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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'OB11 AND B ^ ^ n O C 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 is observed in 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 with deuterons of several energies between 0.8 and 2.2 Mev. Gamma rays of energy .^46 * .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 in B 1 1 and C^, with excellent agreement in almost all 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 BU}(d,p1*)BLl and B ^ ^ n ^ ) C n are primarily of non-resonant character, at least in 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. (British Columbia) 19I4.8 M.A. (British Columbia) 1950 on Friday, August 5, 1955 at 10:30 a.m. in Room 303, Physics Building Committee in 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. Hull E.V. Bonn External Examiners - R.F. Christy T. Lauritsen California Institute of Technology LIST OP PUBLICATIONS Primary Specific Ionization of Electrons in some Gases, Transactions of the Royal Society of Canada, 1 9 5 " 3 , Abstract # 6 9 , (Co-author J.B. Warren). The Elastic 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 1 0(d,p^)BH AND B 1 0 (d,n?»)Ci:L Detailed calculations have been carried out which indicate that the small-angle scattering of fast neutrons by lead depends on the polarization of the neutrons. When the scattering of neutrons whose spin vectors point upward is observed in 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 " intensity ratio of l l4 . .5:l 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 B with deuterons of several energies between 0 .8 and 2 .2 Mev. Gamma' rays of energy lj..lj.6 ± ,0k, k*l$ ± . 0 3 , 5 .03 1 . 0 9 , 5.35 ± . 0 5 , 6.52: ± . 0 5 , 6.78 ± . 0 7 , 7.29 1 .Oil., 8.27 - . 0 9 , and 8.87 - .02 Mev have- been assigned to transitions in B 1 1 and C » with excellent agreement in 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 1 0(d,p^)BH and Bl0(d,ny)cH are primarily of a non-resonant character, at least in this energy region. GRADUATE STUDIES F i e l d o f s t u d y : P h y s i c s Quantum M e c h a n i c s Q u a n t u m ' T h e o r y o f 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 S p e c i a l R e l a t i v i t y T h e o r e t i c a l P h y s i c s S e m i n a r T h e o r y o f t h e 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 C h e m i c a l P h y s i c s N u c l e a r P h y s i c s T h e o r y o f Measurements E l e c t r o m a g n e t i c T h e o r y E l e c t r o n i c s G . M . V o l k o f f F . A . K a e m p f f e r G . M . V o l k o f f W. O p e c h o w s k i ¥ . O p e c h o w s k i H . Koppe J . B . W a r r e n A . J . D e k k e r K . C . Mann A . M . C r o o k e r G . L . P i c k a r d F . K . Bowers O t h e r S t u d i e s : F u n c t i o n s o f a Complex V a r i a b l e F u n c t i o n s o f a R e a l V a r i a b l e I n t e g r a l E q u a t i o n s N o n - l i n e a r M e c h a n i c s O p e r a t i o n a l Methods i n E n g i n e e r i n g W. H . S imons D . C . M u r d o c h T . E . H u l l E . L e i m a n i s W . B . C o u l t h a r d AOKNOWLEDGEMEMTS I take great pleasure in acknowledging the guidance and encouragement of my supervisor, Professor J. B. Warren, during the period the research presented in 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 Title £ags I INTRODUCTION 1 II THE SCATTERING OF POLARIZED NEUTRONS. 6 1. Polarization in Nuclear Physics 6 (a) Electrons 6 (b) Gamma Rays . . . . . . . . . 9 (c) Neutrons, Protons, and Deuterons . . . . . . 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 . . . . . . . . . . . . . 49 (d) Experimental Procedure and Results . . . . . 51 III GAMMA RAYS FROM THE BOMBARDMENT OF BORON TEN WITH DEUTERONS 56 1. The Mirror Nuclei B 1 1 and C 1 1 . . 56 2. The Three Crystal Spectrometer 60 3. Experimental Procedure 63 4. Results and Discussion . 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(<? ) . . . 76 APPENDIX D ' A PROPOSED EXPERIMENT: THE MEASUREMENT OF NEUTRON . . POLARIZATION BY SCATTERING IN HELIUM ........ 88 BIBLIOGRAPHY 92 LIST OF ILLUSTRATIONS Number Subject On or Facing Figures £sg§ 1 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 •• 4-7 6; Plate-holder Mounting 50 7 Angular Distribution of Collimated Neutrons . 55 8 Energy Levels of B 1 1 and C 1 1 . . 57 9 Single Crystal Spectrum from B 1 0 + D . . . . 61 10 Block Diagram of the Three Crystal Spectrometer 62 11 Spectrum from F 1 9(p, oc » )o 1 6 .63 12 Spectrum from B 1 0 + D, 2.0 to 5.5 Mev . . . . 64 13 Spectrum from B 1 0 + D, 4..0 to 6„5 Mev . . . . 65 14 Spectrum from B 1 0 + D, 4.8 to 7.5 Mev . . . . 66 15 Spectrum from B 1 0 + D, 6..5 to 9.0 Mev . . . . 67 16 Held Curves of the 6.12, 6.52, 6.78 and 7.29 Mev Gamma Rays . . . . . . . . . . . . . 70 17 Proposed Fast Neutron Polarimeter 89 On or Facing -Tables: ^M* 1 Assignment of the Gamma Rays to Levels. of B*1 and C 1 1 68 2 Clebsch-Gordan Coefficients. (#> 1/2, m, m' | JM) 2 75 3 Clebsch-Gordan Coefficients ( V > , o, o (LO) V 75 4 Clebsch-Gordan Coefficients (ft, V, o, 1 | LI) 2. . 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 intrinsic 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. If 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 in 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 in some scattering reactions, for example proton scattering by He^ , is polarization dependent. Most of these scattering reactions are resonant, so that their usefulness is restricted to a small energy range. Schwinger (1945) has suggested a non-resonant neutron reaction which is 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 in that the polarization dependent term is 25% larger. While the differential scattering cross-section is large, i t is 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 fifty percent. Maximum polarization should occur at about 600 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 is bombarded with deuterons, the dominant gamma ray producing reactions are B 1 0 (d,p?)BH and B 1 0 (d,nlOC U , occurring simultaneously. Bll and are mirror nuclei, that is, they differ only in the interchange of a proton for a neutron. If, as commonly postulated, the force between a pair of neutrons is the same as that between a pair of protons (except for the Coulomb force in 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 in the case of 0 ^ . A measurement of the energies of emitted gamma rays enables tentative assignment of the energy level schemes, which in turn allows a check on the charge symmetry postulate. A sodium iodide scintillation counter produces an electrical pulse, the magnitude of which is proportional to the energy of the incident gamma photonj i t is a gamma ray spectrometer of high efficiency and fair resolution (Hofstadter, 1948). Because of the three common ways in 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 in 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 spec-trum. If several gamma rays occur in an energy interval, the resulting pulse height distribution is difficult to interpret. If neutrons are produced in the reaction under investigation, a large background spectrum, approximately exponential in shape, is added to the gamma ray spectrum. By sacrificing efficiency, i t is possible to avoid the difficulties mentioned above for gamma energies at which pair production is 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 in time is 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 is 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/cm2) of Boron enriched to better than 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 in Nuclear Physics Specification of position and velocity vectors does not in general completely describe the motion of electrons, protons, neutrons, photons, and nuclei in their ground states. A further degree of freedom, necessary to explain the results of many experiments, is interpreted in terms of the orientation of the intrinsic angular momentum vector, or spin, of these particles. A restriction of this degree of freedom is said to cause polarization or alignment of the particle under discussion, depending on the type of particle and the symmetry of its 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 in several cases to be polarized; measurements of the polarization can provide information about the nuclear energy levels involved, and, in the case of nuclei containing few nucleons, aid in 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, in units of ^ , is l/2, an attempt to measure the spin component in 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 is more probable than the other, the electrons are said to be polarized. There is a direction of maximum difference in probability of the two values, and the polarization vector is defined as lying along this line in the direction of the most probable value, with magnitude equal to the difference in probability. The percentage polarization is 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 in the 3d subshell are aligned in 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 is a function of the initial 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 in gold foils. The 12% asymmetry of the second scattering is in 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 in 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 in the second scattering. The ratio of precession frequency to cyclotron frequency is equal to l/2 of