrometer has been used to investigate the complex gamma ray spectrum arising from bombardment of deuterons of several energies between 0.8 and 2.2 Mev. energy ^.46  with  Gamma rays of  * .04, 4.75 * .03, 5.03 * .09, 5.35 * .05,  6.52 * .05, 6.78 * .07, 7.29 * .04, 8.27 * .09, and 8.87 * .02 Mev have been assigned to transitions i n B  1 1  and C^, with excellent  agreement i n almost a l l cases with the energy level schemes proposed from other experiments. The excitation curves of three of the gamma rays  have been found to rise smoothly between bombarding energies of 0.8 and 2.2 Mev, indicating that the reactions B (d,p1*)B U}  Ll  and B ^ ^ n ^ ) C  n  are primarily of non-resonant character, at least i n this energy region.  THE UNIVERSITY OF BRITISH COLUMBIA Faculty of Graduate Studies PROGRAMME OF THE FINAL ORAL EXAMINATION FOR THE DEGREE OF DOCTOR OF PHILOSOPHY of JOHN THOMAS SAMPLE B.A. M.A.  ( B r i t i s h Columbia) ( B r i t i s h Columbia)  19I4.8 1950  on Friday, August 5 , 1955 at 10:30 a.m. i n Room 303, Physics Building  Committee i n Charge: Dean H.F, Angus, Chairman G.M. J.B. G.M. K.C.  Shrum Warren Volkoff Mann  C.A. Barnes H. Adaskin T.E. H u l l E.V. Bonn  External Examiners - R.F. Christy T. Lauritsen C a l i f o r n i a Institute of Technology  LIST OP PUBLICATIONS Primary S p e c i f i c Ionization of Electrons i n some Gases, Transactions of the Royal Society of Canada, 1 9 5 " 3 , Abstract # 6 9 , (Co-author J.B. Warren). The E l a s t i c Scattering of Protons by Nitrogen Physical Review 9 3 , 9 2 0 , 19^1+. (Co-authors H.E. Gove and A.J. Ferguson). Performance of a Fast Neutron Collimator, Canadian Journal of Physics, 3 3 . , 3 ^ 0 , 1 9 5 £ « (Co-authors G.C. Neilson and J.B. Warren)  THESIS THE SCATTERING OP POLARIZED NEUTRONS AND THE GAMMA RAYS PROM THE REACTIONS B ( d , p ^ ) B H AND B (d,n?»)C 10  1 0  i:L  Detailed calculations have been carried out which indicate that the small-angle scattering of fast neutrons by lead depends on the p o l a r i z a t i o n of the neutrons. When the scattering of neutrons whose spin vectors point upward i s observed i n the horizontal plane, more neutrons should be found scattered to the right than to the l e f t . For completely polarized 3 . 1 Mev neutrons, the theory predicts a maximum "right to l e f t " i n t e n s i t y r a t i o of ll4..5:l at a scattering angle of 0 . 5 ° , the r a t i o decreasing to 1 . 6 : 1 at 5 ° , and approaching unity r a p i d l y as the scattering angle increases. An attempt to detect this effect with neutrons from the reaction D(d,n)He3 f a i l e d because the degree of neutron collimation attainable, while s a t i s f a c t o r y f o r most scattering experiments, was i n s u f f i c i e n t to permit investigation of neutron scattering at very small angles. A three c r y s t a l pair spectrometer has been used to investigate the complex gamma ray spectrum a r i s i n g from bombardment of B with deuterons of several energies between 0 . 8 and 2 . 2 Mev. Gamma' rays of energy lj..lj.6 ± ,0k, k*l$ .03, 5.03 . 0 9 , 5.35 . 0 5 , 6.52: ± . 0 5 , 6.78 ± . 0 7 , 7.29 .Oil., 8.27 - . 0 9 , and 8 . 8 7 - . 0 2 Mev have- been assigned to transitions i n B and C » with excellent agreement i n almost a l l cases with the energy l e v e l schemes proposed from other experiments. The excitation curves of three of the gamma rays have been found to r i s e smoothly between bombarding energies of 0 . 8 and 2 . 2 Mev. indicating that the reactions B ( d , p ^ ) B H and Bl0(d,ny)cH are primarily of a non-resonant character, at least i n this energy region. ±  1  1  ±  1 1  10  GRADUATE STUDIES Field  of  study:  Physics  Quantum M e c h a n i c s Quantum'Theory of R a d i a t i o n The o r e t i c a l N u c l e a r P h y s i c s Special Relativity T h e o r e t i c a l P h y s i c s Seminar Theory of the S o l i d S t a t e X - r a y s and C r y s t a l S t r u c t u r e Chemical Physics Nuclear Physics Theory of Measurements E l e c t r o m a g n e t i c Theory Electronics  Other  G.M. V o l k o f f F . A . Kaempffer G. M. V o l k o f f W. O p e c h o w s k i ¥ . Opechowski H . Koppe J . B . Warren A . J . Dekker K . C . Mann A.M. Crooker G.L. Pickard F . K . Bowers  Studies:  F u n c t i o n s o f a Complex Variable F u n c t i o n s of a R e a l V a r i a b l e Integral Equations N o n - l i n e a r Mechanics O p e r a t i o n a l Methods i n Engineering  W. H . S imons D. C. Murdoch T.E. Hull E. Leimanis W.B.  Coulthard  AOKNOWLEDGEMEMTS  I take great pleasure in acknowledging the guidance and encouragement of my supervisor, Professor J. B. Warren, during the period the research presented i n this thesis was carried out. His suggestions in both the conceptual and practical stages of the work have been of great assistance to me. I wish to thank my collaborators in the experiments, Dr. D. B. James, Mr. G. C. Neilson, and Mr... G. B. Chadwick. To Dr. K. L. Erdman I am indebted for helpful discussions on the design of the equipment, and to Dr. W, Opechowski for checking the theoretical calculations. For his patient help during construction of the apparatus: and in the inevitable modifications, and for processing the nuclear emulsions used in part of the work, I would especially like to thank Mr. J. B, Elliott. I am grateful to my wife for aid in the numerical calculations and in the preparation of the thesis. Finally, I wish to thank the B, C. Telephone Co. for a Fellowship held during part of these studies.  TABLE OF CONTENTS Chapter I II  Title  £ags  INTRODUCTION  1  THE SCATTERING OF POLARIZED NEUTRONS.  6  1. Polarization i n Nuclear Physics  6  (a) Electrons (b) Gamma Rays  6 .........  (c) Neutrons, Protons, and Deuterons  9 ......  17  (dj Nuclei  22  2. The Deuteron and the D + D Reactions  • 28  3. Non-Resonant Scattering of Neutrons by Heavy Nuclei  31  4. Scattering of Neutrons from D(d,n)He^ by Lead  45  (a) The Collimator  45  (b) The Target Assembly  47  (c) Detectors  .............  (d) Experimental Procedure and Results III  ..  49  . . . . . 51  GAMMA RAYS FROM THE BOMBARDMENT OF BORON TEN WITH DEUTERONS 1. The Mirror Nuclei B  56 11  and C  1 1  ..  56  2. The Three Crystal Spectrometer  60  3. Experimental Procedure 4. Results and Discussion  63 66  .  Page APPENDIX A  SOLUTION OF THE RADIAL EQUATION  72  APPENDIX B  CLEBSGH-GORDAN COEFFICIENTS  75  APPENDIX C  EVALUATION OF THE FUNCTIONS A( d ) AND B(<? ) . . .  APPENDIX D . . BIBLIOGRAPHY  ' A PROPOSED EXPERIMENT: THE MEASUREMENT OF NEUTRON POLARIZATION BY SCATTERING IN HELIUM ........  88 92  76  LIST OF ILLUSTRATIONS Number  Subject  On or Facing  Figures 1  £sg§ Reference Frames of Neutron and Scattering Centre  31  2  Orientation of P, k and n with Respect to k  43  3  Differential Scattering Cross-section of Lead for Polarized 3*1 Mev Neutrons . . . . .  44  4  Horizontal and Vertical Sections of the Neutron Collimator .  4&  5  Heavy Ice Target Assembly  6;  Plate-holder Mounting  7  Angular Distribution of Collimated Neutrons  .  55  8  Energy Levels of B  .  57  . . . .  61  9 10  11  ••  4-7 50  and C  .  11  Single Crystal Spectrum from B +D Block Diagram of the Three Crystal Spectrometer 10  62  11  Spectrum from F (p, oc » ) o  12  Spectrum from B  10  13  Spectrum from B  10  14  Spectrum from B  10  15  Spectrum from B  10  16  Held Curves of the 6.12, 6.52, 6.78 and 7.29 Mev Gamma Rays . . . . . . . . . . . . .  70  Proposed Fast Neutron Polarimeter  89  17  19  1 6  .63  + D, 2.0 to 5.5 Mev . . . .  64  + D, 4..0 to 6„5 Mev . . . .  65  + D, 4.8 to 7.5 Mev . . . .  66  + D, 6..5 to 9.0 Mev . . . .  67  On or Facing -Tables: 1  ^M* Assignment of the Gamma Rays to Levels. of B* and C 1  2  68  11  Clebsch-Gordan Coefficients. (#> 1/2, m, m' | JM)  75  2  3  Clebsch-Gordan Coefficients  ( V>, 4  o, o (LO)  V  Clebsch-Gordan Coefficients (ft, V, o, 1 | LI) . 2  75  .  75  Chapter I INTRODUCTION This thesis describes two unrelated research projects, the f i r s t concerning the scattering of polarized neutrons, the second the gamma rays initiated by deuteron bombardment of the Boron isotope of mass 10. A beam of particles with i n t r i n s i c angular momentum, or spin, differing from zero i s said to be polarized i f the average value of a spin component i n some direction differs from zero.  The quotient of this average  and the spin of the particles concerned i s called the percentage polarization. • To illustrate, consider a reaction i n which neutrons are emitted at an angle 0 from the direction of the incident beam. According to a general theorem (Simon and Welton 1953), i f particles emitted i n a nuclear reaction are polarized, they are polarized  TARGET  perpendicular to the plane containing the incident beam and the direction of  observation.  Since neutrons have spin l/Z,  a particular neutron has a spin  component 1/2 or -1/2 perpendicular to the plane of the reaction.  I f more  than one-half of the neutrons possess one of these two possible orientations, the neutron beam at angle 0  i s said to be polarized.  The polarization i s  P - f ( i ) - f ( - z ) , where f(£), f(-£) are the fractions of neutrons with spin component l/2 and -l/2 respectively.  Neutrons and protons emitted i n some  nuclear reactions are expected to be polarized.  Measurement of the percentage  2 polarization as a function of angle of emission and bombarding energy can aid i n determining the properties of the nuclear states involved in the reaction. In order to detect and measure the polarization of particles, they must be allowed to undergo some polarization dependent process. The angular distribution i n some scattering reactions, for example proton scattering by He^, i s polarization dependent. Most of these scattering reactions are resonant, so that their usefulness i s restricted to a small energy range. Schwinger (1945) has suggested a non-resonant neutron reaction which i s strongly polarization dependent, that of small angle scattering by heavy nuclei. The force exerted by the Coulomb field of the nucleus on the magnetic moment of the moving neutron contributes to the Hamiltonian describing the motion of the neutron a term dependent on the spin orientation, and hence the polarization, of the neutron. By using the Born approximation method, Schwinger showed that the differential scattering cross-section contains a term with "left-right asymmetry", proportional to neutron polarization. A more accurate calculation of the "partial wave" type has been carried out.  The result differs from Schwinger's only i n that the  polarization dependent term is 25% larger. While the differential scattering cross-section i s large, i t i s strongly dependent on polarization only for scattering angles less than five degrees. In order to distinguish scattered neutrons from the unscattered beam, strong collimation is necessary, either of the incident beam, or of the scattered neutrons. A baffled paraffin collimator was built to confine the neutron beam incident on the lead scatterer to an angular spread of±2°.  3  The reaction D(d,n) He^ vas chosen as a neutron source because of its large yield and because theoretical estimates indicate that the neutrons may be polarized as much as f i f t y percent. Maximum polarization should occur at about 6 0 0 Kev. bombarding energy, and the polarization should vary as sin(20) about the direction of the deuteron beam. Attempts to measure the angular distribution of neutrons scattered from a lead block, using both nuclear emulsions and a stilbene scintillation counter, shoved that sufficient neutrons to obscure the expected asymmetry penetrate the body of the collimator with enough energy to be recorded. Hence this experiment has been suspended, at least temporarily.  When the Boron isotope of mass ten i s bombarded with deuterons, the dominant gamma ray producing reactions are B B  10  1 0  ( d , n l O C , occurring simultaneously. B l l and U  (d,p?)BH and are mirror nuclei,  that is, they differ only i n the interchange of a proton for a neutron. If, as commonly postulated, the force between a pair of neutrons i s the same as that between a pair of protons (except for the Coulomb force i n the case of protons), then the energy levels of G^J. should be spaced as are those of B^ , the whole level scheme being raised by the extra Coulomb repulsion energy i n the case of 0 ^ . A measurement of the energies of emitted gamma rays enables tentative assignment of the energy level schemes, which i n turn allows a check on the charge symmetry postulate. A sodium iodide scintillation counter produces an electrical pulse, the magnitude of which i s proportional to the energy of the incident gamma  photonj  i t i s a gamma ray spectrometer of high efficiency and fair  resolution (Hofstadter, 1948). Because of the three common ways i n which a photon may interact with matter, the pulse height spectrum related to a single gamma ray energy may contain three peaks, corresponding to the total energy (photoelectric effect, and Compton effect and pair production i n which secondary gamma rays are absorbed), pair creation with one annihilation photon escaping, and pair creation with both annihilation photons escaping from the crystal. The last two are superposed upon the broad Compton spectrum. If several gamma rays occur i n an energy interval, the resulting pulse height distribution i s difficult to interpret.  If neutrons are produced in  the reaction under investigation, a large background spectrum, approximately exponential i n shape, i s added to the gamma ray spectrum. By sacrificing efficiency, i t i s possible to avoid the difficulties mentioned above for gamma energies at which pair production i s appreciable. A three crystal pair spectrometer records only pair production events in which both annihilation photons escape from the spectrometer crystal. Two sodium iodide counters, electronically adjusted to respond only to radiation in the energy region of annihilation photons, closely flank the spectrometer counter. Only when these counters produce pulses coincident i n time i s the pulse from the spectrometer counter recorded. In this way, the pulse height spectrum contains only one peak for each gamma ray present, and the neutron sensitivity i s greatly reduced. A three crystal spectrometer has been developed with five percent energy resolution for 6 Mev gamma rays and very low neutron sensitivity.  5 Thin targets (100y^gm/cm ) of Boron enriched to better than 2  95% BlO have been bombarded with deuterons from the Van de Graaff generator. Fourteen gamma rays have been observed at 0° to the beam, two of which, at 3.08 and 3.68 Mev, are definitely identified as arising from the reaction C-^(d,pf)C^ . Of the remaining twelve, eleven f i t quite well the energy level schemes assigned to fill and Oil , from measurements of proton and neutron energies. The twelfth, at 6.12 Mev, fits neither of these, nor does i t seem due to any of the probable target impurities. Excitation curves, that is, gamma ray yield plotted as a function of bombarding energy, of four of the gamma rays have been determined. In agreement with the work of other investigators on proton and neutron excitation curves and angular distributions, Butler stripping seems to contribute appreciably to the reaction, even at 1 Mev bombarding energy. Broad, low, resonances have been observed, at 0.9 Mev bombarding energy for neutrons, and 1.0 and 1.5 Mev for protons. This may be connected with the crossover of the excitation curves of two of the gamma rays from and c H , at about these energies.  6  CHAPTER II  THE SCATTERING OF POLARIZED NEUTRONS 1. Polarization i n Nuclear Physics Specification of position and velocity vectors does not i n general completely describe the motion of electrons, protons, neutrons, photons, and nuclei i n their ground states. A further degree of freedom, necessary to explain the results of many experiments, is interpreted i n terms of the orientation of the intrinsic angular momentum vector, or spin, of these particles. A restriction of this degree of freedom i s said to cause polarization or alignment of the particle under discussion, depending on the type of particle and the symmetry of i t s angular momentum state. Even-even nuclei do not, of course, possess this additional freedom, since their ground state spins are zero.  