the gyro-magnetic ratio. While the reported measurement, 2.00 * 0.01, is not sufficiently accurate to show the expected radiative correction (Schwinger, 1948a), the method may yield more precise measurements in the future. Electrons and positrons from allowed transitions of aligned nuclei (subsection (d)) may be nearly 100% polarized when emitted in 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 in magnetized iron foils, may make possible investigation of nuclear alignment where no other method is available, as well as of the interactions postulated in the theory of beta decay. If beta decay is followed by emission of a gamma ray, i t is possible that the polarization of the beta particle is 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 is not as simple as in sub-section (a). Following classical electromagnetic theory, a beam of photons is 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 is convenient in calculating distribution and correlation functions to define a polarization vector which does not lie in 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 in 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 in 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 its 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 2# cos2^7 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 is 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 is 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 in the azimuthal distribution of pairs around the direction of the incident photon for several geo-metrical 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 in the radiator; he found, in fact, an anisotropy opposite to that found by Berlin and Madansky. Wick's calculations, in turn, are unsatisfactory because they were based on an approximate expression for the pair cross-section. Although the theoretical situation is not clear, and the experimental difficulties involved are great, pair production is 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 sin2^cos2y = sin^X. N( 6,y ) is the number of neutrons or protons per second ejected in 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, is dominant (Feshbach and Schwinger, 1951). When the photon energy is 3.0 Mev, the magnetic dipole cross-section is 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 is 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 pro-ducing reaction. Despite this, i t is 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 neutron-proton 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 foil has a circularly polarized component, the forward scattered electron intensity changes when the direction of magnetization 13 of the foi l is changed from parallel to the photon propagation vector to antiparallel. Clay and Hereford (1952) have reported an effect of this kind in connection with annihilation photons. Because approximately two of the twenty-six electrons per iron atom are polarized by magneti-zation (Halpern, 1952), the effect is 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 is 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 in opposite directions when a positron annihilates with an atomic electron. Since annihilation in most materials is almost completely from a 2S state (Deutsch, 1951), conservation of angular momentum demands that a pair of annihilation photons be in opposite polarization states, that is, plane polarized perpendicular to one another (Snyder, Pasternack and Hornbostel, 1948), or circularly polarized in the same sense (since the photons proceed in 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 in 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 relat ive circular polarizat ion of pairs of annihi lat ion photons. Their method consisted of measuring the change i n coincidence rate of two counters detecting electrons scattered forward from i ron f o i l s by the photons when the directions of magnetization of the f o i l s were changed from para l le l to ant ipara l le l . In calculating the expected resul t , they have mistakenly assumed that the quanta are polarized oppositely, (see footnote 1, Bleuler and ter Haar, 1948),. and yet their experimental result agrees qual i tat ively with their calculations. In any event, Vlasov and Dzhelepov (1949) have concluded that the most probable, i f not the only possible, mode of polarization of annihilation quanta i s mutually perpendicular plane polar izat ion. A correlation between the l inear polarizat ion of one quantum and the directions of the other two i s expected i n the case of three-quantum annihi lat ion 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 perpen-dicular to the plane of the three. The measurement of Leipuner, S iegel , and de Benedetti (1953) corroborated th i s . In some nuclear reactions, especial ly radiative capture of a par t ic le , the polarization of the emitted gamma rays i s expected to be correlated with direct ion of the incident beam. Wilkinson (1952) measured the polarizat ion of the gamma rays from the reaction D(p,7*)He3 by exposing deuterium-loaded emulsions to the radiation and determining the angular distr ibut ion of proton tracks from photodisintegration normal to the direct ion 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 for a l l directions 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 is 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 difficult. 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 multi-poles (Ling and Falkoff, 1943). However, a measurement of the angular 16 correlation of the polarization of the two gamma rays in 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 is 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 polarization-polarization 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 1 2^ . 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 in the reaction F 1 9(p, * ^ O 1 6 is electric, that is, that there is a parity change in the gamma transition. Since the ground state of O1^ is known to have even parity, 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 is 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)) in the description of their spin states, so percentage polarization may be defined in the same way as for electrons. Because they react with nuclei at low and intermediate energies, polarized protons and neutrons are of greater interest in 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 in the classification of nuclear energy levels as to spin and parity, and in 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 in 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 is magnetized normal to the beam direction than when i t is 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 is achieved. Furthermore, unless the nuclear and magnetic scattering amplitudes are equal, complete polarization is 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 Stern-Gerlach experiment, deflecting the neutrons in an inhomogeneous magnetic field. This information has been used in 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 little experimental work. The most comprehensive theoretical treatment is that of Simon and Welton (1953, 1954), generalizing that of Blin-Stoyle (1951). Their results concerning the polarization of particle "b" produced in the reaction X + a —*X.+ b, when nXtt and ttan are unpolarized, are concisely summarized in section IV of the 1953 paper. It seems likely that protons and neutrons produced in 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 is now fairly well established that the ground and first excited states in both He-* and Li-* are a widely separated, inverted zPyz - 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 in a neutron energy region near 2.5 Mev. A proposed experiment using this reaction to measure neutron polarization is outlined in Appendix D. Dodder (1949) has calculated the yield as a function of second scattering azimuth in the analogous case of double 90° scattering of protons in 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 2Po - 2P,y doublet in I i - ^ i s inverted. The polarization of the protons from the reaction D(d,p)T has been measured by scattering in 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 in terms of the "cloudy crystal ball 1 1 nuclear model of Feshbach, Porter, and Weisskopf (1954). The experimental method involved a determination of the left-right asymmetry in 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 in the scattering by the various heavy nuclei, and calcu-lation, from these and the incident neutron polarization, of the ' polarizations which would be produced in 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 al. Wiliard, Bair, and Kington (1954) have reported a very nice experiment in which the polarization of neutrons between the energies 200 and 600 Kev from Id7(p,n)Be7 was measured by 90° scattering in O1^. Scattering at 90° from d 2 j^g fceen 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 is 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 is 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 is difficult to see how any conclusions can be drawn from their results. Multiple scattering in the large scatterer, together with acceptance in each detector position of neutrons scattered both left and right, renders ridiculous any attempt to analyse the results in terms of Schwinger!s expression for the ratio of the single scattering yields at 0 , y and 6, y + 7T. Double scattering experiments with protons of very high energy have produced useful information about proton-proton forces (a brief discussion is given in 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 in 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 all of the experimental data. 22 Since deuterons have,a spin of unity, a description of the spin states is most concisely expressed in tensor notation (Lakin, 1955). There is then a strong resemblance to the description of photon states, although the condition of transversality imposed on photons is removed. The azimuthal variation in the second scattering of 167 Mev deuterons by carbon (Chamberlain et al., 1954.) is 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 in the introduction to their paper). While there is no spatial orientation, the spins of the protons in 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 neutron-proton force appears as difference in the total cross-sections of molecules in the different spin states. The work proves, among other things, that the singlet state of the deuteron is 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 is 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 is much smaller than thermal energy at al l but very low temperatures, so 23 that transitions take place between the states continually, and there i s no measurable orientation of the nuc le i . Six methods of polarizing, or aligning nuclei at temperatures near 0.1°K have been suggested, involving different interactions of nuclear dipole and quadrupole moments with the applied magnetic f i e l d , either d i rec t ly , or ind i rect ly through interact ion with atomic electrons or the electrostat ic f i e l d i n crystals . 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 fact , this method has been commonly used, requiring temperatures of the order of 0.2°K or lower. True polarization i s produced, that i s , the magnetic moment vector of a nucleus i s preferential ly i n the direct ion of the applied magnetic f i e l d . Another method, the Bleaney (1951), or magnetic hyperfine structure method, has the advantage of requiring no external magnetic f i e l d , but lower tempera-tures, of the order of 0.003°K, are usually necessary to produce appreciable alignment. This method depends on crystal l ine e lec t r i c f i e lds to provide a preferred direct ion, and alignment, that i s orientation of the magnetic moment vector i n either direct ion along a preferred axis i n the crysta l , rather than polarizat ion, is.produced. The third method, the quadrupole coupling method of Pound (1949), has not as yet been successfully carried out. Very recently, the fourth, or "brute force" method has produced nuclear polar izat ion (Dabbs, Roberts, and Bernstein, 1955). This method involves the direct interaction of the nuclei with an external magnetic f i e l d at very low temperatures. The polarization or alignment of radioactive nuclei has a strong effect on the angular d istr ibut ion, polarizat ion 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 in 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 in 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 in 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 4.3 i 0.2 nuclear magnetons (Poppema et al., 1955). Several other varied, the Leiden group concluded that the magnetic moment of Co°0 is 25 • radioactive nuclei have been examined in this way, for example Ce 1^ and NdL47 b y Amblerf Hudson, and Temmer (1955). 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 Mn55 has been shown to be spin dependent by Bernstein et al. (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. Unfor-tunately, insufficient data was available to permit interpretation of this fact in terms of the energy levels of Mh-^ '« In an experiment on the capture of polarized neutrons by polarized 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. in 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., is near that of a resonance at 0.094 ev., the preferential capture is attributed to the energy level of Snr^0 responsible for the resonance. The spin of this level is then I + 1/2, where I is the ground state spin of Sm1^9 , 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, in 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 in 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 in the nuclear magnetic resonance signal from Id? when the conduction electron spins were saturated, indicating a change in the population densities of the nuclear spin states in 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 in that i t utilizes the hyperfine structure coupling of nuclei to electrons experiencing-spin resonance, Honig's method differs in that electrons bound to impurities, in 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 2 7 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 in spin and parity assignments, but i t is 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 its 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 is in 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 is able to explain all 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, is 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 al l energy variation to changes in 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 n&±jn (p. 97, Blatt and Weisskopf, 1952). Agreement between the calculated and empirical • parameters is not good, though there is a marked general similarity. . The approximations made in the calculations were so drastic that i t is not possible to say that theory and experiment are in 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 is a good approximation for bombarding energies greater than 400 Kev, due to the assumption that only ingoing r ,s n and rtpM waves contribute to the 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° in 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 al. may show that one, or none,- of the present theories of nuclear forces is 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 is available on the polarization of protons and neutrons from the D + D reactions to make possible quali-tative statements about the forces contributing to the reactions. Bishop et al. (1952b) measured the left-right asymmetry in the scattering by helium of protons emitted at 135p (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 spin-orbit coupling to account for the angular distribution and polarization. Attempts to measure the neutron polarization by resonant scattering in carbon (Huber and Baumgartner, 1953j Ricamo, 1953a,b) indicated that for bombarding energies near 600 Kev, the neutron polarization is approximately 20$, a value not in disagreement with Blin-Stoyle1s conclusion. 31 3. Non-resonant Scattering of Neutrons by Heavy Nuclei Since neutrons possess a magnetic moment, they may be appreciably scattered by the intense electrostatic fields of heavy nuclei. Because the magnetic moment and spin of a neutron are connected by the relation M = - SJL cr— 2mc CO where M is the magnetic moment vector in erg gauss 7 J^Un| the magnetic moment of the neutron = 1,9135 nuclear magnetons, eln the nuclear magneton = 5.04929 x lO" 2^ erg gauss"^, 2mc and O is the Pauli matrix, this scattering is polarization sensitive. To obtain an expression for the electromagnetic contribution to the Hamiltonian describing the neutron, consider the situation depicted in Figure 1, the K1 system approaching the K system along the z-axis with velocity V. FIGURE I 32 For values of V much less than c, the velocity of light, the magnetic field strength ~E* in the K1 system is given by (pi- 62, Landau and Lifshitz:, 1951): H*' = H + c E. x?, or H» = "c ExV, since"! =0. ( a ) (H has. been taken as zero, even though there are in general, both nuclear and electronic magnetic fields. However, for the case of a 3 Mev neutron incident on a high Z nucleus with a magnetic moment, M, of the order of one Bohr nuclear magneton, H/H' * M /jr J c EV = "V z e V = 0.15 even at the nuclear, surface. Since H/H1 falls off as l/r, H may be safely neglected.. In the case of lead, only Pb 2^, approximately 25$ abundant, has a magnetic moment, 0.6 nuclear magnetons. Only very slow neutrons show appreciable magnetic interaction with electrons, and then only when there is a bulk alignment of spins, as in 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 is not polarization dependent). Because of its magnetic moment M, the neutron possesses potential energy in this field. The Hamiltonian in the K' system may be written: / ¥ - ' = -M.I?. ( 5 ) o 33. Since V << c, the Hamiltonian in the K system is & = + ' (* ) where ^ = mV is the momentum of the neutron in the K system and in is the neutron mass. Combining (z)t (3), and (4-), Inserting (1 ) in (5) and writing V = p/m, we have Since Ei = -^f-r*, f, L = T- x p , and "S = i ^ ' where Z is the atomic number of the target nucleus and ~L and "S* are respectively the orbital and intrinsic angular momenta of the neutron in units of h t ( 6 ) may be written 34 The Schrodinger equation describing the motion of the neutron is then or where k 2 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 nuclear scattering amplitude at angle of scattering 0 , polarization vector of incident beam, the unit vector normal to the plane of the reaction. denotes "imaginary part of". = total neutron energy (conserved throughout the motion). where £(0) = P = — > h = and "Im" 35 0— (d, ~n) is plotted in 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 S7Z operator in terms of spherical coordinates, (S) becomes 36 • ^ 0 ( r ) is a solution of with the boundary conditions -^/©(r) = 0 for r < R, the nuclear radius, and -^J?)