The products of nuclear reactions have  been found i n several cases to be polarized; measurements of the polarization can provide information about the nuclear energy levels involved, and, i n the case of nuclei containing few nucleons, aid i n distinguishing between the postulated types of nucleon-nudeon interaction. The following resume of theory and experiment, while not comprehensive, illustrates the applications and methods of polarization measurement. (a) Electrons Because the electron spin, i n units of ^, i s l/2, an attempt to measure the spin component i n any direction can produce only two results, ± l/Z (p. 57, Hott and Massey, 194-9). If measurements on  7  many electrons show that one of these values i s more probable than the other, the electrons are said to be polarized. There i s a direction of maximum difference i n probability of the two values, and the polarization vector i s defined as lying along this line i n the direction of the most probable value, with magnitude equal to the difference i n probability. The percentage polarization i s then the magnitude of the polarization vector multiplied by one hundred. Atomic electrons may be polarized, and the atoms containing electrons of opposite polarization separated, by the Stern-Gerlach method. This method is not easily applicable to free electrons, as can be shown by a straightforward argument from the uncertainty principle (p. 61, Mott and Massey, 1949.  See, however, the discussion of this point by Louisell,  Pidd, and Crane, 1954-). The ferro magnetic materials iron, cobalt, and nickel provide a very useful (subsection (c)) method of polarizing atomic electrons. When these materials are magnetized to saturation, the spins of the electrons i n the 3d subshell are aligned i n the direction of the field. Fast electrons and positrons may be polarized by nuclear scattering, since the differential scattering cross-section has an azimuthal dependence which i s a function of the i n i t i a l spin orientation (p. 76, Mott and Massey, 1949). The cross-sections for scattering of electrons and positrons should differ markedly when the scattering nucleus has a large atomic number, because of the opposite signs of terms expressing the interference between Rutherford scattering and spin-orbit coupling. The intensity of a beam of electrons or positrons partially polarized by  8 one scattering through 90° should show an azimuthal asymmetry in a second 90° scattering. Shull, Chase, and Mayers (1943) have confirmed this by double 90° scattering of 400 Kev electrons i n gold foils.  The 12%  asymmetry of the second scattering i s i n very good agreement with the calculation of Mott (1932). This double scattering method has been applied recently by Louisell, Pidd, and Crane (1954) to the measurement of the gyromagnetic ratio of the free electrons i n a 420 Kev beam. A magnetic field along the electron trajectory between the scatterers causes, as well as cyclotron rotation, spin precession with attendant rotation of the plane of maxi mm asymmetry i n the second scattering. The ratio of precession frequency to cyclotron frequency i s equal to l/2 of the gyromagnetic ratio. While the reported measurement, 2.00 * 0.01, i s not sufficiently accurate to show the expected radiative correction (Schwinger, 1948a), the method may yield more precise measurements i n the future. Electrons and positrons from allowed transitions of aligned nuclei (subsection (d)) may be nearly 100% polarized when emitted i n the plane perpendicular to the nuclear spin (Tolhoek and de Groot, 1951). The practical difficulties of measurement are at present large, but improved techniques, such as detecting polarization by scattering i n magnetized iron foils, may make possible investigation of nuclear alignment where no other method i s available, as well as of the interactions postulated i n the theory of beta decay. If beta decay i s followed by emission of a gamma ray, i t i s possible that the polarization of the beta particle i s correlated with  the directions of emission of the beta and gamma rays, offering a possibility of polarized beta rays from non-aligned nuclei. (b) Gamma Rays Because a spin of unity must be associated with a vector field to preserve its properties under rotation of the coordinate system (p. 76, Blatt and Weisskopf, 1952), photons differ from particles of spin L/2 in that circular, as well as plane, polarization is a detectable state for photons. Because of this the definition of a polarization vector i s not as simple as in sub-section (a). Following classical electromagnetic theory, a beam of photons i s said to be plane-polarized i f the electric vector of the associated radiation field lies only in one plane containing the direction of propagation, the plane of polarization being that of the electric vector. The beam is said to be circularly polarized when the electric vector has equal orthogonal components, one lagging the other by 90° in phase. Elliptic polarization may be regarded as a combination of plane and circular polarization. In the case of photons emitted from nuclei, i t i s convenient in calculating distribution and correlation functions to define a polarization vector which does not lie i n the plane of the electric vector, so that a simple physical picture is lacking (Biedenharn and Rose, 1953). Plane polarization may be detected by several means. The angular distribution of Gompton-scattered photons is dependent upon the polarization of the incident beam, and the photons scattered from an unpolarized beam are partially plane-polarized  (Wightman, 1948), so that  10 a double scattering experiment shows an azimuthal variation i n intensity dependent on the two scattering angles and the incident energy. This has been verified by Hoover, Faust, and Donne (1952) for the gamma rays from Co^O, of average energy 1.25 Mev. Though the polarization dependence drops as the energy increases, Compton scattering has been used by several investigators (Metzger and Deutsch, 1950; French and Newton, 1952; Kraushaar and Goldhaber, 1953) to investigate the polarization of gamma rays of energies up to 6.13 Mev. The method consists essentially of scattering the gamma rays from one scintillation counter into another, and recording the coincidence counting rate between the counters as the second counter is revolved around the direction of the incident beam. When these counters are placed i n coincidence with a third counter detecting another gamma ray or a particle from the reaction, the correlation between the polarization of the gamma ray and i t s direction relative to the second reaction product may be measured. The cross-section of an atom for photo-electric emission of a K electron depends upon 0, the angle between the propagation vectors of the incident photon and ejected electron, and  the angle between the  plane of 6 and the electric vector, according to o~-( 0  ,(f)oC  sin # cos ^ 2  2  7  when the photon energy is much less than the rest energy of the electron (p. 122, Heitler, 1944).  Since the cross-section is large and strongly  dependent on polarization, the photoelectric effect i s an excellent means of detecting the polarization of low energy photons. For photons of higher energies, relativistic calculations show that electrons are ejected predominantly forward, and that the anisotropy due to polarization  11 decreases, changing when the photon energy i s greater than the rest energy of the electron so that electrons tend to he ejected perpendicular to the electric vector rather than parallel to i t (Sauter, 1931). The measurements of Hereford and Keuper (1953) with 0.51 Mev quanta agree quite well with Sauter's theory. Pair production offers a method of detecting polarization of photons of energies above the region where the photo and Compton effects are appreciably polarization sensitive (lang, 1950). Berlin and Madansky (1950) have calculated the expected anisotropy i n the azimuthal distribution of pairs around the direction of the incident photon for several geometrical configurations of radiator and detectors, but Wick (1951) has objected to their calculations because they have not considered the effects of small angle scattering of the members of a pair i n the radiator; he found, i n fact, an anisotropy opposite to that found by Berlin and Madansky. Wick's calculations, i n turn, are unsatisfactory because they were based on an approximate expression for the pair cross-section. Although the theoretical situation i s not clear, and the experimental difficulties involved are great, pair production i s one of very few means of measuring the polarization of gamma rays of very high energy. In the photon energy range 3 to 10 Mev, protons and neutrons from the photodisintegration of deuterons by plane polarized photons have an angular distribution expressed by N ( # , y ) °c sin ^cos2y = sin^X. 2  N( 6,y ) i s the number of neutrons or protons per second ejected i n unit solid angle at scattering angle 6 from the incident gamma ray beam and azimuthal angle if from the plane of polarization of the beam, or at  12  angle Xfrom the electric vector (Wilkinson, 1952).  This, assumes a pure  electric dipole interaction. Just above the threshold energy, 2.23 Mev, the magnetic dipole interaction, with no polarization dependence, i s dominant (Feshbach and Schwinger, 1951). When the photon energy is 3.0 Mev, the magnetic dipole cross-section i s s t i l l about U & of the total photodisintegration cross-section (p. 609, Blatt and Weisskopf, 1952), so that an isotropic term of approximately 0.05 must be added to the expression for the angular dependence of N ( ^ , y ) .  The isotropic term increases as  the energy i s decreased, lowering the polarization sensitivity. For gamma energies greater than 10 Mev, higher multipole interactions are not negligible, so that N( d ,jf) no longer has the simple form written above (Barita and Schwinger, 1941)*  Because the cross-section is small,  deuteron photodisintegration has been so far used successfully for polarization detection only by integrating the yield over long periods in deuterium loaded nuclear emulsions, with the attendant loss of time reference for correlation with other particles from the gamma ray producing reaction. Despite this, i t i s at present the most promising method of measuring the polarization of gamma rays more energetic than 6 Mev. Above 10 Mev, measurement of the differential cross-section for polarized and unpolarized gamma rays can yield much information about the neutronproton force (Rarita and Schwinger, 1941). Two methods of detecting a circularly polarized state of photons have been discussed in the literature, both involving Compton scattering in magnetized iron. Steenberg (1953a) showed that, i f the gamma ray beam incident on an iron f o i l has a circularly polarized component, the forward scattered electron intensity changes when the direction of magnetization  13 of the f o i l i s changed from parallel to the photon propagation vector to antiparallel. Clay and Hereford (1952) have reported an effect of this kind i n connection with annihilation photons. Because approximately two of the twenty-six electrons per iron atom are polarized by magnetization (Halpern, 1952), the effect i s at best an intensity change of 8%. In a similar way, the transmission of circularly polarized gamma rays through magnetized iron should change with the direction of magnetization. According to Steenberg (1953a), this method i s less polarization sensitive than detection of scattered electrons. Measurements of gamma ray polarization were first performed (except for double scattering of X-rays — Barkla, 1906) on the quanta emitted i n opposite directions when a positron annihilates with an atomic electron.  Since annihilation in most materials i s almost completely from  a S state (Deutsch, 1951), conservation of angular momentum demands that 2  a pair of annihilation photons be i n opposite polarization states, that i s , plane polarized perpendicular to one another (Snyder, Pasternack and Hornbostel, 1948), or circularly polarized in the same sense (since the photons proceed i n opposite directions, both must be either right or left circularly polarized to carry away no angular momentum from the reaction).  The correlation of the plane polarized states has been  measured by several investigators, using the Compton scattering method (Hanna, 1948,* Wu and Shaknov, 1950), with results i n accord with theory. Hereford (1951) found an azimuthal correlation of the photoelectrons ejected from lead radiators by annihilation photons which was later confirmed by comparison with Compton scattering (Hereford and Seuper, 1953). Clay and Hereford (1952) have reported a measurement of the  14 r e l a t i v e c i r c u l a r p o l a r i z a t i o n of p a i r s of a n n i h i l a t i o n photons. Their method consisted of measuring the change i n coincidence rate of two counters detecting electrons scattered forward from i r o n f o i l s by the photons when the d i r e c t i o n s of magnetization of the f o i l s were changed from p a r a l l e l to a n t i p a r a l l e l .  In calculating the expected  r e s u l t , they have mistakenly assumed that the quanta are polarized oppositely, (see footnote 1, Bleuler and t e r Haar, 1948),. and yet t h e i r experimental r e s u l t agrees q u a l i t a t i v e l y with t h e i r c a l c u l a t i o n s .  In  any event, Vlasov and Dzhelepov (1949) have concluded that the most probable, i f not the only p o s s i b l e , mode of p o l a r i z a t i o n of a n n i h i l a t i o n quanta i s mutually perpendicular plane p o l a r i z a t i o n .  A correlation  between the l i n e a r p o l a r i z a t i o n of one quantum and the d i r e c t i o n s of the other two i s expected i n the case of three-quantum a n n i h i l a t i o n from the 3s state of positronium.  I f the three quanta are chosen to be spaced  120° apart, then any one of them i s favoured 3:1 to be polarized perpend i c u l a r to the plane of the three.  The measurement of Leipuner, S i e g e l ,  and de Benedetti (1953) corroborated t h i s . In some nuclear reactions, e s p e c i a l l y r a d i a t i v e capture of a p a r t i c l e , the p o l a r i z a t i o n of the emitted gamma rays i s expected to be correlated with d i r e c t i o n of the incident beam.  Wilkinson (1952)  measured the p o l a r i z a t i o n of the gamma rays from the r e a c t i o n D(p,7*)He3 by exposing deuterium-loaded emulsions to the r a d i a t i o n and determining the angular d i s t r i b u t i o n of proton tracks from photodisintegration normal to the d i r e c t i o n of the gamma rays.  He found, with rather low s t a t i s t i c a l  accuracy, that the photons are plane polarized f o r a l l d i r e c t i o n s of  15 amission, with the electric vector lying i n the plane containing the proton beam and the direction of propagation of the gamma ray.  This confirmed the  electric dipole assignment of Fowler et a l . (1949) and Griffiths (1953). This reaction i s a good source of polarized gamma rays for investigation of photodisintegration, but the small cross-section practically requires the nuclear emulsion technique, so that (^,n) reactions cannot be investigated. A similar reaction.is T(p, T^He^, producing photons of about 20 Mev energy, which should be strongly polarized.  A feasible experiment of great  interest i s the use of these gamma rays i n the photodisintegration of deuterium.  An accurate measurement of the angular distribution of the  protons could provide information about the neutron-proton force. When polarized thermal neutrons are captured by some nuclei, the capture radiation emitted i n the direction of the neutron spin i s expected to be circularly polarized (Biedenharn, Rose, and Arfken, 1951).  Quite  intense beams of polarized thermal neutrons are attainable (subsection (c)), so that such an experiment may be possible, but, as explained above, the detection of circular polarization i s d i f f i c u l t . If two gamma rays are emitted i n cascade during the decay of a nucleus, a measurement of the angular correlation of their propagation vectors can determine the multipolarity of the two transitions, and through this, the difference i n angular momentum of the nuclear states involved (Brady and Deutsch, 1950).  This provides no information as to the electric  or magnetic character of the radiation, and hence the relative parities of the states, unless at least one of the transitions i s a mixture of multipoles (Ling and Falkoff, 1943). However, a measurement of the angular  16 correlation of the polarization of the two gamma rays i n conjunction with the directional correlation can determine the relative parities of the states, since electric and magnetic radiations of the same multipole order are polarized perpendicularly to each other (Falkoff, 1948). An attempt, based on Compton scattering, by Robinson and Madansky (1952) to measure a correlation of this type in the decay of C s ^ 1  led to inconclusive results.  A much easier measurement i s that of the correlation of the polarization of one gamma ray with the direction of the other. This, in most cases, provides as much information concerning parities as the polarizationpolarization correlation (Hamilton, 1948; Zinnes, 1950). Extensive use of this method, involving a polarization measurement by Compton scattering in coincidence with a determination of the direction of the remaining gamma ray, has determined the spins and parities of excited states of several even-even nuclei (Metzger and Dentsch, 1950; Kraushaar and Goldhaber, 1953). The correlation of the polarization of a gamma ray following particle decay with the direction of the particle also determines the relative parity of the states involved in the gamma transition (Biedenharn and Rose, 1953). Stump (1952) has measured by Compton scattering the direction of polarization of the gamma ray emitted at 90° to the most energetic beta particle from Sb ^ 12  . His measurement agrees with the  empirical rule of Goldhaber and Sunyar (1951), that the first excited state of an even-even nucleus has spin two and even parity. In a similar experiment, French and Newton (1952) proved that the 6.13 Mev octopole gamma transition following alpha emission i n the reaction F (p, * ^ O 19  1 6  is electric, that is, that there i s a parity change in the gamma transition. Since the ground state of O ^ is known to have even parity, 1  17 the 6.13 Mev state has odd parity. If the energy of the gamma rays emitted is less than 6 Mev, so that the Compton effect is appreciably polarization sensitive, and the reaction i s sufficiently prolific to permit triple coincidence counting, this is a very useful technique for determination of parities, (c) Neutrons. Protons, and Deuterons Neutrons and protons, being particles of spin 1/2, are identical to electrons (subsection (a)) i n the description of their spin states, so percentage polarization may be defined i n the same way as for electrons. Because they react with nuclei at low and intermediate energies, polarized protons and neutrons are of greater interest i n nuclear physics than polarized electrons. Although few experiments have been reported involving reactions with polarized beams of neutrons or protons or measurement of the polarization of reaction products, this field may prove to be a fruitful one, both i n the classification of nuclear energy levels as to spin and parity, and i n the more fundamental investigation of the actual nuclear forces responsible for the levels. If a beam of neutrons is insufficiently energetic to reverse the spins of the 3d atomic electrons of iron, then i n magnetized iron the neutrons experience a spin dependent force due to the interaction of their magnetic moments with the electron spins, which contributes an appreciable term, positive or negative depending on the direction of the neutron spin, to the elastic scattering cross-section per atom (Halpern and Holstein, 1941). If the transmission by an iron slab of an initially unpolarized beam of thermal neutrons is measured, then, because of the exponential  18 relation between intensity and thickness traversed, more neutrons are transmitted when the slab i s magnetized normal to the beam direction than when i t i s unmagnetized (Bloch, Hamermesh, and Staub, 1943). The transmitted neutrons are polarized as much as 60$, with their spins antiparallel to the direction of magnetization. Because normal iron and steel are polycrystalline, some depolarization occurs at domain boundaries unless a high degree of magnetic saturation i s achieved. Furthermore, unless the nuclear and magnetic scattering amplitudes are equal, complete polarization i s not possible. Shull (1951) has found a solution to both problems. By reflecting neutrons of wavelength 1.204 angstroms from the (220) planes of a single crystal of magnetite magnetized normal to the plane of scattering, he was able to produce a collimated beam of completely polarized monochromatic neutrons containing about 10-* neutrons per second. Transmission experiments have provided knowledge about ferromagnetism, particularly about the approach to saturation (Hughes, Wallace, and Holtzman, 1948). Magnetized iron slabs were used by Bloch, Nicodemus, and Staub (1948) as polarizer and analyzer in the precise measurement of the magnetic moment of the neutron by magnetic resonance. In order to prove that thermal neutrons totally reflected from magnetized iron are polarized parallel to the magnetic field, Sherwood, Stephenson, and Bernstein (1954.) performed a SternGerlach experiment, deflecting the neutrons i n an inhomogeneous magnetic field.  This information has been used i n three experiments on the  interaction of polarized neutrons with polarized nuclei (subsection (d)).  19  In the medium energy range, 0.5 to 10 Mev, there has been relatively l i t t l e experimental work. The most comprehensive theoretical treatment i s that of Simon and Welton (1953, 1954), generalizing that of Blin-Stoyle (1951). Their results concerning the polarization of particle "b" produced i n the reaction X + a —*X.+ b, when X n  tt  and a tt  n  are unpolarized, are concisely summarized i n section IV of the 1953 paper. I t seems likely that protons and neutrons produced i n several reactions of lighter elements are polarized to some degree at particular angles of emission. The specialized case of scattering of polarized beams has been discussed by Oehme (1955). Experimental work has consisted mostly of investigations of scattering of neutrons and protons by helium. It i s now fairly well established that the ground and first excited states i n both He-* and Li-* are a widely separated, inverted  Py  z  z  -  2  P ^ doublet (Ajzenberg and Lauritsen, 1955), indicative of  strong spin-orbit coupling.  Schwinger (1946) first suggested the use  of this coupling to produce beams of fast polarized neutrons by scattering in helium. This experiment has not as yet been performed, although Adair (1952)  and Seagrave (1953) have found, by calculations based on the  measured scattering phase shifts, that 90° scattering should be strongly polarizing except i n a neutron energy region near 2.5 Mev. A proposed experiment using this reaction to measure neutron polarization i s outlined in Appendix D. Dodder (1949) has calculated the yield as a function of second scattering azimuth i n the analogous case of double 90° scattering of protons i n helium. The results of Heusinkveld and Freier (1952)  on the double scattering of a proton beam from an electrostatic  generator agree sufficiently well to establish definitely that the  20 2  Po  - P, 2  y  doublet i n I i - ^ i s inverted.  The polarization of the  protons from the reaction D(d,p)T has been measured by scattering i n helium (section 2). The results of the measurements of Adair and co-workers (summarized by Adair, Darden and Fields, 1954) on 90° scattering of polarized neutrons by heavy nuclei have been analysed i n terms of the "cloudy crystal ball (1954).  11  nuclear model of Feshbach, Porter, and Weisskopf  The experimental method involved a determination of the left-  right asymmetry i n the 90° (Centre of mass) scattering by 0 ^  of 400  Kev neutrons from Li'''(p,n)Be''', calculation of the polarization (53 -6%) from the scattering phase shifts, measurement of the left-right asymmetries i n the scattering by the various heavy nuclei, and calculation, from these and the incident neutron polarization, of the ' polarizations which would be produced i n scattering an unpolarized beam. The results agree qualitatively with those obtained by adding a spin-orbit interaction term to the "absorptive square well" potential of Feshbach et a l . Wiliard, Bair, and Kington (1954) have reported a very nice experiment i n which the polarization of neutrons between the energies 200 and 600 Kev from Id7(p,n)Be was measured by 90° scattering i n O ^. 7  Scattering at 90° from d 2 j^g fc  1  een  U S e (  j ^o determine the polarization  of neutrons from the reaction D(d,n)He^ (section 2). With the exception of the work of Adair on heavy nuclei, where the polarization asymmetry i s very small, the methods so far discussed have involved resonant scattering with the attendant rapid variation with energy of the polarization sensitivity and dependence on accurate knowledge  21 of the scattering phase shifts.  Schwinger  (19AS\)  suggested measuring  the polarization of neutrons by small-angle scattering from heavy nuclei. The polarization sensitivity varies slowly with neutron energy, and accurate calculation of the differential cross-section as a function of energy, polarization, scattering angle, and azimuthal angle i s possible (section 3). An attempt to measure the polarization of neutrons from D(d,n)He3 by this method has been reported (Longley, Little, and Slye, 1952). From the published details of their experimental setup, i t i s difficult to see how any conclusions can be drawn from their results. Multiple scattering i n the large scatterer, together with acceptance i n each detector position of neutrons scattered both left and right, renders ridiculous any attempt to analyse the results i n terms of Schwinger s !  expression for the ratio of the single scattering yields at and  6, y  +  0 , y  7T.  Double scattering experiments with protons of very high energy have produced useful information about proton-proton forces (a brief discussion is given i n the introduction to the paper of Oxley, Cartwright, •and Rouvina, 1954). A typical experiment involves polarization of a beam of 415 Mev protons by scattering from a carbon target, producing approximately 5C# polarization (Kane et. al., 1954), and measurement of the left-right asymmetry of a second scattering i n liquid hydrogen. A similar experiment on the scattering of high energy polarized neutrons by hydrogen has been reported by ^outers (1951). These experiments illustrate the inability of any theoretical model yet proposed to explain a l l of the experimental data.  22  Since deuterons have,a spin of unity, a description of the spin states i s most concisely expressed i n tensor notation (Lakin, 1955). There i s then a strong resemblance to the description of photon states, although the condition of transversality imposed on photons i s removed. The azimuthal variation i n the second scattering of 167 Mev deuterons by carbon (Chamberlain et al., 1954.) i s more elementary than that permitted by Latin's expression for the angular distribution of polarized deuterons scattered by carbon. (d) Nuclei The first experiment with "aligned nuclei" was the scattering of slow neutrons by ortho- and para-hydrogen (Sutton et al., 1947, have discussed the early work i n the introduction to their paper). While there i s no spatial orientation, the spins of the protons i n the hydrogen molecule are either parallel (ortho-) or antiparallel (para-). Neutrons of wavelength greater than the diameter of the molecule react with the molecule as a whole, so that spin-dependence of the neutronproton force appears as difference i n the total cross-sections of molecules in the different spin states. The work proves, among other things, that the singlet state of the deuteron i s virtual. Those nuclei whose ground state spins differ from zero possess a magnetic moment, and therefore should enter a definite quantum state when a magnetic field i s applied, either by direct interaction with the field or through coupling with those of the atomic electrons which are paramagnetic. However, the energy difference of these magnetic states i s much smaller than thermal energy at a l l but very low temperatures, so  23 that t r a n s i t i o n s take place between the states continually, and there i s no measurable orientation of the n u c l e i .  Six methods of p o l a r i z i n g , or  a l i g n i n g nuclei at temperatures near 0.1°K have been suggested, i n v o l v i n g d i f f e r e n t i n t e r a c t i o n s of nuclear dipole and quadrupole moments with the applied magnetic f i e l d , either d i r e c t l y , or i n d i r e c t l y through i n t e r a c t i o n with atomic electrons or the e l e c t r o s t a t i c f i e l d i n c r y s t a l s .  Four of  these have been discussed by Simon, Rose, and Jauch (1951), who conclude that the Rose-Gorter, or hyperfine coupling (Gorter, 1948), method i s the most favourable experimentally.  In f a c t , t h i s method has been commonly  used, requiring temperatures of the order of 0.2°K or lower.  True  p o l a r i z a t i o n i s produced, that i s , the magnetic moment vector of a nucleus i s p r e f e r e n t i a l l y i n the d i r e c t i o n of the applied magnetic f i e l d .  Another  method, the Bleaney (1951), or magnetic hyperfine structure method, has the advantage of r e q u i r i n g no external magnetic f i e l d , but lower temperatures, of the order of 0.003°K, are u s u a l l y necessary to produce appreciable alignment.  This method depends on c r y s t a l l i n e e l e c t r i c f i e l d s to provide  a preferred d i r e c t i o n , and alignment, that i s o r i e n t a t i o n of the magnetic moment vector i n either d i r e c t i o n along a preferred axis i n the c r y s t a l , rather than p o l a r i z a t i o n , is.produced.  The t h i r d method, the quadrupole  coupling method of Pound (1949), has not as yet been successfully carried out.  Very r e c e n t l y , the f o u r t h , or "brute f o r c e " method has produced  nuclear p o l a r i z a t i o n (Dabbs, Roberts, and Bernstein, 1955).  This method  involves the d i r e c t i n t e r a c t i o n of the nuclei with an external magnetic f i e l d at very low temperatures. The p o l a r i z a t i o n or alignment of radioactive nuclei has a strong e f f e c t on the angular d i s t r i b u t i o n , p o l a r i z a t i o n and angular  24  correlation of the emitted radiation*  Steeriberg (1952) has derived an  expression for the angular distribution of gamma radiation as a function of temperature, angle of emission measured from the axis of alignment, the spins of the nuclear states involved, and multipole order. In another paper Steenberg (1953b) has presented calculations of the magnitude and angular variation of the polarization as a function of the same parameters.  As well as indicating the electric or magnetic  character of the radiation, a measurement of the polarization can determine the sign of the magnetic moment of the decaying nucleus. Cox and Tolhoek (1953) have extended the theory of the angular correlation of two radiations emitted i n cascade to the case of emission from aligned nuclei. In the particular case of completely aligned nuclei emitting i. X 2 * and 2  -pole gamma rays i n cascade via states of spin j — • j  - J-j, —> j -  - -^4. » "the correlation becomes isotropic.  