-*(&ckZ *^f(fi)X^\,y + *MXh-y) (*>> as Y > o o where the expression describes the spin orientation of the neutron, and "X^, being the usual spin eigenfunctions, and and obey The solution of (% ) and U o ) is the familiar "hard sphere" or "potential scattering" wave function (p. 329, Blatt and Weisskopf, 1952), and may be written o m'= -'fa X f % nsR l(?) + cH^%)] \ Q (6) dM \ ^ }3 37 where ^ = kr, (?) = "regular solution" = (~^)*J, +J  (?), /2AAP) = "irregular solution" = - N„ (P) Xc*,) = Bessel function /y'pC^ J = Neumann function y • of order p, defined in Jahnke & Emde (1945), V (&, tyO = spherical harmonic, as in Blatt and Weisskopf (1952); b = kR. The functions defined above obey the following relations: ^ (?) > sin (f ~ IT ) v as f —» 0 0 (p)—* cos ( f - 2. / J ( 22 ) To obtain the radial equation corresponding to ( f a ) , i t is convenient to expand -fy0 and <¥L in terms of eigenfunctions of the - * —*• operator J = L- + S. These may be written 38 where the coefficiente ( A .^.m, m' |j"rl) are the Clebsch-Sordan coefficients defined as in Condon and Shortley (1935). Since J 2 = (L +"S^ )2 = L 2 + S 2 + zZj?, and the y's are eigenftmctions of J 2 , L 2 , and S2, 4) Using in (11 ) the relation T-U-JU M--J and applying ( l ^ ) , -£-J J--U-H.I M--J m ' . - a where = 0 f o r J= O. Expanding -t/^ in similar form, 39 Inserting these expressions in C^ *-), and making the transformation r = ? . there results k oa A*+'A. J~ '/z. •> •> •> hA-fr'*- r h«>h» • tfl <fir>  + W % i * Taking the scalar product of each side with ^ r , * n^ s becomes, since <T, I, k,r\ \ j\ X 'A, M') = ^ ^ fa, + f t _ _ *±0] \ L e f r £ M i l The problem is now reduced to that of finding a particular integral of (16) satisfying the boundary conditions ^il (b) = 0, i*e, (?) «C e 1^ for large f . Solution of (16 ) in terms of tabulated functions is carried out in Appendix A. The asymptotic form of ^ (j>) may be written 07) 40 2. where ^ (?) ^  (?) b ? Substituting (l7) in (X^), and putting e - £ , t'p oo ^ h. T fj. The term fjJ"(j* + i) --tU+i) - ^ J in D7j 4 has the values JL9 when X- Yz. , and -f-/-ri) when X= Jk. Putting this in (l£>), replacing ^ j - , 4'/z by the expression (i>3 ), expressing the Clebsh-Gordan coefficients in terms of , (Appendix B), and carrying out all summations but the one over U/ , there results %Cr) = -IT* ^ ' T j l ^ + i f LMJ.*i)fSfCk) X The scattered wave, 1J, , is the difference between the total wave -V„ + ^ i and the incident wave e'^&te/X/ + <C-k.)\, , 1 Expanding e. in spherical harmonics, and taking the asymptotic form of the wave functions, 41 OO Using the Legendre polynomials defined by Jahnke & Emde (1945), '2.1 +J. Y rt^= - l 4 ^ ^ + l ) J / ] U - ^ e , and Off (21) where 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 is velocity, and VgC is the adjoint of "t^. From (21) 2 e 77 [<UW-«e' y - <(^)^)e^lA>)B(e) + Afc)B*(«]. How, A B + AB = 2(Re A Re B + Im A Im B), (z3) where nRen and wImn indicate respectively the real and imaginary parts of the quantity, and il°f(yz)cL(-!i) cos If + (24) Following Schwinger, (1948), the polarization vector, P , of the incident wave is defined by Taking x and y components, 43 A3 Then, from (24 where l l Is. a unit vector normal to the plane of the reaction, that is, 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 ) in (2.2), - £|A(e)f + f-2|B^)p .+ f (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 is chosen so that P is normal to the plane of the reaction. In this case the inter-ference term, the third term in (2.6), has its maximum absolute value. This term changes sign accordingly as the scattering is 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 in 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 is plotted as a function of scattering angle in Figure 3. The reaction is appreciably polarization sensitive only for scattering angles 8, smaller than ten degrees. 4 4 9 < Q < L U C O C O < Q Q O V O U J C O I co o a: o CD 5E L U < o C O II 10 8 \ \ \ \ A A -.Equation ( 26 ), P.n = +1 B - Equation ( 26 ), P.n = -1 C - Schwinger, P.n = +1 D - Schwinger, P.n = -1 E - Equation ( 26 ), P.n = 0 E - Hard-sphere scattering. \ \ D B Fig. 3. Differential scattering cross-section of lead for polarized 3.1 Mev neutrons. 8 10 II 12 13 14 15 POLAR ANGLE 0 , DEGREES .1 44 For comparison, Schwinger's expression for the cross-section is plotted in Figure 3, with A(6 ) inserted for £ Q(& ), the nuclear scattering amplitude. It can be seen that there is 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) is approximately 25% larger than Schwinger1 s. The divergence of the cross-section at zero scattering angle resembles that in Rutherford scattering, and may be removed in 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 MAM and MB" of Figure 3 show that scattering of 3.1 Mev neutrons by lead is 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 in the energy range of 2.5 to 4*2 Mev produced in 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, in 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 in preference to collimation in front of the detector because the small size of photo-graphic 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 in 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 V « • • • • • • • • • • • • • m • 0 • 0 • r • • • « * • t • 0 • 0 * 0 0 • • • • • • • • • • « • • • • • • • • 0 0 • • 9 0 » 0 0 0 0 0 0 • 0 0 * • 9 • • • • • 0 • • • • • 0 • 0 0 0 » 0 • 0 0 0 0 9 9 0 • 0 « 0 ' 0 0 0 « 0 0 • • • • • • • • • • o « 0 e • • 0 • • • • • • • • • • • • • • l • 0 0 0 0 0 * 0 • • • 0 0 0 A: A; vi • • • ^ ' 9 t 0 ' "9 0 9 0 ' s * • 9 " 9 9 0 0 ' ' 9 ' - 0 0 • -x • • • • ' ' 0 0 • ' 9 0 9' ' • • 0 0 0 0 9 9 0 0 0 0 0 0 0 0 0 0 0 0' ' , • 0 9 9 ; . • . • 0 0* C • 9 • 0 9 0 9 • 0 0 0 0 9 9 9 9 0 0 0 0 0 • 0 0 • 0 0 0 • O • 0 0 0 0s 0 0 9 ' 9 9 9 0 ' 9 0 0 ' * * ' ~ • • • • " , 0 • . ' - • • • • * x • • • • ' : 0 . . : ' 0 * 0 , , 0 • 9 , • 9 0 0 , * # # , 0 9 m , • 9 0 0 • • 0 0 • • 0 • 0 • 9 9 0 0 • 0 9 , 9 , 0 0 9 ' 9 9 0 < 9 0 0 , 0 0 0 0'' ' ' , 0 * 0 • 90 • 0 0 0 • 9 9 • 0 0 9 ^ > J ^ 7 ^-:> STEEL • • • • • • PARAFFIN g g ] WOOD LEAD - i 1 1 I 0 3 inches Fig. 4. Horizontal and vertical' sections of the neutron collimator. 46 machined. For neutron energies greater than 3 Mev, iron is effective in 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 M thick steel plates with 3/4" x 1 l/4 w holes were interspersed with the paraffin blocks at the entrance of the collimator, and one with a l/2" x 1M hole served as a mount for the scatterer at the exit. The parts of the collimator were aligned on a mandrel in order, and a flame was played gently over the surface to fuse the paraffin blocks. The assembly was mounted in a plywood box for protection. During runs using a stilbene scintillation counter as a detector, a 1 l/2 n lead plate was added to the exit end of the collimator to absorb the 2.2 Mev gamma rays from the reaction H(n,T)V3 occurring prolifically in the collimator. A further lead-lined paraffin shield was added to provide additional shielding from the target over the 47 SLIT / 8 x \ MOLYBDENUM STOP I, WINDOW 3 - / 8 NEOPRENE GASKETS DEUTERON BEAM DRAW TUBE Details of the vacuum seals are not shown. CD =f^>LUCITE SPACER l=i RING LIQUID AIR RESERVIOR LUCITE CENTERING RING TARGET SUPPORT WINDOW STOP 0-RING SEAL( •PINHOLE IN DISPENSER DIVIDED CIRCLE Fig. 5. Heavy ice target assembly. 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 inter-sected 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 in 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 in 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, in 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 non-uniformity 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 in 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 1/8M 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 slit, 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 all three objects were centred on the telescope cross-hairs. 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 in place during alignment. 