of the crystal axes (Bishop et al., 1952a), workers at Oxford confirmed the electric quadrupole assignment of both gamma rays i n the cascade. Their results are in fair agreement with the calculations of Steenberg (1952, 1953a) for this special case where the two gamma rays following decay are not resolved by the detectors. By a series of very precise measurements of the angular distribution of the same gamma rays, in which the temperature and the chemical composition of the crystal were varied, the Leiden group concluded that the magnetic moment of Co°0 i s 4.3 i 0.2 nuclear magnetons (Poppema et al., 1955). Several other  25 • radioactive nuclei have been examined in this way, for example C e ^ and 1  NdL47  b y  Ambler Hudson, and Temmer (1955). f  Two experiments have been reported on the interaction of polarized thermal neutrons with nuclei polarized by the Rose-Gorter method. The slow neutron capture cross-section of Mn  55  has been shown to be spin  dependent by Bernstein et a l . (1954). Neutrons, polarized by passage through magnetized iron caused less .Mn56 activity when the nuclear and neutron spins were parallel than when they were antiparallel. Unfortunately, insufficient data was available to permit interpretation of this fact i n terms of the energy levels of Mh-^'« the capture of polarized neutrons by polarized  In an experiment on nuclei, the same  group (Roberts et al., 1954) used a different method. Unpolarized thermal neutrons were passed through a sample containing partially polarized SnM9 nuclei, and the polarization of the transmitted, neutrons was measured by scattering from the (220) planes of a magnetized magnetite crystal, the Bragg angle being set to reflect neutrons of 0.07 ev. i n the first order. The results show that Snr^9 captures preferentially the neutrons with spins parallel to the nuclear spin. Since the energy of the neutrons detected, 0.07 ev., i s near that of a resonance at 0.094 ev., the preferential capture i s attributed to the energy level of Snr^  0  responsible for the resonance. The spin of this level i s then I + 1/2, where I i s the ground state spin of Sm ^ 1  9  , either 5/2 or 7/2 (Brockhouse,  1953). In a similar experiment, (Dabbs, Roberts, and Bernstein, 1955), the measurement of the transmission of polarized neutrons through In-^-5 polarized by the "brute force" method proved that the energy level of In-^ corresponding to the 1.458 ev. resonance has spin 5, i n disagreement with Brockhouse (1953).  26 Recently, two slightly different new methods of polarizing nuclei have been proposed. Overhauser (1953) has calculated the nuclear polarization produced i n powdered metals by radio-frequency saturation of the spin-resonance of conduction electrons (Griswold, Kip, and Kittel, 1952). An example given by Overhauser predicts a polarization of 42% at 2°K with a static field of 10^ gauss. Carver and Slichter (1953) observed an enhancement i n the nuclear magnetic resonance signal from Id? when the conduction electron spins were saturated, indicating a change i n the population densities of the nuclear spin states i n accordance with Overhauser's theory. Due to r.f. heating of the sample, this experiment was performed at temperatures above room temperature. Cooling the sample would have increased the magnitude of the effect, according to theory, as well as reducing the r.f. power necessary to produce saturation. A higher magnetic field than the 30 gauss used would also have increased the effect, at the expense of raising the frequency of the spin resonance into the microwave region. The variation of nuclear polarization with both temperature and static magnetic field is exponential, so that the observation of an effect under the conditions of the experiment promises a large percentage polarization under more favourable conditions. Honig (1954) has reported a method capable of producing nearly 100% polarization of nuclear spins. Similar to Overhauser's method i n that i t utilizes the hyperfine structure coupling of nuclei to electrons experiencing-spin resonance, Honig's method differs i n that electrons bound to impurities, i n the present case arsenic, in silicon crystals are excited. While the temperature, static field, and r.f. power required are moderate, the method suffers from a low concentration  27  of the impurity atoms (only 1.3 x lO^/asP in the experiment reported), so that investigation of some radioactive nuclei may be difficult. Reactions between fast polarized neutrons and polarized nuclei are of interest i n spin and parity assignments, but i t i s difficult to obtain sufficiently intense beams of fast neutrons. For the same reason, experiments with polarized gamma rays and polarized nuclei are very difficult.  Bombardment with charged particles releases too much heat to  permit experiments with nuclei polarized by any of the known methods. It seems that, at present, polarization and alignment of nuclei is of more interest to solid state physicists than nuclear physicists. This situation may well change i f Overhauser's method, with i t s possibility of bulk polarization of nuclei in a metal, proves successful.  28  2. The Deuteron and the D + D Reactions The deuteron, being the simplest stable system-of nucleons, has been the subject of much experimental and theoretical research. An excellent survey of both has been given by Blatt and Weisskopf (1952). For low energies, the theory of two nucleon systems i s i n excellent general agreement with experiment, essentially because the interactions are quite insensitive to the details of inter-nucleon forces, but at higher energies, no one theoretical model i s able to explain a l l of the experimental data. Measurements of total cross-sections and angular distributions of nucleon-nucleon scattering, photodisintegration. of deuterium, and reactions between protons, neutrons, and deuterons have provided most of our knowledge about the nature of nuclear forces; further measurements, particularly at higher energies, may provide much more. Bombardment with polarized beams, or measurement of the polarization of reaction products, i s of considerable interest. By empirically fitting several constants to experimental data, Beiduk, Pruett, and Konopinski (1950) have obtained an expression for the differential cross-sections of the reactions D(d,n)He^ and D(d,p)T, assuming them to be the same. This expression fits the neutron data very well, but disagrees considerably with the proton angular distribution measurements of Blair et al. (1948). They attributed a l l energy variation to changes i n the barrier penetrability factors of the various ingoing partial waves. Very strong spin-orbit coupling had to be assumed to explain the angular distributions. In another paper (Pruett, Beiduk, and Konopinski, 1950.) the same authors have made approximate calculations of  29 the coefficients of the angular distributions, using a commonly assumed form of the nucleon-nucleon potential. Spin-orbit coupling was assumed to be due entirely to the tensor operator &±j n  n  (p. 97, Blatt and  Weisskopf, 1952). Agreement between the calculated and empirical • parameters i s not good, though there i s a marked general similarity. . The approximations made i n the calculations were so drastic that i t i s not possible to say that theory and experiment are i n disagreement, but i t appears that tensor forces alone do not provide sufficient spin-orbit coupling. Blin-Stoyle (1951) and Wolfenstein (1949) have derived expressions for the polarization of the outgoing neutrons and protons due to the spin-orbit coupling. These expressions differ, and neither i s a good approximation for bombarding energies greater than 400 Kev, due to the assumption that only ingoing s and p waves contribute to the r,  n  rt  M  reactions. Both indicate that the percentage polarization (for both protons and neutrons) should lie between 0 and 50% and be a ma-riim-nn for scattering angles near 45° and 135° i n the centre of mass system. The magnitude of the percentage polarization of the protons and neutrons and its variation with bombarding energy and angle of emission are more sensitive than the angular distributions to the values of some of the matrix elements of the transitions. Comparison of measurements and more accurate calculations than those of Pruett et a l . may show that one, or none,- of the present theories of nuclear forces i s adequate (Blin-Stoyle, 1952). These accurate calculations, however, involving internal wave functions of the deuteron, triton, and He3. nucleus, would demand the use of an electronic computer. According to the calculations of Fairbairn (1954), who found fair agreement with  30 experiment, the Butler stripping process contributes strongly to the reactions at bombarding energies greater than 5 Mev.  Since the four  particle interaction theory of Beiduk et al. does not contain any assumption of compound nucleus formation, this theory should resemble stripping theory at higher energies, providing that suitable assumptions are taken in evaluating the transition matrix elements. As yet, only enough data i s available on the polarization of protons and neutrons from the D + D reactions to make possible qualitative statements about the forces contributing to the reactions.  Bishop  et al. (1952b) measured the left-right asymmetry i n the scattering by helium of protons emitted at 135  p  (Centre of mass system) from the direc-  tion of a 300 Kev deuteron beam. The value for the proton polarization calculated from this measurement, (30 ± 6)#, has led Blin-Stoyle (1952) to the conclusion that tensor forces alone may provide sufficient spinorbit coupling to account for the angular distribution and polarization. Attempts to measure the neutron polarization by resonant scattering i n carbon (Huber and Baumgartner, 1953j Ricamo, 1953a,b) indicated that for bombarding energies near 600 Kev, the neutron polarization i s approximately 20$, a value not i n disagreement with Blin-Stoyle s conclusion. 1  31 3. Non-resonant Scattering of Neutrons by Heavy Nuclei Since neutrons possess a magnetic moment, they may be appreciably scattered by the intense electrostatic fields of heavy nuclei. Because the magnetic moment and spin of a neutron are connected by the relation  M =  where  -  SJL  2mc  cr—  CO  M i s the magnetic moment vector i n erg gauss 7 J^U | the magnetic moment of the neutron n  = 1,9135 nuclear magnetons,  eln the nuclear magneton = 5.04929 x lO" ^ erg gauss"^, 2mc 2  and  O  i s the Pauli matrix,  this scattering i s polarization sensitive. To obtain an expression for the electromagnetic contribution to the Hamiltonian describing the neutron, consider the situation depicted i n Figure 1, the K system approaching the K system along the 1  z-axis with velocity V.  FIGURE I  32  For values of V much less than c, the velocity of light, the magnetic field strength ~E* i n the K system is given by (pi- 62, Landau and 1  Lifshitz:,  1951):  H*' = H + H» =  or  c  E. x ? , ( a )  "c E x V , since"! = 0 .  (H has. been taken as zero, even though there are i n general, both nuclear and electronic magnetic fields. However, for the case of a 3 Mev neutron incident on a high Z nucleus with a magnetic moment, M, of the order of one Bohr nuclear magneton, H/H' * M /jr J c EV =  "V z V e  =  0.15 even at  the nuclear, surface. Since H/H falls off as l / r , H may be safely 1  neglected.. In the case of lead, only Pb ^, approximately 25$ abundant, 2  has a magnetic moment, 0.6 nuclear magnetons. Only very slow neutrons show appreciable magnetic interaction with electrons, and then only when there i s a bulk alignment of spins, as i n ferromagnetic materials. In any event, both of these contributions to the magnetic field are zero when averaged over many randomly oriented atoms, so that, even i f there is a small contribution to the differential cross-section, i t i s not polarization dependent). Because of i t s magnetic moment M, the neutron possesses potential energy i n this field.  The Hamiltonian i n the K' system may  be written: /¥-'  =  -M.I?.  ( 5  )  o  33. Since V << c, the Hamiltonian i n the K system i s  & where ^  =  +  '  (* )  = mV i s the momentum of the neutron i n the K system and in  is the neutron mass.  Combining  Inserting  (z)  (1 ) i n (5)  Since  Ei =  f, L "S  and  ( 3 ) , and (4-),  t  and writing V = p/m, we have  -^f-r*,  = T- x p ,  =  i^'  where Z i s the atomic number of the target nucleus and ~L and "S* are respectively the orbital and intrinsic angular momenta of the neutron i n units of h  t  ( 6 ) may be written  34  The Schrodinger equation describing the motion of the neutron  is then  or  k = total neutron energy (conserved throughout  where  2  the motion). and  £  Schwinger (194&) has obtained the Born approximation to the solution of equation ( 7 ) by calculating the electromagnetic contribution to the scattering amplitude and adding to i t the specifically nuclear scattering amplitude. The resulting differential scattering cross-section may be written  where  £(0) = nuclear scattering amplitude at angle of scattering P  = polarization vector of incident beam,  — >  h  0 ,  the unit vector normal to the plane of the =  reaction. denotes "imaginary part of".  and  "Im"  35 0 — (d, ~n) i s plotted i n Figure 3 for completely polarized 3.1 Mev neutrons scattered by lead, with ~n parallel and antiparallel to  .  A more accurate solution may be obtained by calculating the perturbation of a "hard sphere" wave function due to the electromagnetic interaction. The experimental work of Whitehead and Snowdon (1953) shows that the differential elastic scattering cross-section of lead for 3.7 Mev neutrons resembles closely that of a perfectly elastic sphere for scattering angles less than 60°. The "hard sphere" wave function should then be a good approximation from which to begin perturbation calculations. In equation (7),  =  let  <f>. + <fc, where  is a  solution of ( 7) f with its boundary conditions, when 6 = O . (7) becomes  (V* + O-V;  *  -  %t).  Neglecting tfc with respect to % on the right hand side,  C W  k*)y.  -  e ^#  (6)  Expressing the S7 operator i n terms of spherical coordinates, ( S ) Z  becomes  36  • ^ ( r ) i s a solution of 0  with the boundary conditions -^/©(r) = 0 for r < R, the nuclear radius,  and -^J?)-*(& ckZ  as  Y  >  *^f(fi)X^\,y  +  *MXh-y)  (*>>  o o  where the expression  describes the spin orientation of the neutron, being the usual spin eigenfunctions, and  and "X^, and  obey  The solution of (% ) and U o ) i s the familiar "hard sphere" or "potential scattering" wave function (p. 329, Blatt and Weisskopf, 1952), and may be written  o  X  f % ns ( ) R  l  ?  m'=  + cH^%)]  -'fa  \  Q  (6) dM \ ^  }  3  37  where  ^ = kr, (?) = "regular solution" =  /2AAP) =  J+  N„ (P)  "irregular solution" = -  Xc*,) = Bessel function /y'pC^J = Neumann function V  (~^)*J,, (?),  •  of order p, defined i n Jahnke & Emde (1945),  y  (&,tyO spherical harmonic, as i n Blatt and Weisskopf (1952); =  b = kR. The functions defined above obey the following relations:  ^  (?)  > sin (f ~ IT ) v  (p)—*  cos ( f -  2.  / J  as f —»  0  0  (  22 )  To obtain the radial equation corresponding to ( f a ) , i t i s convenient to expand -fy and <¥ i n terms of eigenfunctions of the 0  operator  - *  —*•  L  J = L- + S. These may be written  38  where the coefficiente  (A  ^..m, m'  |j"rl)  are the Clebsch-Sordan  coefficients defined as i n Condon and Shortley (1935). Since J  2  = (L +"S^)  2  = L  2  + S  2  + zZj?, and the y's  are eigenftmctions  of J , L , and S , 2  2  2  4)  Using i n (11 ) the relation  T-U-JU  M--J  and applying ( l ^ ) ,  -£-J  J--U-H.I  where  = 0  for  J = O.  Expanding -t/^ i n similar form,  M--J m ' . - a  39 Inserting these expressions i n  C^*-), and  making the transformation  r = ? . there results k oa  A*+'A.  J~  '/z.  •> •> •> hA-fr'*- r h«>h» • tfl <fir> Taking the scalar product of each side with since <T, I, k,r\ \ j\ X 'A, M')  +  ft  __  =  *±0]  ^  ^r,  ^  \ L e f  r  W%i  +  *  * ^ becomes, n  s  fa,  £  M  i  l  The problem i s now reduced to that of finding a particular integral of  (16)  ^il  satisfying the boundary conditions (b) =  0,  i*e, (?) «C e ^ 1  Solution of  for large f .  (16 ) i n terms of tabulated functions i s carried out i n  Appendix A. The asymptotic form of  ^  (j>) may be written  07)  40 2.  where  ^ b  (?) ^ (?) ?  Substituting ( l 7 ) i n (X^), and putting t'p  oo  ^  h.  