49 (c) Detectors The detection of fast neutrons may be accomplished by the detection of energetic charged particles produced in 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 in 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, in 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 is usual to make phosphors, may be placed closer to the scatterer for the same w w g n i a y 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 back-ground. During scanning of the plates, proton tracks due to room-scattered neutrons may be rejected to a considerable degree, since the length of a track is 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 n by the relation E p = E n cos2 Q. Emulsions effectively insensitive to gamma rays can be obtained, thus further reducing the background. However, the information contained in an emulsion is obtained only by lengthy and tedious scanning, and during the experiment, knowledge as to its progress is 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 = En) was about 80 microns for incident neutrons of energy 3.3 Mev, so 100 micron emulsions were used in 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 in the same position in 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 in 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 in slowly running filtered tap water, they were immersed in 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 in 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 in a dust-free cabinet warmed to about 35°C by 100 watt bulbs. (d) Experimental Procedure and Results From the discussion in Section 2, neutrons from the reaction D(d,n)He3 are expected to have maximum polarization when the bombarding energy is about 0.6 Mev, and the angle of emission is 45° in 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 is nearly equal to that from a thick target, or approxi-mately 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, is 0.26, so that approximately 25% of the incident neutrons suffer single scattering and less than (0.26)2, or 7% suffer double scattering. For comparison an 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 is 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 is 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 cross-section, 0.55 neutrons/second are scattered by hydrogen in the right plate, and 0.46/second in the left. Water absorbed in the emulsion 53 adds approximately 25$ to this, and there is a further small increment due to hydrogen in 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 n cos2 6 > these lay in a cone of half-angle 26.7° about the direction of the neutrons incident on the emulsion from the scattering block. This corresponds to 53,4° in the centre of mass system, or 20,2$ of the sphere. Since n-p scattering is isotropic in 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 in the left, due to the dry emulsion alone, A three hour run thus should produce 1190 tracks in the right emulsion and 1000 in the left, a statistically significant difference. In practice, three pairs of plates were exposed during each run, one with the lead scattering block in 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 in al 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 in 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 luminat ion. With a tota l magnification of 450X, the square graticule i n the r ight eyepiece of the instrument covered an area of the plate 250 microns square. In the preliminary scanning, the cr i ter ion for McountableM tracks was applied by v isual estimation, with only approximate allowance for shrinkage of the emulsion i n processing (Rotblat, 1950). Five traverses, uniformly spaced along the length, were made across the width of each plate, and "countable" tracks beginning or ending within the confines of the graticule were accepted, so that on each plate an area 5 x 2.5 x (250 + 64.) x 10"*^ , equal to 0.39 cm. 2 , was scanned. The term 64. x 10"^ -, twice the average projection of a track on the direct ion perpendicular to the microscope traverse, allows for tracks not ly ing ent ire ly within the grat icule. The average count per traverse was 95, equivalent to 46OO per emulsion. This large count per plate indicated that neutrons scattered near the exit end of the collimation channel penetrated the remainder of the collimator with suff ic ient energy to give "countable" tra'cks i n the emulsion. To investigate this poss ib i l i t y , a more fac i l e detector was used, a 2 x 2 x 4. cm. trans-stilbene crystal mounted on a 1P21 photomultiplier. The counter was moved i n small steps along an arc 67.5 cm. from the target. At each point the pulse height spectrum was recorded on a th i r t y channel kicksorter, and the neutron f lux was monitored by means of a BF3 "long counter" surrounded by paraf f in . 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, is 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 OF BORON TEN WITH DEUTERONS 1. The Mirror Nuclei B 1 1 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 is 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 neutron-neutron and proton-proton forces are equal, except for Coulomb forces, implies that the energy level diagrams of mirror nuclei should be identical in the energies of the levels measured from the ground states, and in 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 A E = 0^ - mp)c2 - - l ^ C A - l ) , (27) where 1 % , nip are the neutron and proton masses, e is the proton charge, A the mass number of the isobars, and R ^  1,45 A x lO"^ is the nuclear radius (p. 219, BLatt and Weisskopf, 1952). An implicit assumption in ( 27 ) is 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 9-234 B + d-p E •9-28 •^19 •-8-92 (3/2"5/2) T F T V w Y ¥ o 8-57 799 •7-30 ^6 81 "N676 503 2-14 B J 5/2 TT + 4 4 6 5, /2 3 A E J TT 913 8-97 8-68 C 5 / 2 , 7 / 2 ) + 8-44 ( 5 / 2 / / 2 ) + 812 6-472 B,0+d-n 7-39 6-87 6 4 6 (%,V + 4-77 •4-23 1-90 II Fig. 8. Energy levels of B ^ " and C^. Transitions shown were found i n the present experiment. 57 The deuteron bombardment of B 1 0 produces the mirror nuclei B 1 1 and C 1 1 simultaneously through the reactions ^ ( d j p T j B 1 1 and B 1 0 ( d , n / ) C 1 1 » The energy leve l diagrams of B n and C n (Ajzenberg and Lauritsen, 1955) are shown i n Figure 8 with the ground state of C 1 1 placed opposite that of B U for ease of comparison. (The high leve ls , unstable to part ic le emission, are not shown.) According to ( 27 ), the ground state of C 1 1 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 indicat ion that the charge symmetry postulate i s incorrect, since the electrostat ic term i n ( 27 ) i s derived on the assumption of uniform charge distr ibut ion throughout the nuclear volumej furthermore, the nuclear radius i s not a well defined quantity. C^- decays by positron emission to B^, with a ha l f- l i fe of approximately 20.5 minutes. Unfortunately, there i s as yet insuff ic ient information, part icular ly spin and parity assignments, about the energy levels to permit detailed comparison, but the pattern of levels i s certainly s imi lar . The f i r s t f ive excited levels show a marked s imi lar i ty i n spacing, with those of C 1 1 l y ing, on the average, 250 Kev below the corresponding levels of B 1 1 . It i s not f r u i t f u l to compare the higher energy levels , because of the much closer spacing, part icu lar ly since the spins are largely unknown. The only certain spin assignment of those shown i n Figure 8 i s that of the B 1 1 ground state (Gordy, Ring and Burg, 1948). There i s , for example, considerable difference between the spin and par i ty assignments l i s t ed by Ajzenberg and Lauritsen (1955) and those by Jones and Wilkinson (1952). The energies of most of the levels 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 less accurate measurements on other reactions. Because the energy resolution attainable i s poorer for neutrons than protons, i t i s possible that some levels are not resolved i n 0^1; for example, the 6.46 Mev leve l i n may correspond to the 6.76, 6.81 Mev pair i n B 1 1 . Proton groups corresponding to a l l the known energy levels 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 lk ind, 1953). Measurements of the angular distr ibutions of some of the groups with bombarding energies between 0.20 and 8 Mev indicate that "Butler stripping" contributes appreciably to. the reaction even at bombarding energies below 1 Mev for some of the groups. There i s some disagreement between different authors as to the orb i ta l angular momentum the cap-tured neutron imparts to and as to the par i t ies and probable spins of the levels (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 excitation curve of the more energetic proton groups; these were observed at the same time i n the aggregate gamma ray excitation curve (Burke, Risser, and Ph i l l i ps , 1954). The relat ive intensi t ies of the proton groups measured at .90 ° for 1.51 Mev bombarding energy are l i s t ed 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 levels 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 in 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 in the forward direction. Burke, Risser and Phillips (1954) found an indication of a very low, broad resonance in the neutron yield at a deuteron energy of 0.9 Mev. Other than the weak resonances noted in 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 in 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 in Table 1. 60 2. The Three Crystal Spectrometer Scintillation counters, particularly with thallium activated sodium iodide crystals, have made possible gamma ray spectro-scopy with fair resolution even when the gamma ray intensity is very low (Hofstadter, 1948j Griffiths, 1955). While the resolution is 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 in the crystal and the charge collected by the anode of the photomultiplier is accurately linear i f reasonable care is taken in 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 in the crystal. With crystals of normal size (l 3 A M dia. x 2" long) and gamma rays in 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 in 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 corres-pond to one or both annihilation photons escaping from the crystal when the positron from a pair creation event annihilates with an electron in 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 CO D O I I-i 8I 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 8 2 0 - 2 6 L _ Eg = 0.95 Mev, 230 miorocoulombs. 