T  The term fjJ"(j* + i) --tU+i) - ^ J in D JL when X9  Yz. , and -f-/-ri)  when X=  e  -  £  ,  fj.  7j  4  has the values  Jk. Putting this i n  (l£>), replacing ^ j - , 4'/z by the expression (i>3 ), expressing the Clebsh-Gordan coefficients i n terms of out a l l summations but the one over  %Cr)  = -IT* ^  wave -V„ + ^ Expanding e.  U/ , there results  'Tjl^+if  The scattered wave, 1J,  , (Appendix B), and carrying  LMJ.*i)fSfCk)  X  , i s the difference between the total  i and the incident wave e'^&te/X/  +  <C-k.)\,  i n spherical harmonics, and taking the asymptotic form  of the wave functions,  , 1  41  OO  Using the Legendre polynomials defined by Jahnke & Emde (1945), '2.1  Y  rt^=  +J.  -l4^^ l)J +  /]U-^e  ,  and  (21)  where  Off  op  Since (22) represents a wave travelling radially away from the scattering centre, the differential scattering  cross-section,  Cr (0, C^) , may be defined by: -  Cr(ff,LfJ<Lu  =  probability flux into solid angle d o-> incident probability flux  42  where V i s velocity, and Vg  i s the adjoint of "t^.  C  From (21)  2  e 77 [ < U W - « e ' How, A B + AB  y  - <(^)^)e^lA>)B(e)  +  Afc)B*(«].  = 2(Re A Re B + Im A Im B),  (z3)  where Re and Im indicate respectively the real and imaginary parts n  n  w  n  of the quantity, and  il°f(y )cL(-!i) z  cos  If  +  Following Schwinger, (1948), the polarization vector, P , of the incident wave i s defined by  Taking  x and  y components,  (24)  43  A3 Then, from (24  where l l Is. a unit vector normal to the plane of the reaction, that i s ,  where ko and k are respectively the incident and scattered propagation vectors. Figure 2 shows the relationship between 6, if , P, ICQ, k, and "ff. Putting  (2^") and  - £|A(e)f  f  ) i n (2.2),  +  f- |B^)p .+ 2  (RK)[ReA^)ReB(6)  + ImA«)ImBWj.  It can be seen from (2-6) that polarization has maximum effect on the cross-section when the direction of observation i s chosen so that P  i s normal to the plane of the reaction. In this case the inter-  ference term, the third term i n (2.6), has i t s maximum absolute value. This term changes sign accordingly as the scattering i s in the right or the left sense, that is, as .(f is changed by IT . The necessary functions of A( 0 ) and B( 6 ) are evaluated i n Appendix C for neutrons of energy 3.1 Mev scattered by lead. The differential scattering cross-section for one hundred percent polarized (P = l ) neutrons of this energy i s plotted as a function of scattering angle i n Figure 3. The reaction i s appreciably polarization sensitive only for scattering angles  8, smaller than ten degrees.  4 4  II  10  < Q <  9  LU CO  CO  < Q Q  8  A -.Equation ( 26 ), P.n = +1  \  B - Equation ( 26 ), P.n = -1  \  A  \  C - Schwinger,  P.n = +1  D - Schwinger,  P.n = -1  E - Equation ( 26 ), P.n = 0 E - Hard-sphere scattering.  \ \  O  \  V O UJ CO  I  co  o a: o CD  5E LU  < o CO  D B F i g . 3. Differential scattering cross-section of lead for polarized 3.1 Mev neutrons.  8  POLAR ANGLE 0 , DEGREES  10  II  12  13  14  15  .1  44 For comparison, Schwinger's expression for the cross-section is plotted i n Figure 3, with A(6 ) inserted for £ (& ), the nuclear Q  scattering amplitude. It can be seen that there i s a very strong resemblance between 0~  from equation (2 6)  and Schwinger'a  solution, the difference being that the polarization dependent term from equation (2.6)  i s approximately 25% larger than Schwinger s. 1  The divergence of the cross-section at zero scattering angle resembles that i n Rutherford scattering, and may be removed i n the same way, by taking into account the screening by atomic electrons.  45 L.  Scattering of Neutrons from D(d.n)He3 by Lead The curves A and B" of Figure 3 show that scattering M  M  M  of 3.1 Mev neutrons by lead i s appreciably sensitive to neutron polarization only for scattering angles less than ten degrees. The angle at which polarization has maximum effect decreases very slowly with increasing neutron energy, so these curves represent quite accurately the theoretical differential scattering cross-section for neutrons i n the energy range of 2.5 to 4*2 Mev produced i n the reaction D(d,n)He3 at bombarding energies up to 1 Mev.  Measurement of small  angle scattering calls for collimation sufficiently close to separate scattered particles from the unscattered beam. In this experiment i t was, i n fact, desirable to be able to detect neutrons scattered only two degrees from the direction of the incident beam. Collimation of the beam incident on the scatterer was chosen i n preference to collimation i n front of the detector because the small size of photographic plates, the most promising detector, would have made collimation of scattered neutrons rather awkward. (a) The Collimator The choice of material for the construction of the collimator depends upon the mean distance a neutron travels i n the material before being degraded to an energy below detection threshold, and upon the structural qualities. Paraffin, with a mean constitution of  Gy^Zt  is satisfactory, since the large hydrogen concentration causes rapid degradation and absorption of neutrons; i t is also easily cast and  46  « ••  • • •  • •• • • • • • • • •  • • •  •  9 •• •  •• •  •  0  « • • •  • •••  •  •  •  •  • 0  •  0  •• •  • ••  • •• • • ••• • • •  • •  •  0  • •  0  0  0  •  m •  0  •  •  « * • 0  •  0  *  0  0  0  •  9  » 0  r • • • t  0 0  •  0  »  0  0  •  0  0  *  V  9 0 «  0  0  «  A:  •  •  •  ' 9 t "9 0 9  A; s  9  -  0  9 0  ~ •  0 '' 0 ' '  0  vi :  0  - •  0 •  • 0  ,  x  • 9  *  " 9  '  ^  •  0  •  •  0  9  ''  0  '  •  0  9  *  , 0 9 m ,  0  •  •  0  0  0  0  0  0 9  0  0  9  9  •  0  0  0 0  0  9  9  0  0  O  •  0  9  0  0  9  •  0 0  0  •  0  90 0  0  • •  0  9  • 0  9  •  0  0  9 •  0  •  9  0  9  0  9  9  STEEL  ^-  7  0  1  0  '  9  9 ' 0  0 0  0  0  < ,  0''  ' '  :>  g g ] WOOD • •PARAFFIN • - i  '  0 '  9 , 9 ,  :  J^  0s  0  9  9  0  ' 0  0  0 0  0'  0  9  • •0  0  9  0  0  0  •  0  •  •  0  0  •  •  0  0  0 • 9 , • 9 0 0  ,  •  0  0  •  #  e  0  0  ' 0 * 0 ,  #  o «  0  0  9  9  • 0  9  0  0*  0  • • •I Fig. 4.  0  ',  x• •••'  ^>  0  ; . • .• 0 0  *C  • *  .  0  , • 0 9 9 9'  , 0 * 0 .  •  •  '  "  •  •  -*  . •  •  '  • • •  •  •  0  0 '  •  *  •  0  0  9  0  0  •  0 0  0  l  0  0  0 •  •  •  0  •  LEAD  1  3 inches  Horizontal and vertical' sections of the neutron collimator.  46 machined. For neutron energies greater than 3 Mev, iron i s effective i n absorbing energy by inelastic scattering, so that i t may be beneficial to include iron or steel near the entrance end of the collirontor (Munn and Pontecorvo, 1947)* The dimensions of the collimator depend upon the thickness of material necessary to prevent energetic neutrons reaching the detector except via the collimation channel, the desired angular width of the emerging beam, and the tolerable loss of neutron intensity. Figure 4 shows the details of the collimator, built for this experiment, which resembles that mentioned by Segel, Schwartz, and Owen (1954)* Paraffin baffle sections with 3" diameter holes punched out were alternated with sections containing l/2" x 1" holes, the actual collimation channel. In this way, neutrons scattered by the walls of the collimation channel had opportunity to travel well into the body of the collimator, decreasing the probability of multiple scattering down the collimation channel. Three l/4 thick steel plates with 3/4" x 1 l/4 M  w  holes were interspersed with the paraffin blocks at the entrance of the collimator, and one with a l/2" x 1 hole served as a mount for the M  scatterer at the exit. The parts of the collimator were aligned on a mandrel i n order, and a flame was played gently over the surface to fuse the paraffin blocks. for protection.  The assembly was mounted i n a plywood box  During runs using a stilbene scintillation counter as  a detector, a 1 l/2 lead plate was added to the exit end of the collimator n  to absorb the 2.2 Mev gamma rays from the reaction H(n,T)V  3  occurring  prolifically i n the collimator. A further lead-lined paraffin shield was added to provide additional shielding from the target over the  47  SLIT  / x 8  \ CD  MOLYBDENUM STOP  3-/  I, 8  = f ^ > L U C I T E SPACER l=i RING LIQUID AIR RESERVIOR  WINDOW NEOPRENE GASKETS  LUCITE CENTERING RING TARGET SUPPORT  DEUTERON BEAM  WINDOW  •PINHOLE IN DISPENSER  DRAW TUBE STOP Details of the vacuum seals are not shown.  0-RING SEAL( Fig. 5. Heavy ice target assembly.  DIVIDED CIRCLE  47 angular range of interest. An aluminum plate was screwed to the bottom of the collimator, projecting out to carry the bushing which constrained the collimator to rotate about a rod fixed on. the vertical axis of the target assembly. Also mounted on the aluminum plate was a pointer which indicated on a divided circle the inclination of the collimator's axis to the direction of the deuteron beam from the Van de Graaff generator. The divided circle was centred accurately on the rod about which the collimator rotated. Cross-hairs were centred on the entrance to the collimator and permanently cemented. Removable cross-hairs, mounted on a piece of 1/2" x. 1" waveguide, could be slid into the collimator exit. The two sets of cross-hairs were aligned by eye on lines scribed on the target assembly at -45°, 0°, and +45° to the deuteron beam, and the pivot bushing was adjusted laterally until the axis of the collimator intersected the vertical axis of the target assembly. The divided circle was then rotated until the pointer read correctly the angle between the deuteron beam and the collimator axis. (b) The Target Assembly The essential features of the target assembly are shown i n the simplified diagram, Figure 5.  A stainless steel liquid air  reservoir, the neck thinned to reduce conduction losses, cooled the copper target mount. A measured volume of DgO vapour, admitted through the pinhole i n the dispenser, was frozen on a clean copper blank clamped to the target mount, after which the dispenser was rotated out of the path of the beam. Although the target is shown perpendicular to  43  the beam direction, i n actual runs i t was inclined at 45° to present a minimum of scattering material to the neutron beam emerging at 45°• The dispenser was far enough from the target that no serious nonuniformity of target thickness resulted over the 1/8" width of the incident deuteron beam. To enable the beam current striking the target to be measured, the liquid air reservoir was insulated by lucite rings from the rest of the assembly.. Details of the "o" ring vacuum seals are not shown i n the diagram. The accurate alignment necessary for this experiment was achieved by several precautions.  The liquid air reservoir was centred  in the vacuum chamber by a lucite ring, perforated for pumping. This placed the face of the target blank on the vertical axis of the assembly when the top clamp was screwed down. A molybdenum stop with a vertical 1/8  M  x L/2" slot was placed close to the target to confine the deuteron  beam, and hence the source of neutrons, to a small central region.  To  align the target assembly with the axis of the deuteron beam from the Van de Graaff generator, a telescope with a cross-hair eyepiece was focussed from a distance of six feet on, successively, the small glass window in the vacuum chamber, the beam defining s l i t , and the exit stop of the vacuum box between the pole pieces of the resolving magnet, three feet from the target. The bolts clamping the three neoprene gaskets were adjusted until a l l three objects were centred on the telescope crosshairs. This procedure was carried out with the system evacuated, and the bolts were tightened sufficiently during adjustment to retain the alignment when air was admitted. The target blank was, of course, not i n place during alignment.  49 (c) Detectors The detection of fast neutrons may be accomplished by the detection of energetic charged particles produced i n neutron induced reactions, usually elastic scattering of hydrogen or helium ions. For the experiment under discussion, recoil ion chambers and proportional counters may be ruled out immediately because of their low efficiency and large size. Organic phosphors such as anthracene and trans-stilbene, used as scintillation counters, offer relatively high efficiency i n a small sensitive volume, but have low sensitivity to variations in neutron energy and direction. This, coupled with their high gamma ray sensitivity, may cause a very high background counting rate due to room-scattered neutrons, X-rays from the electrostatic generator, and gamma rays from neutron capture. Photographic emulsions, i n which the tracks of recoil protons may be examined by use of a high power microscope, have several advantages, and some serious disadvantages (Rotblat, 1950). They have approximately the same detection efficiency per unit volume as organic phosphors, and, being thinner than i t i s usual to make phosphors, may be placed closer to the scatterer for the same  wwgniay  resolution, thus  improving the ratio between the neutrons of interest and room-scattered neutrons. Improved angular resolution can be obtained by greater source to detector distance only at the expense of increased percentage background. During scanning of the plates, proton tracks due to roomscattered neutrons may be rejected to a considerable degree, since the length of a track i s approximately proportional to proton energy, and  50  The arrow indicates neutron beam direction.  50 the energy Ep of the scattered proton and its angular deviation  6 from  the direction of the incident neutron are related to the neutron energy E by the relation E n  = E cos Q. 2  p  n  Emulsions effectively insensitive  to gamma rays can be obtained, thus further reducing the background. However, the information contained i n an emulsion is obtained only by lengthy and tedious scanning, and during the experiment, knowledge as to its progress i s not available. Plates with Ilford C-2 emulsion were chosen for the experiment because, while proton tracks show a high grain density, electrons, and hence gamma rays, are not recorded. The longest possible proton range (Ep = E ) was about 80 microns for incident neutrons of energy 3.3 Mev, n  so 100 micron emulsions were used i n preference to thicker ones, making processing relatively easy. Figure 6 shows the method of mounting the plates during a run. A rigid, yet Light, aluminum frame, screwed to an extension of the plywood collimator box, ensured that plates were i n the same position i n successive runs. The alignment of this plate-holder with respect to the collimation channel was checked between runs by sliding a piece of 1/2" x 1" waveguide into the collimation channel so that i t projected through the plate-holder, and sliding milled spacing blocks between the waveguide and the sides of the plate-holder. The plates were wrapped tightly i n black paper envelopes' sealed with #33 Scotch Electrical Tape. After exposure the plates were developed for 45 minutes at 22°C in Ilford ID-19 (Kodak D-19b) diluted ten to one. After a five minute  51 wash i n slowly running filtered tap water, they were immersed i n a 2 l/2$ potassium metabisulphite stop bath for 30 minutes.  The plates were fixed  in 305S hypo until clear (usually about 45 minutes), then placed i n Kodak F-5 a further 15 minutes to harden. During processing, the chemical trays were placed on a motor-driven agitator, so that the solutions were gently stirred. After hardening, the plates were washed for one hour in running water and dried at least four hours i n a dust-free cabinet warmed to about 35°C by 100 watt bulbs. (d) Experimental Procedure and Results From the discussion i n Section 2, neutrons from the reaction D(d,n)He3 are expected to have maximum polarization when the bombarding energy i s about 0.6 Mev, and the angle of emission i s 45° i n the centre of mass system.  