2 6 - 3 9 16 ~T~" 18 * 3 2 - 5 0 O ^ Q — C L - O — O - J 2 0 10 12 14 C H A N N E L NUMBER Fig. 9. Single crystal spectrum from B10+ D. 2 2 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 in the same reaction, a large background tends to obscure 127 the gamma ray peaks. This is due mainly to neutron capture by I ' in the crystal, which results in the prompt emission of gamma rays in 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 is 25 minutes, A typical single crystal spectrum obtained from deuteron bombardment of is shown in Figure 9, The three crystal pair spectrometer, at the expense of a factor of approximately 103 in efficiency, completely eliminates the first difficulty mentioned above, and reduces the second to a level tolerable in 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 in the introduction to this thesis. The spectrometer used in the present experiment differs in detail, but not in principle, from those described by the above authors. Figure 10 is a block diagram of the complete spectrometer, excluding the high voltage and "B-plus" supplies. A detailed description of the components is to be given elsewhere (Chadwick, 1955). The side channel differential discri-minators were adjusted to pass pulses corresponding to 0.51 Mev annihilation quanta by placing a Na^ 2 source near each side crystal in 63 C A T H O D E F O L L O W E R D I F F E R E N T I A L D I S C R I M I N A T O R 6 3 4 2 C O L L E C T O R C E N T R E C R Y S T A L 2 x ^ x 5 cms. S IDE C R Y S T A L l "x l^'dlam. Power supplies are not shown. 6 3 4 2 6 3 4 2 5 C A T H O D E F O L L O W E R I C A T H O D E F O L L O W E R D E L A Y G A T E P U L S E G E N E R A T O R I C A T H O D E F O L L O W E R 3D Y N O D E ^ 4 D I F F E R E N T I A L D I S C R I M I N A T O R T R I P L E C O I N C I D E N C E M I X E R I B I A S E D A M P L I F I E R V K I C K S O R T E R A N D G A T E Fig. 10. Block diagram of the three crystal spectrometer. 62 turn, displaying its 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 in F ^ p ^ T " ) ^ . The resolution for the 2.62 Mev line from radio-thorium (shown dotted in Figure 12) is 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 in the gain of the centre channel. Since two hours was the usual length of a B?-0 run, slow drifts caused a considerable broadening of the gamma ray peaks. A change of only 0.5% in gain is equivalent to a 40 Kev change in 7.5 Mevj this is of the order of the standard deviation in 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 coinci-dences, the side channel crystals were shielded from the target by 5 inches of lead. 63 6- I3MEV. •i Fig. 1 1 . Spectrum from F 1 9(p,ocy ) o 1 6 . 63 3. Experimental Procedure The targets, kindly supplied by the Isotopes Division, A.E.R.E., Harwell, were 100yxgm/cm2 of 95$ enriched B 1 0 on platinum backings. They were approximately 40 Kev thick to 1,5 Mev deuterons. The target assembly shown in 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 slit shown in Figure 5, a 3/l6" diameter stop was placed 6" from the target, reducing the gamma rays from G^(dfp 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 in the centre, channel, its 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 in the experiment. Voltage calibration was accomplished by inserting pulses of accurately measured height at some point in the centre channel circuit - in the later runs, at the grid of the cathode follower. By adjusting the gain and bias of the amplifier (actually two amplifiers in 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 3 0 9 MEV. I 4 0 l \Z0\ UjlOOf 2 < X o or UJ CL 80 0) 6 0 l 3 o 4 0 2-62 MEV. 2 - 5 7 MEV. = 1.40 Mev, 3300 microcoulombs. The dotted curve i s the spectrum from Radio-thorium. J 4 - 5 6 MEV. I A 4 9 5 MEV. 5 - 2 6 MEV. O PULSE HEIGHT-VOLTS X H-97 14-12 8 U 1 1 T 10 12 14 16 CHANNEL NUMBER T~ 18 —r~ 2 0 2 2 I 2 4 2 6 2 8 Eig. 12. Spectrum from BlO + D, 2.0 to 5.5 Mev. 64 two hour run.. Gamma rays of known energy were used for energy calibration, usually those from F 1 9(p, ol / ) 0 1 6 (6.13, 6.94, and 7.1 Mev) and radio-thorium (2.62 Mev). This was repeated at least twice each day, two or more B-1-0 runs intervening between calibration runs. To check the linearity of the centre channel gain, several other energy points were used occasionally.. The centre channel could be operated as a single-crystal 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 Na22. 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 8 indicated that the gain was linear to 17.6 Mev, but the peaks were broad and asymmetrical due to Bremsstrahlung losses and wall effects in 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 in 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 all gamma rays determined from the peaks deviated in the same direction from the respective mean values of other determinations, the energy scale was "normalized11 to the mean value for the energy of the most prominent gamma ray present in the 65 PULSE HEIGHT - VOLTS 1 2 2 8 1 4 4 8 1 6 4 3 18-76 i 1 1 1—i 1 1 L-r 1 1 U — 8 IO 12 14 16 18 2 0 2 2 2 4 2 6 2 8 CHANNEL NUMBER Fig. 13. Spectrum from B 1 0 +• D, 4 . 0 to 6 . 5 Mev. spectrum, but this procedure was only necessary for one spectrum retained in the final analysis. 66 2801 2 4 0 LU Z200I Z < X (J £ 1 6 0 a. CO h-2 120 ID o o 80 4 0 = 1.40 Mev, 19,300 micro coulombs. 7-29 MEV I4O0 PULSE HEIGHT-VOLTS 16-27 18-47 J I 20-61 22-75 I 2 T 4 - i 1 r 8 10 12 14 16 18 2 0 CHANNEL NUMBER Fig. 14. Spectrum from B10+- D, 4.8 to 7i5 Mev. 22 ~~r~ 24 2 6 2 8 66 Lm Results and Discussion Typical 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 label led according to actual gamma ray energy, as experimentally determined, rather than pair peak energy. The integrated beam current for each run i s indicated i n the captions of the f igures. Direct comparison of intensi t ies between the various spectra i s very rough, because of the loss of target material during bombardment. The energies and relat ive intensit ies of the gamma rays assigned to transitions of B 1 1 and C 1 1 are l i s t ed i n Table 1. The assignments are indicated by arrows i n Figure 8. The energy errors l i s ted 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, Sippel, and Bonner (1955), l i s t ed i n Table 1 for comparison, were corrected for Doppler sh i f t , whereas the present measurements were not corrected. Doppler corrections for centre of mass motion: (for 1.4 Mev bombarding energy and observation at 0 ° ) range from 28 Kev for the 4.46 Mev gamma to 57 Kev for 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, Risser, and Ph i l l i ps , 1954$ Johnson, 1952; G.C. Neilson, private communication), tending to reduce the mean Doppler correction of the corresponding gamma rays. 67 6-51 MEV. 67 The relative intensities listed in 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 cross1* 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 in intensity were of this order. Agreement between successive runs was not good, due to loss of target under bombardment, and possible variations in 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. All 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 in intensity of the proton group, and gamma ray corresponding to the 4.46. Mev state in B?-1 may be explained by the 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 * PRESENT WORK BENT et al.ti955) PROTON GROUPS 1 rel * PRESENT WORK BENT etal.Ci955) NEUTRON GROUPS 'rel E X •rel E X •rel E r 'rel E X lrel 0 — — — — // 0 — — — 2.2 — • — . — — 1.9o — — — — o.6 4 4 6 ±. 04 4 so ± io 6 5 4 23 — — — 2 8 S.03 5". OJ ± • O 9 6 SO 3 ± .04 4 i 5.5 4-77 4- 7^T + o3 6 4- 74 ± .o 4 6.7 2- O 6- 76 6- 6 i 6- 75 to 7 6 6- 7? 72, 6.46 6SZ ±.o5 1Z ± . 04- 12. /2-7 3 0 7 Z9 5 73 1 ±.o + 65 6-87 — — 7. oi ± .o£ 6 2 o Z9? — ± • o 7 2 8 1-6 7 3 ? S~. 3 5 ± . OS 7 — o 4 Q57 8 2 7 ± . o ? 8 62 ± 0 7 !•? 1 6 a. ii 6-8 7 i . oz // 8-98 ±o + 7 Z Z7 • ?./?• 4 7JT ± .03 6 4.74 ± o + 4- + — 9 2 8 — 22 — — Table 1. Assignment of the gamma rays to levels of and 0 68 9.28 Mev. The 8.92 Mev ground state transition is 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 in part arise from the low intensity of the radiation, and perhaps from conflicting counts due to 8.87 Mev photons which fai l to produce the full pulse height because of Bremsstrahlung loss and wall effects. A similar effect, though much smaller in proportion, has been observed with the clean 6.13 Mev gamma ray from F^(p, ot / ) 0 ^ . The neutron group intensities in Table 1 were measured by Johnson (1952) at 0° and 3.4 Mev bombarding energy; the difference in 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 in 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 6 9 4-. 75 Mev gamma ray observed has been attributed in part to the. ground state transition from the 4.77 Mev state in C 1 1, as well as to the 4.73 Mev transition between the 9.19 and 4 .46 Mev states in B 1 1. The 7.01 Mev gamma ray attributed by Bent, Sippel, and Bonner (1955) to the 6.87 Mev state of C1^ was not observed in this experiment. A 5.35 Mev gamma 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 in B^ - reported by Bent, Sippel, and Bonner (1955), although comparison of neutron and gamma ray intensities is 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^f for the 3.09 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, in 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 O l I L I I I I L_ 0-8 I O 1-2 1-4 1-6 1-8 2 0 2-2 B O M B A R D I N G E N E R G Y — M E V . Fig. 16. Yield curves of the 6.12, 6.52, 6.78, and 7.29 Mev gamma rays. 