This corresponds to a neutron energy of 3.31 Mev at an  angle of 39° with respect to the deuteron beam in the laboratory system. Because the reaction cross-section rises steeply with bombarding energy, (Hanson, Taschek, and Williams, 1949), the neutron yield from a target 100 Kev thick i s nearly equal to that from a thick target, or approximately 2 x 10? neutrons/steradian/second for the 15 microampere deuteron current used during the runs. The angular distribution of the neutrons does not seriously affect this estimate. The lead scattering block slid snugly into the exit end of the collimator. The thickness was chosen to be 1.5 cm. as a compromise between scattering yield and excessive multiple scattering. For this thickness, No-, the product of the number of atoms per square centimeter  52 of scatterer and the total scattering cross-section, i s 0.26, so that approximately 25% of the incident neutrons suffer single scattering and less than (0.26) , or 7% suffer double scattering. For comparison an 2  aluminum scatterer with the same value of N c r , or a thickness of 1.7 cm., was used. Since the scattering asymmetry due to polarization i s proportional to atomic number, aluminum should show an asymmetry only 16% of that due to lead. An accurate calculation of the number of proton tracks expected in each plate for a given neutron exposure i s very difficult.  An  estimate has been obtained for a simplified geometry approximating the actual case. With the centres of the 2.5 x 7.5 cm. plates 17 cm. from the scattering block and 1.65 cm. from the collimator axis, 8 in equation (Z6)  ranges from 2.5° to 15°, with the smaller angles more  strongly weighted. The term P.n  in equation  (2.6) varies from  0.93 l"P*l to 1.0 iTl for the plate to the right of the scatterer, looking in the direction of the incident neutron beam (Assuming P* is upward), and from -0.93lPl to  -1.01 Pi for the left plate (Figure 2).  Assuming |PI = 0.3, and an average value for 6 of 4.5°, the curves of Figure 3 give, for the neutron flux and absorber thickness given above, nu = 90/second for the scattered neutron flux through the right plate, and  njj = 76/second for that through the left plate. Taking the  hydrogen concentration given by Rotblat (1950) for Ilford emulsions and the value 2.3 barns (Adair, 1950) for the hydrogen scattering crosssection, 0.55 neutrons/second are scattered by hydrogen in the right plate, and 0.46/second in the left. Water absorbed i n the emulsion  53 adds approximately 25$ to this, and there i s a further small increment due to hydrogen i n the black paper wrapping. In order to reduce the background from room-scattered neutrons, only those proton tracks were counted with lengths between 65 microns and the maximum of 80 microns. Since Ep = E  cos 6 > these lay i n a cone 2  n  of half-angle 26.7° about the direction of the neutrons incident on the emulsion from the scattering block. This corresponds to 53,4° i n the centre of mass system, or 20,2$ of the sphere. Since n-p  scattering  is isotropic i n the centre of mass system, a fraction 0,202 of the proton tracks were counted. Then 0,11 "countable" tracks per second are formed in the right emulsion, and 0,093 per second i n the left, due to the dry emulsion alone, A three hour run thus should produce 1190 tracks i n the right emulsion and 1000 i n the left, a statistically significant difference. In practice, three pairs of plates were exposed during each run, one with the lead scattering block i n place, one with the aluminum scattering block, and one with no scatterer, each pair being exposed for three hours. The first run showed a large (8:1) asymmetry i n a l l three pairs of plates, indicating misalignment of the apparatus. After careful re-alignment of the target assembly, collimator, and plate-holder, by the methods outlined i n subsections (a), (b), and (c), the second run showed no appreciable asymmetry in any of the pairs of plates, and the total number of "countable" tracks per plate exceeded that calculated above by a factor of 5,  54 The plates were scanned with a Cook, Troughton and Simms type M4005 nuclear research microscope, using bright f i e l d i l l u m i n a t i o n . With a t o t a l magnification of 450X, the square graticule i n the r i g h t eyepiece of the instrument covered an area of the plate 250 microns square.  In the preliminary scanning, the c r i t e r i o n f o r countable M  M  tracks was applied by v i s u a l estimation, with only approximate allowance f o r shrinkage of the emulsion i n processing (Rotblat, 1950).  Five  traverses, uniformly spaced along the length, were made across the width of each p l a t e , and "countable" tracks beginning or ending within the confines of the g r a t i c u l e were accepted, so that on each plate an area  5 x 2.5 x (250 + 64.) x 10"*^, equal to 0.39 c m . , was scanned.  The term  2  64. x 10"^-, twice the average projection of a track on the  d i r e c t i o n perpendicular to the microscope traverse, allows f o r tracks not l y i n g e n t i r e l y within the g r a t i c u l e .  The average count per traverse  was 95, equivalent to 46OO per emulsion. This large count per plate indicated that neutrons scattered near the e x i t end of the collimation channel penetrated the remainder of the collimator with s u f f i c i e n t energy to give "countable" tra'cks i n the emulsion. was used, a  To investigate t h i s p o s s i b i l i t y , a more f a c i l e detector  2 x 2 x 4. cm. trans-stilbene c r y s t a l mounted on a 1P21  photomultiplier.  The counter was moved i n small steps along an arc  67.5 cm. from the t a r g e t .  At each point the pulse height spectrum was  recorded on a t h i r t y channel k i c k s o r t e r , and the neutron f l u x was monitored by means of a BF3 "long counter" surrounded by p a r a f f i n . The background due to room-scattered neutrons  «wri  capture gamma rays  55  I  COUNTER POSITION .DEGREES  Fig. 7. Angular distribution of collimated neutrons.  55 was obtained at each point by recording the pulse height spectrum with a lucite plug f i l l i n g the collimation channel*  By choosing a suitable  pulse height interval between noise pulses and pulses due to 2.2 Mev gamma rays from the capture of neutrons by hydrogen i n the collimator, and summing the counts recorded by channels i n this interval, the ratio of collimated neutron counts to background was made 8*7:1. Each count was normalized to the monitor count for the same period.  The normalized  count, less background, i s plotted as a function of counter angle i n Figure 7. The number of neutrons recorded beyond the geometric cut-off, while small compared to that at smaller angles, was sufficient to obscure the expected asymmetry i n scattering by lead, hence this attempt to detect polarization of neutrons was suspended.  Another experiment,  involving resonant scattering i n helium, i s proposed i n Appendix D.  /  56 CHAPTER III GAMMA RAYS FROM THE  pflMRAwraiBiKFC  1. The Mirror Nuclei B  11  OF BORON TEN WITH DEUTERONS  and C  1 1  Nuclei differing only by the interchange of a neutron for a proton are said to be mirror nuclei. Comparison of the properties of mirror nuclei i s of great interest in nuclear theory, since i t provides a means of checking some of the simplifying assumptions commonly made concerning nuclear forces,- The charge symmetry postulate, that neutronneutron and proton-proton forces are equal, except for Coulomb forces, implies that the energy level diagrams of mirror nuclei should be identical i n the energies of the levels measured from the ground states, and i n spins and parities. The ground states should differ in energy only by the neutron-proton mass difference and the extra Coulomb energy of the proton, according to  AE  =  0^  - mp)c  2  -  - l ^ C A - l ) ,  (27)  where 1 % , nip are the neutron and proton masses, e i s the proton charge, A the mass number of the isobars, and R ^ 1,45 A  x lO"^ i s the nuclear  radius (p. 219, BLatt and Weisskopf, 1952). An implicit assumption in ( 27 ) i s that "many-body" forces are either negligible or independent of the interchange of a neutron and a proton (p. 125, Blatt and Weisskopf, 1952).  57  E  9-234  J  •9-28 ^•19  B + d-p  /2  5  TT +  E 913 8-97  •-8-92 ( / " /2) 3  5  2  8-68  8-57  8-44  ^6 81 " 676  6-472  6 4 6  B +d-n ,0  503 4-77 5,/ 2  •4-23  2-14  T  V  B  w  Y  ¥  o  (  7  2  5/ // 2  +  2  2  )  +  6-87  N  F  5  7-39  •7-30  446  C / , / )  812  799  T  TT  J  1-90  3  A  II  F i g . 8. Energy levels of B ^ " and C^. Transitions shown were found i n the present experiment.  (%,V +  57 The deuteron bombardment of B and C B  1 0  1 1  10  produces the mirror n u c l e i  simultaneously through the reactions ^ ( d j p T j B  (d,n/)C  1 1  »  The energy l e v e l diagrams of B  n  and C  n  1 1  U  f o r ease of comparison.  unstable to p a r t i c l e emission, are not shown.) the ground state of C  1 1  1 1  and  (Ajzenberg and  Lauritsen, 1955) are shown i n Figure 8 with the ground state of C placed opposite that of B  B  1 1  (The high l e v e l s ,  According to (  27 ),  i s 1.39 Mev higher: experimentally i t i s 1.98  Mev higher than the ground state of  This i s by no means an  i n d i c a t i o n that the charge symmetry postulate i s i n c o r r e c t , since the e l e c t r o s t a t i c term i n ( 27 ) i s derived on the assumption of uniform charge d i s t r i b u t i o n throughout the nuclear volumej furthermore, the nuclear radius i s not a w e l l defined quantity. emission to B^,  C^- decays by p o s i t r o n  with a h a l f - l i f e of approximately 20.5 minutes.  Unfortunately, there i s as yet i n s u f f i c i e n t information, p a r t i c u l a r l y s p i n and p a r i t y assignments, about the energy l e v e l s to permit detailed comparison, but the pattern of l e v e l s i s similar.  certainly  The f i r s t f i v e excited l e v e l s show a marked s i m i l a r i t y i n  spacing, with those of C  1 1  corresponding l e v e l s of B . 11  l y i n g , on the average, 250 Kev below the I t i s not f r u i t f u l to compare the higher  energy l e v e l s , because of the much closer spacing, p a r t i c u l a r l y since the spins are l a r g e l y unknown.  The only c e r t a i n spin assignment of those  shown i n Figure 8 i s that of the B Burg, 1948).  1 1  ground state (Gordy, Ring and  There i s , f o r example, considerable difference between  the spin and p a r i t y assignments l i s t e d by Ajzenberg and Lauritsen (1955) and those by Jones and Wilkinson (1952).  The energies of most of the  l e v e l s are assigned from the measurement of the energies of proton and  58 neutron groups from deuteron bombardment of BlO, with corroboration i n several cases from l e s s accurate measurements on other r e a c t i o n s .  Because  the energy r e s o l u t i o n attainable i s poorer f o r neutrons than protons, i t i s possible that some l e v e l s are not resolved i n 0^1; f o r example, the 6.46 Mev l e v e l i n  may correspond to the 6.76,  6.81 Mev p a i r i n  B . 11  Proton groups corresponding to a l l the known energy l e v e l s of B H up to 10.32 Mev have been analyzed magnetically to within 8 Kev uncertainty i n energy (Van Patter, Buechner, and Sperdute, 1951; E l k i n d , 1953).  Measurements of the angular d i s t r i b u t i o n s of some of the groups  with bombarding energies between 0.20 and 8 Mev indicate that "Butler s t r i p p i n g " contributes appreciably to. the r e a c t i o n even at bombarding energies below 1 Mev f o r some of the groups.  There i s some disagreement  between d i f f e r e n t authors as to the o r b i t a l angular momentum the captured neutron imparts to  and as to the p a r i t i e s and probable spins  of the l e v e l s (discussed by Ajzenberg and Lauritsen, 1955).  Broad> low  resonances at bombarding energies of 1.0 and 1.5 Mev have been reported i n the e x c i t a t i o n curve of the more energetic proton groups; these were observed at the same time i n the aggregate gamma ray e x c i t a t i o n curve (Burke, R i s s e r , and P h i l l i p s , 1954).  The r e l a t i v e i n t e n s i t i e s of the  proton groups measured a t . 9 0 ° f o r 1.51 Mev bombarding energy are l i s t e d with other data i n Table 1 (Van Patter, Buechner, and Sperduto, 1951). The energies of the neutron groups from B  1 0  (d,n)C  1 1  were  measured with an uncertainty of 60 Kev by Johnson (1952), who used the photographic emulsion technique.  At a bombarding energy of 3.6 Mev he  found groups corresponding to a l l the l e v e l s of C-^ shown i n Figure 8.  59 His values for the relative intensities of the neutron groups observed in the direction of the deuteron beam are listed i n Table 1, although these are only a qualitative indication of the relative total yields; since the lower energy groups were found to be strongly peaked i n the forward direction. Burke, Risser and Phillips (1954) found an indication of a very low, broad resonance i n the neutron yield at a deuteron energy of 0.9 Mev.  Other than the weak resonances noted i n the proton and  neutron excitation curves, both reactions appear to be stripping processes even at bombarding energies less than 1 Mev. The energies of the gamma rays following emission of a proton or neutron have been measured by several investigators, principally with magnetic pair spectrometers. Their results are presented i n table form by Ajzenberg and Lauritsen (1955, 1952). The recent work of Bent, Sippel, and Bonner (1955) was reported after the experiment discussed here was completed. For comparison their results are listed i n Table 1.  60 2. The Three Crystal Spectrometer Scintillation counters, particularly with thallium activated sodium iodide crystals, have made possible gamma ray spectroscopy with fair resolution even when the gamma ray intensity i s very low (Hofstadter, 1948j Griffiths, 1955). While the resolution i s not as good as that of magnetic pair spectrometers, the efficiency may be greater than 50%, depending on the gamma ray energy and crystal size. The relationship between the gamma ray energy expended i n the crystal and the charge collected by the anode of the photomultiplier i s accurately linear i f reasonable care i s taken i n mounting the crystal and adjusting the photomultiplier electrode voltages (Griffiths, 1953). Thus a record of the peak voltages of pulses from the photomultiplier may be interpreted as the spectrum of energies dissipated by gamma photons i n the crystal. With crystals of normal size (l 3 A dia. x 2" long) and M  gamma rays i n the energy range 2.5 to 10 Mev, the pulse height spectrum corresponding to a single gamma energy contains three peaks. The peak of greatest pulse height corresponds to the total gamma ray energy, expended i n the crystal by the photo-electric effect, and by secondary processes when Compton scattered photons and annihilation photons do not escape from the crystal. The two peaks at smaller pulse heights correspond to one or both annihilation photons escaping from the crystal when the positron from a pair creation event annihilates with an electron i n the crystal. These two peaks are superposed on a very broad peak due to Compton events (Griffiths, 1953). While the three uniformly spaced  61  14  121  CO Q  Z , «*IO  Eg = 0.95 Mev, 230 miorocoulombs.  CO  D  O I  I-  i I 8  J UJ  z z  2* o  X  Ul CO  I-  z  .§21 P U L S E HEIGHT, V O L T S 14 0 6 T" 2  6  T  20-26 L _  8  10  * 32-50 O^Q—CL-O—O  26-39 12  CHANNEL  14  16  ~T~" 18  -J 20  NUMBER  Fig. 9. Single crystal spectrum from B + D. 10  22  61 peaks are often useful for calibration purposes, when the spectrum under investigation contains several gamma rays considerable confusion can result from the multiplicity of overlapping peaks. If neutrons of an intensity similar to that of the gamma rays are produced i n the same reaction, a large background tends to obscure 127 the gamma ray peaks. This is due mainly to neutron capture by I ' i n the crystal, which results i n the prompt emission of gamma rays i n the energy range 4 to 6 Mev, followed by 2,0 Mev beta decay, or 1,6 Mev beta decay coincident with a 0,4 Mev gamma ray (Griffiths, 1953), The beta decay half-life i s 25 minutes, A typical single crystal spectrum obtained from deuteron bombardment of  i s shown i n Figure 9,  The three crystal pair spectrometer, at the expense of a factor of approximately 103 i n efficiency, completely eliminates the first difficulty mentioned above, and reduces the second to a level tolerable i n most experiments. The principle of the three crystal spectrometer has been discussed by several authors (Hofstadter and Mclntyre, 1950; Griffiths and Warren, 1952; West and Mann, 1954), as well as i n the introduction to this thesis. The spectrometer used i n the present experiment differs i n detail, but not i n principle, from those described by the above authors. Figure 10 i s a block diagram of the complete spectrometer, excluding the high voltage and "B-plus" supplies. A detailed description of the components i s to be given elsewhere (Chadwick, 1955). The side channel differential discriminators were adjusted to pass pulses corresponding to 0.51 Mev annihilation quanta by placing a Na^2 source near each side crystal i n  63  CATHODE  6342  FOLLOWER  DIFFERENTIAL DISCRIMINATOR  6342 COLLECTOR  ^  FOLLOWER  FOLLOWER  I 2x^x5 SIDE  DIFFERENTIAL DISCRIMINATOR  4  CATHODE  CATHODE  TRIPLE COINCIDENCE MIXER  I  GATE PULSE  DELAY  CRYSTAL  3  FOLLOWER  DYNODE  5  CENTRE  CATHODE  6342  GENERATOR  cms.  