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 in 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 in Figure 16, differ in shape by an amount littie, i f any, greater than the errors in determining the relative intensities. The apparent maximum near 1.8 Mev in 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) in 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 initial single crystal survey, or in the later measurements with the three crystal spectrometer, of high energy gamma rays from deuteron capture by B10, leading to excited states of C12.. The excitation energy at a deuteron energy of 0.95 Mev is 26.1 Mev, well above all 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 1 2 reaction is less than lO"^1 cm. 2 at 0.95 Mev bombarding energy. 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 in the data. The 4.23 Mev ground state transition in 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 in the present work may be explained by the differences in target thickness and bombarding energy, but this does not explain why they did not detect the 5*35 Mev gamma which was quite evident in 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 is 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 in an intense neutron flux. 72 APPENDIX A SOLUTION OF THE RADIAL EQUATION The Green's function of equation (lb) is (p. 516, Margenau and Murphy, 1943) i h C 2 8 ) A and B adjust f ( f , ?') to satisfy the same boundary conditions as u^ (?). That is, (2 7) f (?,?') ^ e i 5 > f o r l a r g e * Using the asymptotic forms of ^ (°) and ( ? ) * - e 2. i i ( F - f ) * ±_ + A[-—^—J+ B r Equating the coefficient of e. to zero, I A B - - ^ U R V ) - < ^ j 7 (30) Solving ( 2.9) and (3 O) for A and B, and using the identities (equation 12) satisfied by H and , 74-Then SIX Y9 -fee L X / z £ (?) + <^/z£C?;>] X / " * / t i p ' f f and as p —* oo, i(y - — ) 75 (/-i-mm'UM)2 m1 = -j m'= - j /+ M + T /-M+F 2-^ + 1 2/+ 1 7+M + l" 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 The symbol * indicates negative square root must be used. ( i i ' 0 1 LI) L 7 8 0.1 1 0,2 0.3 0 4 0.5 1 1,1 * 1 Z _/_ z 1.2 * 3_ /o * L 6 JL i s 1.3 * - _ 8 Zt iz /s 2 8 14 / 2 / 8 1.5 24. * -L 3*1 66 2.1 / lo 2 2. 2.2 5^ to /4-J5 7 2.3 A. 3S J_ 7 * 2. zo * 3. £ 8 J 7 24 _/£ £3 iZ 2Q9 * J-fS ]_±_ 33 25 II 3 SS * 2 7-130 2 2 60_ z s_ 32 3S ^2 7 3 0 ' 4 - 8. 2 / 3.3 4 2 6 4-2 2 £ 66 3.4 42 * _S 4-2 S 66 81 770 7.73 O 66 3.5 23/ /fa /Q83 /ooto 19* * J-3 3 -* IS z & 6 /OS 2 65 4.1 * -L Z j_ 3 42 * 8_ 63 5" /8 /3> 7 _3£ 7*7 43 1+ /Z6 I /?8 2 7 * IZI /63Q / ? 8 SQ_ /+3 4.4 +6Z * 2 . 2 2 4 ^ zooz 3_ -26 * J 7 _ 4 6 * 2 ? / 4 3 45 II 2 3 4 27 2 ©6 40 SQS 693 S S * 98 4 n 2 7 2 9 3 2 7 2 2 5.2 * s 33 3_ II * JL 78 * JL 3 2 ± 8 1+3 53 2S Z3t * zs /3Z 7 3 9 3 3 + _7S . S7Z 189 S1Z 5.4 * A 33 5 33 * 81 17/6 57Z I 39 33 *2 6+S 2% 172 * 4-9 572 7 8 4 2 4 3 / Table 4. Clebsch-Gordan coefficients {J?,/,0,1 L 1)". U/oo|i_o) : 0 2 4 6 8 10 12 0,0 1 1,1 * _L 3 2 J 2,2 / S * 2 7 /8 35" 3,3 * / 7 J ± 2/ 77 / O O 23/ 4,4 / /oO 4 ? 3 /62 / ooi •** 2 O 99 /Z87 5,5 * / // So * /8 /43 8Q Sbt * 4 9 0 2 7/7 79 3 8 *6/89 6,6 / / J ¥r /4-I&3 2 Si 2431 * 8 0 3SS"3 «3J"o 2 7/7 * /^"8 76 96S77 Z7 3 92 96S77 0,2 0,4 1 0,6 J 1,3 7 7 1,5 l< / / . 2,4 7 * ZO 77 // • 2,6 * /4 ss 63" 3,5 ¥* .TO 2 3 / t&O JOOI * 7 3 3 s4 /43 4,6 2>" / - f 3 * Zo /+* 2 8 * 5^ >4-271 7 /+7o <+/99 1 3 5 7 9 0,1 0,3 ; 0,5 I 1,2 * 2 5 3 3" 1,4 9 s 7 • 1,6 _7_ 9 33" IS 1 o 21 -2,5 /o 33 *• /o 3 ? / 4 J 3,4 *" 4. 2/ Z // * ZO 9/ I7S 3,6 * /OO 7 39 * so* 243I 64 22/ 4,5 33 * 2 0 /43 2 /3 ¥• /4 o o' 72 93 8 8 2 243/ The symbol *" indicates negative square root must be used. [ ( # O O | L O H / / O O | L O ) ] Table 3 . Clebsch-Gordan coefficients ( i , ^ ' , 0 , 0 L 0 ) 2 . 75 APPENDIX B CLEBSCH-GORDAN COEFFICIENTS 1. In deriving equation coefficients of the form (2, 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 1 , 0,o| £ 0), 0,l) Ll) are needed. These are tabulated in 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 is 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 ( 3 4 - ) (b) is calculated from recurrence relations: 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, = ^ = - V*. , C and C = J : J. b 5 or 79 Similarly, ' The series for B(6 ) converges very slowly, so that i t is 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) is true to the desired degree of approximation. Then 80 where a. = >4( A +l)K^ . Then, putting (3 7 ) in (3Z), i Tg, may be written in one of the forms of the Laplace integral (p. 127, MacRobert, 1948): T j (cos 6) = ~~1T~ I Ccos 8 - L S>n Vcostf) cosCp cLlj . Substituting in the second sum in (3 3), X 7 zi+i w . _ t- v 7 ilii t ]_ ^(Jt+i) £ Uosd) - 7 f / ^ X JCtosd - L sindcos(f)tosjfdy, (39) where z = cos & - isin^cos y . Since )z) <. 1 when d fi 0, the power series in (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 \ i- i~z.  z * \ 7 z f \— z Substituting these values in (37), and rewriting the finite sums in terms of associated Legendre polynomials, (The only term with 2 = 0 vanishes, since / l,cosy &</ = 0). The evaluation of the integral 1(8 ) in ( + °) is straight-forward. Inserting the expression for z in terms of 6 and </ , and integrating the log term by parts, 1(8) becomes: lid) - / ^ w ^ " isin8smz(p) d ( f J -• Cos d + L5m6cosg> 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 &)5inILtf] sm^d cos* or TT sin 6 cot J2 z ( 4 1 ) Substituting (4-0 and (4°) in (38), 3(0) = ) [{ui+l)[$a) ' J^Tnl^U^O)} (4 2 ) + d c o l - • Numerical calculation of the cross-section as a function of angle is aided by application of the relation (equation 2.3, Blatt and Biedenharn, 1952), 83 ^ -£+ -t' L . X ( 1 , 1 O , O IL O )U *-m, m' \ L Tl) \ n (6, if), giving for the corresponding products of associated Legendre polynomials the relations si + J,' r } ( c o . ^ ( c o - ( 7 ) = ) ^ ( / / O j O l L o / f r t o a f l , , ,U,Ao,o\io)Ual-ij\L o)vLuosd), 84 and A + JL' X i / . / • .7? (cos fl) A U i , o, ol L o)U, ^ , o, 111 i) [ L ( L + L)]k Then the necessary functions of k(6 ) and B($) become: 24 , -4 L-O t ^ = 0 + ^ ^ ^ ( 2 ^ * 2)7?e R GO) 'jz/+1 )R* \L (b)[uX o, OIL 0)f X 4 A where i x is the value of 1< after which the terms in A.( 6 ) may be neglected to the desired degree of accuracy; 85 |B(*)f = dL*cot*f + £ d cot | X +::terms negligible to 1$ of 0"~($,ri) in the case considered here; a. cot * ^-o x L A + 4, t ^ \ 7 "PL (COS 0, \ ' 86 A(e)ImB(0)= 2 > r i o + # 2 it*+ 1)1*^) X X J'= 1 X f l m ^ ( b ) ~ J^lj{iJfO,Q\Lo)Uj\o^Ll\, The necessary Clebsch-Gordan coefficients are tabulated in Appendix B, If a coefficient appearing in the above expressions does not appear in the tables, the corresponding term is negligibly small» For neutrons of 3.1 Mev scattered by lead, the parameters in expression: (2.6) for <r~(6, la ) have the values: k = -28%. = 3.85 x 10 1 2 cm."1, R = 7.8 x lO"^ cm. (p. 482, Blatt and Weisskopf, 1952), b = kR = 3.00, € = 2 I u | ^  = A.81 x lO" 1^ cm., / n. 2 mc 87 - i - = 6.75 x 10" 2 6 cm.2 , k 2 £ = 1»25 x 10" 2 6 cm.2 , k = 5.78 x 1 0 ' 2 8 cm.2 . 4 A conservative value of Jx for 1% accuracy is -4 = 4, since H§(3) = 5 x 10"^ + 7.3i x 10"^ , negligible compared to Hi(3) = .968 - .1761. The value - 4 = 5 satisfied equation (36 ) very well, since ^-L K5X3) = .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). The constant a = A ( X + l)K^(b) then has the value 0.506. o—(^, H) is plotted in Figure 3 for |1? | = 1 and "n parallel and antiparallel to P*, that is, 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 in helium. The wide splitting of the 2P> - 2P> doublet in He^*(Ajzenberg and Lauritsen, 1955) indicates strong spin-orbit coupling, which in turn should produce polarization sensitivity in the scattering of neutrons by He^ . The analogous case of proton scattering by He^  in the energy region of the 2Pj, - 2P 3 doublet in IS? shows strong polarization sensitivity. Double 90° scattering of a proton beam in He^  shows an asymmetry ratio> of 1.9 in 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 in 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 is a possible check on the qualitative experiment of 89 HEAVY.ICE TARGET ANODES OF-COUNTERS 5 MIL. TUNGSTEN WIRE MOUNTED ON KOVAR SEALS TRIPLE PROPORTIONAL COUNTER 5 CMS. DEEP -rs" BRASS. 16 LEAD ^ ^ ^ ^ ^ © r/s////y////Ar/s///jy^^^^ 3 CMS. 0 _ _ _ 5 CMS : I CM. st_ 0 COLLIMATING GRIDS V9 BRASS AS MANY^" DIAM. HOLES AS POSSIBLE, INCLINED 45° TO FACE OF GRID. Fig. 17. Proposed fast neutron polarimeter. 89 Ricamo (1953b), in which the neutrons from D(d,n)He3 are assigned a polarization P > 20% from measurements of scattering by C 1 2 . Figure 17 is a schematic diagram of the apparatus. Three helium-filled proportional counters are constructed in 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 is 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)°, Cf = (90 * 10)°, and 6 = (45 ± 10)°, Lf = (-90 * 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 in the laboratory system are related to the corres-ponding angles in the centre of mass system by @Xab = \ @ c.m. * Cj> = y c.m.