CRYSTAL  l " x l^'dlam.  BIASED AMPLIFIER  Power supplies are not shown.  AND  GATE  I  V  KICKSORTER  F i g . 10. Block diagram of the three crystal spectrometer.  62 turn, displaying i t s cathode follower output on an oscilloscope triggered by the differential discriminator output, and adjusting the top and bottom "cuts" until only the line corresponding to annihilation quanta remained on the oscilloscope trace. The performance of the spectrometer has been very satisfactory; its resolution was found to be about 4% at 6 Mev, as shown by Figure 11, an energy calibration spectrum of the 6.13, 6.94- and 7.1 Mev gamma rays from the 0873 Mev resonance i n F ^ p ^ T " ) ^ .  The resolution for the  2.62 Mev line from radio-thorium (shown dotted in Figure 12) i s 6.5%. Comparison of Figure 9 with Figures 12 and 13 shows that the neutron rejection of the spectrometer is very good indeed.  The pulse height  scales on the various spectra do not agree because different injection points for the calibration pulses from a standard pulse generator were tried, to avoid a troublesome drift i n the gain of the centre channel. Since two hours was the usual length of a B?- run, slow drifts caused a 0  considerable broadening of the gamma ray peaks. A change of only 0.5% in gain i s equivalent to a 40 Kev change in 7.5 Mevj this is of the order of the standard deviation i n successive determinations of the gamma ray energies. In the final set-up, although only the centre channel crystal and photomultiplier were outside the calibration loop, gain drifts persisted. Some correlation with ambient temperature was noted, but no attempt was made at temperature control. To reduce accidental coincidences, the side channel crystals were shielded from the target by 5 inches of lead.  63  6-I3MEV.  •i  Fig. 1 1 . Spectrum from F ( p , o c y ) o . 19  16  63 3. Experimental Procedure The targets, kindly supplied by the Isotopes Division, A.E.R.E., Harwell, were 100yxgm/cm of 95$ enriched B 2  backings.  10  on platinum  They were approximately 40 Kev thick to 1,5 Mev deuterons.  The target assembly shown i n Figure 5 was adapted to this experiment by clamping the targets to a copper blank on the target mount, and sealing off the D2O dispenser. No coolant was used, since some heating was desirable to reduce the build-up of carbon on the targets. Instead of the beam-defining s l i t shown i n Figure 5, a 3/l6" diameter stop was placed 6" from the target, reducing the gamma rays from G^(d p f  7^)0^  reaching the spectrometer from carbon on the stop. The spectrometer was located at 0° to the deuteron beam, the distance from the target to the centre of the centre crystal being 13 cm. To reduce the probability of overlapping pulses i n the centre, channel, i t s total counting rate was kept below 8000 pulses per second by using low beam currents, of the order of 5 micro-amperes. Because of the low efficiency of the spectrometer, 2 hour runs were needed to obtain statistical accuracy, and maintaining constant centre channel gain for this length of time was the greatest difficulty i n the experiment. Voltage calibration was accomplished by inserting pulses of accurately measured height at some point i n the centre channel circuit - i n the later runs, at the grid of the cathode follower. By adjusting the gain and bias of the amplifier (actually two amplifiers i n series), the desired range of pulse heights was made to cover the 30 kick-sorter channels.  This setting was checked at the beginning and end of each  64  309 I40l  2-62  MEV.  MEV.  \Z0\  UjlOOf  2  = 1.40 Mev, 3300 microcoulombs.  < X  The dotted curve i s the spectrum from Radio-thorium.  o 80 or  UJ CL  0) 6 0 l 2-57  4-56  MEV.  3  o  I  40  O  MEV.  A J  495  MEV. 5-26  PULSE HEIGHT-VOLTS H-97  T~ U 1 T —r~ 18 10 12 14 16 20 E i g . 12. CHANNEL Spectrum fromNUMBER BlO + D, 2.0 to 5.5 Mev.  8  1  22  I  24  26  MEV.  14-12 28  X  64 two hour run.. Gamma rays of known energy were used for energy calibration, usually those from F (p, ol / ) 0 19  thorium (2.62 Mev).  1 6  (6.13, 6.94, and 7.1 Mev) and radio-  This was repeated at least twice each day, two or  more B-- runs intervening between calibration runs. To check the 1 0  linearity of the centre channel gain, several other energy points were used occasionally.. The centre channel could be operated as a singlecrystal spectrometer by disabling the gate, permitting determination of the photo-electric peak of the 2.62 Mev line from radio-thorium, and those of the 0.51 and 1.28 Mev lines from Na . 22  This was not repeated  often, as the linearity was always very good, at least as far as 7 Mev. Checks with the 17.6 and 14*8 Mev gamma rays from the 440 Kev resonance in Li^(p, /)Be indicated that the gain was linear to 17.6 Mev, but the 8  peaks were broad and asymmetrical due to Bremsstrahlung losses and wall effects i n the rather small centre channel crystal. Even though power supply and heater voltages were stabilized and mfcnitored, small gain drifts persisted. The practice was adopted of reading off the kick-sorter channel registers three or more times during a run, without stopping the run. If i t appeared that gain drifts were occurring, the run was rejected and the voltage calibration repeated before starting another run. In analyzing the results, i f the peaks i n a particular spectrum were abnormally broad, the spectrum was not used in determining the gamma ray energies. If the peaks of a spectrum were of normal width, but the energies of a l l gamma rays determined from the peaks deviated i n the same direction from the respective mean values of other determinations, the energy scale was "normalized to the mean 11  value for the energy of the most prominent gamma ray present i n the  65  PULSE  HEIGHT - VOLTS  1228  i  8  IO  1448  1  12  1—i  1  14  16  CHANNEL NUMBER  Fig. 13. Spectrum from B  1 0  1643  1  18  1  20  +• D, 4 . 0 to 6 . 5 Mev.  L-r 22  18-76  1  24  1  26  U — 28  spectrum, but this procedure was only necessary for one spectrum retained i n the final analysis.  66  = 1.40 Mev, 19,300 micro coulombs.  2801  240  LU  Z200I  Z < X  7-29 MEV  (J £160  a. CO h-  2 120  ID o o  80  40  I4O0 I  2  T  4  16-27  -i 8  J  10  PULSE HEIGHT-VOLTS 18-47  1 12  20-61  I  r 14  16  CHANNEL NUMBER  18  20  Fig. 14. Spectrum from B +- D, 4.8 to 7i5 Mev. 10  22  22-75  ~~r~ 24  26  28  66 Lm Results and Discussion T y p i c a l spectra, obtained at 0  6  to the 1.4 Mev deuteron  beam, covering the range of gamma ray energies from 2 to 9.5 Mev, are shown i n Figures 12, 13, 14, and 15.  The peaks are l a b e l l e d according  to actual gamma ray energy, as experimentally determined, rather than p a i r peak energy.  The integrated beam current f o r each run i s indicated  i n the captions of the f i g u r e s .  D i r e c t comparison of i n t e n s i t i e s between  the various spectra i s very rough, because of the l o s s of target material during bombardment. The energies and r e l a t i v e i n t e n s i t i e s of the gamma rays assigned to t r a n s i t i o n s of B  1 1  and C  1 1  are l i s t e d i n Table 1.  assignments are indicated by arrows i n Figure 8.  The  The energy errors  l i s t e d i n the table are standard deviations of several determinations of each gamma energy, ranging from three determinations of the 4.75 Mev gamma ray to twelve of the 7.29 Mev gamma.  The measurements of Bent,  S i p p e l , and Bonner (1955), l i s t e d i n Table 1 f o r comparison, were corrected f o r Doppler s h i f t , whereas the present measurements were not corrected.  Doppler corrections f o r centre of mass motion: (for 1.4 Mev  bombarding energy and observation at 0 ° ) range from 28 Kev f o r the 4.46 Mev gamma to 57 Kev f o r the 8.87 Mev gamma, of the order of the standard deviations.  However, several of the neutron and proton groups  are emitted predominantly forward (Burke, R i s s e r , and P h i l l i p s , 1954$ Johnson, 1952; G.C. Neilson, private communication), tending to reduce the mean Doppler correction of the corresponding gamma r a y s .  67  6-51 MEV.  67  The relative intensities listed i n Table 1 were obtained by measuring the areas tinder the peaks in the spectra, subtracting a somewhat arbitrary background, normalizing to integrated beam current, and applying a correction factor for the variation of the pair cross * 1  section with energy. A correction, of the order of 30% for the higher energy gamma rays, due to Bremsstrahlung loss and wall effects in the centre channel crystal, has not been applied, since the uncertainties i n intensity were of this order. Agreement between successive runs was not good, due to loss of target under bombardment, and possible variations i n the distribution of the deuteron beam on the target, so the intensities from overlapping spectra were normalized by use of gamma rays common to both. A l l intensities in Table 1, including those of the proton and neutron groups, are normalized to be directly comparable. The gamma ray intensities of Bent, Sfcppel, and Bonner (1955) were measured for thick targets and 2 Mev bombarding energyj the difference in conditions perhaps explains why there is only qualitative resemblance to the intensities from the present experiment. The intensities of the proton groups listed in Table 1 were measured at 90° and 1.51 Mev bombarding energy (Van Patter, Buechner, and Sperduto, 1951); because of differences in the angular distributions of the groups, only qualitative comparison with the gamma ray intensities is possible. The difference i n intensity of the proton group, and gamma ray corresponding to the 4.46. Mev state in B?- may be explained by the 1  proposed cascade through this state from the 9.19 Mev state. Serious discrepancies arise for the three highest states at 8.92, 9.19, and  68  *  E  6- 76 6- 6 i  73 0  6- 75  to  4  7  7 Z9  ±  6 6 5  —  Z9? Q57  ii  ?./?•  928  E  •rel  X  1  — — — •— .— —  4 46 ± . 04 5". O J ± • O9  S.03  a.  •rel  X  — —  0  *  PROTON PRESENT WORK BENT et al.ti955) GROUPS  82 7 ±.o? 6-8 7 i . oz 4 7JT ± .03  ± .04 6- 7?  // 6  —  i  8-98  +  4.74  ± o+  5  5.5  72,  73 1  ±o  — —  0  6 4  E  1.9o 4  r  23  4-77 6.46  65  6-87  28  1-6  7 3?  !•?  1  7 Z  Z7  ±.o + ±•o7 8 62 ±07  rel  //  so io  SO 3  NEUTRON PRESENT WORK BENT etal.Ci955) GROUPS  4-  7^T  +  o3  6SZ  ±.o5  —  S~. 3 5 ± . OS  'rel  — — —  E  X  — —  l  rel  — — —  6  4- 74 ± .o 4  6.7  1Z  ± . 04-  12.  —  7. oi ± .o£  7  'rel 2.2 o.6 2  8  2-  O  /2-  6  2o  —  o 4  6  4- +  22 Table 1. Assignment of the gamma rays to levels of  •  — and 0  — —  68 9.28 Mev.  The 8.92 Mev ground state transition i s much weaker than the  proton group exciting i t , the 9.19 Mev state decays apparently only by a 4.73 Mev cascade gamma ray much less intense than the corresponding proton group, and no gamma rays were attributed to the 9.28 Mev state. There was some indication of a gamma ray of energy greater than 9 Mev in some early runs which suffered from poor resolution and gain drifts, but the efficiency was probably somewhat greater, due to broader side channels. These conclusions do not agree with the gamma ray transition scheme proposed by Jones and Wilkinson (1952) from measurements on the reaction Li7( ol , /) The 8.27 Mev gamma ray has been assigned to the 8.57 Mev state in B^-, although the energy discrepancy is three times the standard deviation of the energy measurements. This discrepancy may i n part arise from the low intensity of the radiation, and perhaps from conflicting counts due to 8.87 Mev photons which f a i l to produce the f u l l pulse height because of Bremsstrahlung loss and wall effects. A similar effect, though much smaller i n proportion, has been observed with the clean 6.13 Mev gamma ray from F^(p, ot / ) 0 ^ . The neutron group intensities i n Table 1 were measured by Johnson (1952) at 0° and 3.4 Mev bombarding energy; the difference i n bombarding energy and the strong forward peaking of some of the groups makes comparison with the gamma ray intensities rather hazardous. G.C. Neilson (private communication) has found that, at 1.5 Mev deuteron energy, the neutron groups corresponding to states i n C ^ at 6.46 and 4.77 Mev are much more intense than other groups, with the possible exception of the ground state group (not observed). Therefore, the  69  4-. 75 Mev gamma ray observed has been attributed i n part to the. ground state transition from the 4.77 Mev state in C , as well as to the 4.73 11  Mev transition between the 9.19 and 4.46 Mev states i n B . The 7.01 11  Mev gamma ray attributed by Bent, Sippel, and Bonner (1955) to the 6.87 Mev state of C ^ was not observed i n this experiment. A 5.35 Mev gamma 1  was assigned to the 5.49 Mev transition between the 7.39 and 1.90 Mev states, analogous to the 5.87 Mev transition from the 7.99 Mev state i n B^- reported by Bent, Sippel, and Bonner (1955), although comparison of neutron and gamma ray intensities i s not encouraging. Four peaks corresponding to gamma ray energies of 2.57, 3.09, 3.52, and 6.13 Mev have been observed (Figures 12, 13, and 1 4 ) . The 2.57 Mev gamma ray may be from the 2.38 Mev transition between the 9.19 and 6.81 Mev states of B-^.  Carbon accumulated on the target and beam  stop was responsible, through the reaction C^(d,p ^)0^ for the 3.09 f  and 3.52 Mev gamma rays, since their intensities were much smaller from a new target and freshly cleaned stop. The 3.52 Mev gamma ray, probably from the 3.68 Mev state of C^-, was seen only with very dirty targets, and had about one-fortieth of the intensity of the 3.09 Mev gamma. The excitation curve of these gamma rays also showed a resonance near 1 Mev deuteron energy, i n agreement with the assignment to C^. The 6.13 Mev peak may be attributed to the intense 6.12 Mev gamma ray from the reaction  Using the yield values given by Ajzenberg and  Lauritsen (1955) and assuming 1% isotopic abundance for 0^3, the 3.09 Mev gamma ray peak should have an intensity larger by a factor of 170 than that of the 6,12 Mev gamma, allowing for the energy variation of the pair  70  Ol 0-8  I  I O  L  1-2  I  1-4  I  1-6  BOMBARDING  I  1-8  I  2 0  E N E R G Y — MEV.  Fig. 16. Yield curves of the 6.12, 6.52, 6.78, and 7.29 Mev gamma rays.  L_ 2-2  70 cross-section. The intensity ratio of the two peaks was found by experiment to be approximately 60, fair agreement, considering that the intensity comparison was between different runs, so that the amount of carbon had probably changed. There may be some contribution to this peak from Bremsstrahlung losses and wall effects of the 6.52 Mev gamma ray, as discussed above i n connection with the 8.27 Mev peak. The relative yields of the 6.12, 6.52, 6.78, and 7.29 Mev gamma rays were determined at four bombarding energies between 0.8 and 2.2 .Mev.  The excitation curves, drawn i n Figure 16, differ in shape by  an amount l i t t i e , i f any, greater than the errors i n determining the relative intensities. The apparent maximum near 1.8 Mev i n the excitation curve for the 6.79 Mev gamma ray from B"^ may correspond to the 1.5 Mev resonance observed by Burke, Risser, and Phillips (1954) i n the proton yield.  The excitation curves indicate that the reactions are primarily  of a non-resonant character, probably Butler stripping. No evidence was found, either during the i n i t i a l single crystal survey, or in the later measurements with the three crystal spectrometer, of high energy gamma rays from deuteron capture by B , leading to 10  excited states of C .. 12  The excitation energy at a deuteron energy of  0.95 Mev i s 26.1 Mev, well above a l l single crystal background except cosmic rays.. Assuming that a total count three times background corresponds to the smallest detectable gamma ray intensity, and allowing for the severe Bremsstrahlung losses and wall effects, this indicates that the cross-section of B^Cd, / ) C at 0.95 Mev bombarding energy.  1 2  reaction i s less than lO"^ cm. 2 1  71 These results provide additional data on. the B  1 1  and C^- nuclei,  and in general confirm the mirror character, although, in addition to those discussed above, there are several conflicting details i n the data. The 4.23 Mev ground state transition i n G"^ should have been detectable, since the intensity should have been comparable to that of the 4*46 Mev transition in  The fact that gamma rays at 5.87 and 7.01 Mev  reported by Bent, Sippel, and Bonner (1955) were not detected i n the present work may be explained by the differences i n target thickness and bombarding energy, but this does not explain why they did not detect the 5*35 Mev gamma which was quite evident i n the present work. Measurements of the angular distributions of some of the gamma rays, for example of the 6.52 and 6.76 Mev gammas, could aid in comparing the mirror levels. Since i t has been found (G.C. Neilson, private communication) that the neutron groups are strongly peaked forward even at deuteron energies of 1.5 Mev, i t i s preferable to measure the gamma ray energies at 90° rather than at 0°, to reduce neutron background. The experiment reported here has demonstrated the usefulness of a three crystal spectrometer in accurate measurements of gamma ray energies i n an intense neutron flux.  72  APPENDIX A  SOLUTION OF THE RADIAL EQUATION The Green's function of equation (lb) i s (p. 516, Margenau and Murphy, 1943)  i h C28)  A and B adjust f ( f , ?') to satisfy the same boundary conditions as u^ (?). That i s ,  (2 7 )  f (?,?')  ^  e i 5 >  f  o  r  l  a  Using the asymptotic forms of ^  r  g  *  e  (°)  -  and  (?) *  e  2. i i(F-f)  *  +  A[-—^—J r +  Equating the coefficient of e.  I A  ±_  B  to zero,  ^  B - -^URV) - <  j  7  Solving ( 2.9) and (3 O) for A and B, and using the identities (equation 12) satisfied by H  and  ,  (30)  74-  Then SIX  Y  -fee L X / z £ (?)  9  + <^/z£C?;>]  X  / t i p '  /"* f  and as p —* oo, f  i(y - — )  75  (/-i-mm'UM)  2  m = 1  -j  /+ M + T  m'= - j /-M+F 2-^ + 1  7+M + l" 2/+ 1  2-/+I  (m+m' = M)  The symbol * indicates negative square root must be used.  Table 2. Clebsch-Gordan coefficients (X,i,m,m* J M) .  75  ( i i ' 0 1 LI)  The symbol * indicates negative square root must be used.  7  L  0.1  8  1  0,2 0.3 04 0.5 1,1 1.2  1 * *  _/_  1  z  Z  3_ /o  1.3 14  *  JL is  L  6 *-_8 Zt  /s  iz  28  /2  1.5 2.1  lo  2  to  /4-  2.3 24  A. 3S  J_  J5  7  *  7 _/£ £3  2.  *  zo  J  7 *  3 SS  II  *  7  3.3 *  3.5  81  S  66  770  4-2  66  7.73 O  66  /Q83  /fa  23/  *  *  8_ 63  4.4  *  /8  *  *  +6Z  45  4^  2 .  22  zooz  II  27 2 ©6  234  IZI /63Q  *  53  5.4  2S Z3t  * A 33  5 33  *  33  3_  s  II  zs * 17/6  Table 4.  81 57Z  2 65  z & 6  3_ -26  /?8 *  JL  78  J 7 _  *2? S S  40  / 4 3  *  693  SQS  *  /+3  46  98 4 n  2 7293  7  22  *  7 39  /3Z  /OS  SQ_  2  5.2  33  IS  _3£ 7*7  7  /?8  /Z6  -*  3  /3> 27  J-  j_  -L Z  5" I  1+  19*  /ooto  4.1 42  22  2£  6  _S 4-2  60_  130 7  8. 2/  '4-  3 0  42  2  s_  ^2  3S  ]_±_ 33  JfS  z  43  3. £ 8  2Q9  iZ  25  42  3*1 66  -L  2.  /  2.2  3.4  *  24.  ^5  32  8  /  33  Clebsch-Gordan coefficients  1+3  + _7S . S7Z *2  I  39  ± 8  JL 32  33 {J?,/,0,1  6+S  2% 172  L 1)".  189 S1Z  *  4-9  572  4 243/ 78  U/oo|i_o) 0,0 1,1  *  12  10  8  2 J  _L 3 *  /  2 7  S  *  / 7  *  /8 35" /OO  J±  2/  77  /  /oO 4?3  /62  /  So  4,4 5,5  6  1  2,2 3,3  4  2  0  :  //  /  6,6  I&3  /J  O  99  /8  8Q  /43 2 Si 2431  /4-  ¥r  •** 2  ooi  /  *  23/ /Z87  Sbt  *  79 3  * 490 2 7/7  80  «3J"o 2 7/7  3SS"3  8 *6/89 Z7 3 92 96S77  * /^"8 76 96S77  0,2 0,4  1  J  0,6 1,3  7  7  1,5  l  *  2,4  7  ¥*  3,5 4,6  23/ 2>" /-f 3  *  3  0,1 0,3  77  •  //  *  1,4  63"  s4  33  Zo  /43 * 5^>4271 7  28  /+*  7  /+ o <+/99 7  9  I  3 3"  2 5  /4 ss * 7  5  ;  0,5  s  9  •  7  _7_  1,6  9 33"  1o 21  IS  2,5  /o  *"  *  33  3?  *  Z //  4. 2/  /OO  *  20  /43  The symbol *" indicates negative square root must be used. Table  -  *• /o  33  3,6 4,5  ZO  t&O JOOI  .TO  1  3,4  .  *  2,6  1,2  //  <  ZO 9/ 7  39 2 /3  / 4 J  I7S *  64  so*  243I  ¥• /4 o o' 72 93  22/ 882 243/  [(#OO|LOH//OO|LO)] 3.  Clebsch-Gordan coefficients  (i,^',0,0  L  0) . 2  75  APPENDIX B  CLEBSCH-GORDAN COEFFICIENTS 1. In deriving equation (2,  coefficients of the form  m, m* | J M) are inserted as functions of L . These are given  in Table 2 (taken from p. 792, Blatt and Weisskopf, 1952). 2. In calculating the functions of k(6)  and B(#) needed  in equation (Z6), the coefficients ( I , i , 0,o| £ 0), 1  0,l) Ll)  are needed. These are tabulated i n Tables 3 and 4» Some of these are taken from the tables of Sharp, Kennedy, Sears and Hoyle (1953), Others are calculated from formulae of Condon and Shortley (1935), Falkoff, Colladay, and Sells (1952), and Hess (1955)*. N.B. In the tables the squares of the coefficients are listed. An asterisk before a number indicates that the negative square root i s to be taken.  The author wishes to thank Mr, Hess for making these formulae available prior to publication.  76  APPENDIX C  EVALUATION OF THE FUNCTIONS OF k(6 ) AND B(6) IN THE EXPRESSION FOR 0- (0.T?)  A(8 ) and B(6 ) are defined by: oo -t-0  *  OO  H^ (b) may be evaluated directly, since  H»  77 Then 2  £  and  <jfl>) - i -  ax  (b) i s calculated from recurrence relations:  (34-)  It can be shown (p. 136, Watson, 1945), that  (<J + yU + V) J f  CJJ, ( ? ) Cj,C9) d o  where C and C are any cylinder functions. Let g = -1,  = ^ =  -  J. or  V*.  ,  C and C = J :  b5  79  Similarly,  '  The series for B(6 ) converges very slowly, so that i t i s necessary to obtain an approximate closed form for the sum of high order terms. As  increases, H. — > 0 and G  > 1, hence  S.  > • K ,  From (3J"),  Let -4 be the lowest value of J , for which (36) i s true to the desired degree of approximation.  Then  80 +l)K^ . Then, putting (3 7 ) i n (3Z),  where a. = >4( A  i Tg, may be written i n one of the forms of the Laplace integral (p. 127, MacRobert, 1948):  T j (cos  6)  =  ~~1T~  I Ccos 8 -  cosCp  L S>n Vcostf)  cLlj  .  Substituting i n the second sum i n (3 3),  X  ]_  7  zi+i  ^(Jt+i)  w . £  _ t- v  Uosd) -  7f/  7  ilii ^ X  t JCtosd - L  sindcos(f)tosjfdy, (39)  where z = cos & - isin^cos y . Since )z) <. 1 when d fi 0, the power series i n (37) are absolutely and uniformly (in terms of (f ) convergent, and the interchange of summation and integration is permissible, provided that 8 differs from zero by a finite amount. The sums are:  81  Z  \  7  \ i-  i~z.  z  f  z  *  \—  z  Substituting these values i n (37), and rewriting the finite sums i n terms of associated Legendre polynomials,  (The only term with 2 = 0 vanishes, since  / l,cosy &</ = 0).  The evaluation of the integral 1(8 ) i n ( + °) i s straightforward. Inserting the expression for z i n terms of 6 and integrating the log term by parts, 1(8) becomes:  lid)  -  / J  ^  w  ^ " isin8sm (p) z  -• Cos d +  L5m6cosg>  d ( f  </ , and  When numerator and denominator are multiplied by the complex conjugate of the denominator, and the parts of the integrand antisymmetric around tr/Z are dropped,  1(e)  (1- cos  -  &)5in tf] IL  sm^d cos*  or  TT sin  cot  6  J2 z  (41)  Substituting (4-0 and (4°) i n (38),  3(0)  = )  '  [{ui+l)[$a)  J^Tnl^U^O)} (4 2 )  +  d col -  •  Numerical calculation of the cross-section as a function of angle i s aided by application of the relation (equation 2.3, Blatt and Biedenharn, 1952),  83  ^  -£+ -t'  X  ( 1 , 1 O , O IL O )U  *-m,  L  m' \ L Tl) \  .  n  (6, if),  giving for the corresponding products of associated Legendre polynomials the relations  si + r}(co.^(co-(7)  = )  J,'  ^(//OjOlLo/frtoafl,,  ,U,Ao,o\io)Ual-ij\L  o)v uosd), L  84 and  A + JL'  i  X  A  /  .  /  •  .7? (cos  U i , o, ol L o)U, ^, o, 111 i)  [ L ( L+  fl) L)  ]k  Then the necessary functions of k(6 ) and B($) become: 24  , -4  L-O  t ^  + ^^^(2 ^  X  where i  x  *  =  0  2)7? R GO)  'jz/+1  e  )R* \L  (b)[uX  4  i s the value of 1< after which the terms i n A.( 6 ) may be  neglected to the desired degree of accuracy;  o, OIL  0)f  A  85 |B(*)f  =  dL*cot*f  + £ d cot |  X  +::terms negligible to 1$ of 0"~($,ri) i n the case considered here;  a. cot * ^-o  A \  + 4,  t 7  "PL (COS  ^  0,  \  '  x  L  86  A(e)ImB(0)= 2  it*+ 1)1*^)  >rio #2 +  X  X J'=  1  flm^(b)  X  ~  J^ j{iJ O,Q\Lo)Uj\o^Ll\, l  f  The necessary Clebsch-Gordan coefficients are tabulated i n Appendix B, If a coefficient appearing i n the above expressions does not appear i n the tables, the corresponding term is negligibly small» For neutrons of 3.1 Mev scattered by lead, the parameters i n expression: (2.6) for <r~(6, la ) have the values: k = -28%. = 3.85 x 1 0 cm.", 12  1  R = 7.8 x l O " ^ cm. (p. 482, Blatt and Weisskopf, 1952), b  = kR = 3.00,  € = 2 I u |^ = A.81 x lO" ^ cm., / n. 2 mc 1  87 -ik  = 6.75 x 1 0 "  26  cm. ,  £  = 1»25 x 1 0 "  26  cm. ,  =  2 8  cm. .  2  2  k  4  5.78 x 1 0 '  2  2  A conservative value of J  x  for 1% accuracy i s -4 = 4, since  H§(3)  = 5 x 10"^ + 7.3i x 10"^ , negligible compared to  Hi(3)  = .968 - .1761. The value - 4 = 5  very well, since ^-L K5X3)  satisfied equation (36 )  = .01203 compared to the value .01205  6 2_ +  calculated from equation (35) • However, A = 6 has been used, since the term  2^5(3)05(3)0*5(3) contributes 5% to the value of 85(3).  constant a = A ( X  The  + l)K^(b) then has the value 0.506.  o — ( ^ , H) i s plotted i n Figure 3 for |1? | = 1 and "n parallel and antiparallel to P*, that i s , for "right" and "left" handed scattering of 100% polarized neutrons.  88  APPENDIX D  A PROPOSED EXPERIMENT: THE MEASUREMENT OF NEUTRON POLARIZATION BY SCATTERING IN. HELIUM Schwinger (1946) has suggested investigating neutron polarization by scattering i n helium. The wide splitting of the P>  2  - P> 2  doublet i n He^*(Ajzenberg and Lauritsen, 1955) indicates  strong spin-orbit coupling, which i n turn should produce polarization sensitivity i n the scattering of neutrons by He^.  The analogous case  of proton scattering by He^ i n the energy region of the Pj, - P 2  2  3  doublet i n IS? shows strong polarization sensitivity. Double 90° scattering of a proton beam i n He^ shows an asymmetry ratio> of 1.9 i n the second scattering (Heusinkveld and Fjjier, 1952). This scattering reaction has been used successfully to measure the polarization of protons from the reaction D(d,p)H^ at 300 Kev bombarding energy (Bishop, et al,, 1952b). In the case of neutron scattering, relatively high detection efficiency can be obtained by detecting the recoil alpha particles rather than the scattered neutrons, at least at higher neutron energies. Preliminary design of the detector, and an approximate calculation of the expected yield i n the case of neutrons from D(d,n)He^ at 600 Kev bombarding energy have been carried out. The numerical values are taken from the results published by Adair (1952), and Seagrave (1953), The experiment i s a possible check on the qualitative experiment of  89  ANODES OF-COUNTERS 5 MIL. TUNGSTEN WIRE MOUNTED ON KOVAR SEALS  ^  ^  ^  LEAD  ^  ^  © r/s////y////Ar/s///jy^^^^ 3 CMS.  0 _ _ _ 5  HEAVY.ICE TARGET  I CM.  st_  TRIPLE PROPORTIONAL COUNTER 5 CMS. DEEP -rs" BRASS. 16  CMS:  0  COLLIMATING GRIDS V BRASS 9  AS MANY^" DIAM. HOLES AS POSSIBLE, INCLINED 4 5 ° TO FACE OF GRID.  Fig. 17. Proposed fast neutron polarimeter.  89 Ricamo (1953b), i n which the neutrons from D(d,n)He3 are assigned a polarization P > 20% from measurements of scattering by C  1 2  .  Figure 17 i s a schematic diagram of the apparatus. Three helium-filled proportional counters are constructed i n a single cubic chamber surrounded by a lead-lined paraffin collimator and shield. The output pulses of the three counters are fed to two coincidence mixers, so that the coincidence rate of each outer counter with the central counter i s measured. The collimator, by allowing neutrons to impinge, only on the central counter, reduces the accidental coincidence rate. The counters are separated by grids which pass only alpha particles scattered within cones described by 6 = (45 * 10)°, and 6 =  (45 ± 10)°, Lf =  (-90  Cf = (90 * 10)°,  * 10)°, where 6 and (J> are respectively  the polar and azimuthal angles of the recoil alpha particles in the laboratory system (Figure 17). .Smaller deviations than 10° from the median values have equal probability, so that errors introduced by assuming 6 = 45°,  = i90°, can be shown to be less than 5%,  0 and (j i n the laboratory system are related to the corresponding angles i n the centre of mass system by @Xab  = y c.m.*  Cj>  C* 1  1636  =  \ @ c.m. *  relations apply to recoil particles i n  elastic collisions, regardless of particle masses and bombarding energy). Thus, for the situation specified above, 0 y>  c # m #  =  c # m <  = 90°  and  *90°. The left right asymmetry ratio i n scattering, and  hence i n the two coincidence rates, i s R =  *p-p  » where P i s  the neutron polarization and P i s the polarization which would be 1  produced by 90° scattering of an unpolarized beam of neutrons  90 (Adair, 1952). For 30J6 polarized 3 . 3 Mev neutrons, R has the value 1.27. Since the differential scattering cross-section of 3.3 Mev neutrons for  - % i s 0.15 barns/steradian, a neutron flux of  2 x loT/steradian/second produces 150 recoil alpha particles per minute for the geometry of Figure 17, when the counters are filled with l/2 atmosphere of helium.. The two coincidence rates are then 1^0(1 + PP»)  = 85/minute and 1^(1 - PP ) = 65/minute, assuming 1  there i s complete transmission of recoil particles; through the collimating grids. A realizable transmission factor i s 0.25, giving 2l/minute and 16/minute for the coincidence rates. A forty minute run i s then expected to produce 850 coincidences on one side and 650 on the other, a statistically significant result. The pressure of helium i s chosen to permit recoil alpha particles to reach the outer counters with detectable energy. recoil energy  E  E  r  e  c  rec.  <  i s related to the incident neutron energy  = 7  2mjm2  Tn  +  Since the E  i  n  c  #  by  /D £/c.m.) inc. »  0 0 8  E  where m-j_ and m^ are the masses of the neutron and alpha particles respectively,  E  r  e  c  #  =r  1.05 Mev when  The longest recoil path i s (3 + l) J~2  (?.m.. = ^ and c  -  E  i  n  c  #  = 3.3 Mev.  5.6 c.m. Using the values of  Livingston and Bethe (1937) for the range i n air, 0.59 cm., and stopping power of helium relative to air, 0.42, the range i n one atmosphere of helium i s approximately 2.8 c.m. Half an atmosphere of helium thus matches the neutron energy to the geometry.  9i:: • An asymmetry produced by faulty construction of the apparatus can be cancelled by inverting the counter assembly and repeating the run. Variation i n neutron intensity across the central counter due to non-isotropic neutron angular distribution should produce no asymmetry in the coincidence rates, but this can be checked by a run at the opposite 39 position. d  This apparatus i s adaptable to other neutron energies by varying the helium pressure, since the required geometry i s independent of neutron energy,. At lower energies, the low pressure necessary decreases the efficiency, and there may not be sufficient ionization to produce detectable pulses. Furthermore, P  1  changes rapidly, becoming  zero at 2.4 Mev, (Seagrave, 1953), eliminating the polarization sensitivity.  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