* C1*1636 relations apply to recoil particles in elastic collisions, regardless of particle masses and bombarding energy). Thus, for the situation specified above, 0 c # m < = 90° and y> c # m #= *90°. The left right asymmetry ratio in scattering, and hence in the two coincidence rates, is R = *p-p » where P is the neutron polarization and P 1 is the polarization which would be 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 - % is 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 - PP1) = 65/minute, assuming there is complete transmission of recoil particles; through the collimating grids. A realizable transmission factor is 0.25, giving 2l/minute and 16/minute for the coincidence rates. A forty minute run is then expected to produce 850 coincidences on one side and 650 on the other, a statistically significant result. The pressure of helium is chosen to permit recoil alpha particles to reach the outer counters with detectable energy. Since the recoil energy E r e c < is related to the incident neutron energy E i n c # by 2mjm2 /D Erec. = 7 Tn + 0 0 8 £/c.m.)Einc. » where m-j_ and m^  are the masses of the neutron and alpha particles respectively, E r e c # =r 1.05 Mev when (?c.m.. = ^  and E i n c # = 3.3 Mev. The longest recoil path is (3 + l) J~2 - 5.6 c.m. Using the values of Livingston and Bethe (1937) for the range in air, 0.59 cm., and stopping power of helium relative to air, 0.42, the range in one atmosphere of helium is 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 in 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 d position. This apparatus is adaptable to other neutron energies by varying the helium pressure, since the required geometry is 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, P1 changes rapidly, becoming zero at 2.4 Mev, (Seagrave, 1953), eliminating the polarization sensi-tivity. P1 increases in magnitude toward higher energies, becoming essentially constant between 6 and 10 Mev. In this energy range, R has the value 12 for 100$ polarized neutrons. 92. BIBLIOGRAPHY References are given in the text by author*s name and year of publi-cation. A l l references quoted are listed alphabetically below. Adair, R. K, (1950). Rev. Mod. Phys., 22, 249 (1950). Adair, R. K. (1952). Phys. Rev., 86, 155 (1952). Adair, R. K., Darden, S. E., and Fields, R. E. (1954). Phys. Rev., $6, 503 (1954). -Ajzenberg, F. and Lauritsen, T. (1952). Rev. Mod. Phys., 2 4 , 321 (1952). Ajzenberg, F. and Lauritsen, T. (1955). Rev. Mod. Phys., 22, 77 (1955). Ambler, E.., Hudson, R. P., and Temmer, G. M. (1955). Phys. Rev., 2 2 , 1212 (1955). Barkla, C. G. (1906). Proc. Roy. Soc,, .22, 247 (1906). Beiduk, F. M., Pruett, J. R.., and Konopinski, E. J. (1950). Phys. Rev., XL, 622 (1950). Bent, R. D., Sippel, R. F., and Bonner, R. W. (1955). Private communication to Ajzenberg and Lauritsen (1955). Berlin, T. H. and Madansky, L. (1950). Phys. Rev., J8, 623 (1950). Bernstein, S., Roberts, L. D., Stanford, C. P., Dabbs, J. W. T., and Stephenson, T. E. (1954). Phys. Rev., 2 4 , 1243 (1954). Biedenharn, L. C., Rose, M. E., and Arfken, G. B. (1951). Phys. Rev., 82, 683 (1951). Biedenharn, L. C. and Rose, M. E. (1953). Rev. Mod. Phys., 2fj, 729 (1953). Bishop, G., Daniels, J. M., Goldschmidt, G., Halban, H., Kurti, N., and Robinson, F. Wi H. (1952a). Phys. Rev., 88, 1432 (1952). Bishop, G. R., Preston, G., Westhead, J. M., and Halban, H. H. (1952b). Nature, 12S, 113 (1952). Blair, J. M., Freier, G., Lampi, E., Sleator, W., and Williams, J. H. (1948). Phys. Rev., JZ4, 1599 (1948). Blatt, J. M., and Biedenharn, L. C. (1952). Rev. Mod. Phys., 2 4 , 258 (1952). Blatt, J. M., and Weisskopf, V. F. (1952). "Theoretical Nuclear Physics", John Wiley and Sons (1952). Bleaney, B. (1951). Proc. Phys. Soc, A64, 315 (1951). Bleuler, E. and ter Haar, D. (1948). Science, 108, 10 (1948). Blin-Stoyle, R. J. (1951). Proc. Phys. Soc, A64, 700 (1951). Blin-Stoylej R. J. (1952). Proc. Phys. Soc, A65, 949 (1952). Bloch, F.., Hamermesh, M., and Staub, H.- (1943). Phys. Rev., 64, 47 (1943). Bloch, F., Nicodemus, D., and Staub, H. H. (1948). Phys. Rev., 2At 1025 (1948). Brady, E.- L. and Deutsch, M. (1950). Phys. Rev., .78, 558 (1950). Brockhouse, B. N. (1953). Can. Journ. Phys. 2L* 432 (1953). Burke, W. H., Risser, J. R., and Phillips, G. C. (1954). Phys..Rev., 22, 188 (1954). Carver, T. R. and Slichter,-C. P. (1953). Phys. Rev., 22, 212 (1953). Chadwick, G. B. (1955). M. A. Thesis, University of British Columbia, -(1955). Chamberlain, 0., Segre, E., Tripp, R., Wiegand, C, and Ypsilantis, T. (1954). Phys. Rev., 2 5 , H 0 4 (1954). Clay, F. P. and Hereford, F. L. (1952). Phys. Rev., 85, 675 (1952). Condon, E. U. and Shortley, G. H. (1935). "The Theory of Atomic Spectra", Cambridge University Press, (1951). Cox, J. A. M. and Tolhoek, H. A. (1953). Physica, 12, 1178 (1953). Dabbs, J. W. T., Roberts, L. D., and Bernstein, S. (1955). Bui. Am. Phys. Soc, JO, #4, S6 (1955). Daniels, J. M«, Grace, M. A., and Robinson, F. H. (1951). Nature, 168. 780 (1951). Deutsch, M. (1951). Phys. Rev., 8g, 455 (1951). Dodder* D. C. (1949). Phys. Rev., .76, 683 (1949). Elkind, M. M. (1953). Phys. Rev., 22, 127 (1953). 94 Fairbairn, W. M. (1954). Proc. Phys. Soc.,, A62, 990 (1954). Falfcoff, D. L. (1948). Phys. Rev., 21» 518 (1948). Falkoff, D. L., Colladay, G. S., and Sells, R. E. (1952). Can. Journ. Phys., 20, 253 (1952). Feshbach, H. and Schwinger, J. (1951). Phys. Rev., 84, 194 (1951). Feshbach, H., Porter, C. E., and Weisskopf, V. F. (1954). Phys. Rev., 24, 448, (1954). Fowler, W. A., Lauritsen, C. C., and Tollestrup, A. V. (1949). Phys. Rev., J6, 1767 (1949). French, A. P. and Newton, J. 0. (1952). Phys. Rev., 86, 249 (1952). Goldhaber, M. and Sunyar, A. W. (1951). Phys. Rev., 82, 906 (1951). Gordy, W.., Ring, E., and Burg, A. B. (1948). Phys. Rev., 24, U91 (1948). Gorter, C. J. (194SX Physica, 14, 504 (1948)." Griffiths, G. M. and Warren, J. B. (1952). Proc. Phys. Soc., A65. 1050 (1952). . Griffiths, G. M. (1953). Ph.D. Thesis, University of British Columbia, (1953).-Griffiths, G. M. (1955). Can. Journ. Phys., 22* 209 (1955). Griswold, T. W., Kip, A. F„ and Kittel, C. (1952). Phys. Rev., 88, 951(1952). Halpern, 0. and Holstein, T. (1941). Phys. Rev., jj2» 960 (1941). Halpern, 0. (1952). Phys. Rev., 85, 747 (1952). Hamilton, D. R. (1948). Phys. Rev., 24, 782 (1948). Hanna, R. C. (1948). Nature, 162, 332 (1948). Hanson, A. 0., Taschek, R. F., and Williams, J. H. (1949). Rev. Mod. Phys., 21, 635 (1949). Heitler, W. (1944). "Quantum Theory of Radiation", (Second Edition), . Oxford University Press (1944). Hereford, F. L. (1951). Phys. Rev., 81, 4S2 (1951). Hereford, F. L. and Keuper, J. P. (1953). Phys. Rev., 2Q, 1043 (1953). Hess, F. G. (1955). (To be published, 1955). Heusinkveld, M. and Freier, G. (1952). Phys. Rev., 85, 80 (1952). Hofstadter, R. (1948). Phys. Rev., 24, ioO (1943). Hofstadter, R. and Mclntyre, J. A. (1950). Phys. Rev., 22* 389 (1950). Honig, A. (1954). Phys. Rev., £6, 234 U 9 5 4 ) . Hoover, J. I., Faust, W. R., and Dohne, C. F. (1952). Phys. Rev., 85, 58 (1952). - -Huber, P. and Baumgartner, E. (1953). Helv. Phys. Acta., 26, 420 (1953). Hughes, D.. J., Wallace, J. R., and Holtzman, R. H. (1948). Phys. Rev., 22, 1277 (1948). Jahnke, E*. and Emde, F. (1945). "Tables of Functions", (Fourth Edition), -Dover Publications (1945). Johnson, V. R.. (1952). Phys. Rev., 86, 302 (1952). Jones, G. A. and Wilkinson, D. H. (1952). Phys. Rev., 88, 423 (1952). Kane, J. A.., Stallwood, R. A., Sutton, R. B., Fields, T. H., and Fox, J.G. (1954). Phys. Rev.,. 25, 1694 (1954). Kraushaar, J. J. and Goldhaber, M. (1953). Phys. Rev., 82, 1081 (1953). Lakin, W. (1955). Phys. Rev., 28, 139 (1955). Landau, L. and Lifshitz, E. (1951). ."The Classical Theory of Fields", Addison-Wesley Press (1951). Leipuner, L., Siegel, R., and de Benedetti, S. (1953). Phys. Rev., 2i» 198 (1953). Ling, D. S. and Falkoff, D. L. (1948). Phys. Rev., 24, 1224 (1948). Livingston, M. S. and Bethe, H. A. (1937). Rev. Mod. Phys., 2, 245 (1937). Longley, H. J., Little, R. N., and Slye, J. M. (1952). Phys. Rev., 86, 419 (1952). Louisell, W. H., Pidd, R. W., and Crane, H. R. (1954). Phys. Rev., 24, 7 (1954). MacRobert, T. M. (1948). "Spherical Harmonics", (Second Revised Edition), Dover Publications (1948)* Margenau, H. and Murphy, G. M.. (1943). "The Mathematics of Physics and Chemistry", D. Van,Nostrand Co. (1943). Metzger, F. and Deutsch, M. (1950). Phys. Rev., ^8, 551 (1950). Mott, N. F. (1932). Proc. Roy. Soc., A135. 429 (1932). Mott, N. F. and Massey, H. S. W.. (1949). "The Theory of Atomic Co l l i s ions " . (Second,Edition), Oxford University Press (1949). . Munn, A. M. and Pontecorvo, B. (1947). Can. Journ. Phys., g$, 157 (1947). Oehme, R. (1955). Phys. Rev., 22, H 7 (1955). Overhauser, A. W. (1953). Phys. Rev., 22, 411 (1953). Oxley, C. L., Cartwright, W. F.., and Rouvina, J . (1954). Phys. Rev., 22, 806 (1954). Poppema, 0. J . , Steenland, M.. J.., Beun, J . A.,, and Gorter, C. J . (1955). Physica, 21, 233 (1955). Pound, R. V. (1949). Phys. Rev., .76, 1410 (1949). Pruett, J . R „ , Beiduk, F. M.., and Konopinski, E. J.. (1950). Phys.. Rev., 32, 628 (1950). Rarita, ¥ . and Schwinger, J . (1941)* Phys. Rev., j>2, 556 (1941). Ricamo, R. (1953a). Helv. Phys. Acta, 3 6 , 423 (1953). Ricamo, R.. (1953b). Nuovo Cimento, 10, 1607 (1953). Roberts, L. D., Bernstein, S., Dabbs, J.. W. T . , and Stanford, C. P. (1954). Phys. Rev., 25, 105 (1954). Robinson, B. L. and Madansky, L. (1952). Phys. Rev., 88, 1065 (1952). Rotblat, J . (1950).. "Progress i n Nuclear Physics", Volume I, Editor .0 . R. Fr isch, Butterworth-Springer Ltd. (1950). Sauter, F. (1931). Ann. d. Phys., 11, 454 (1931). Schwinger, J . (1946). Phys. Rev.., 62, 681 (1946). Schwinger, J.. (1948). Phys. Rev., 22, 407 (194$). Schwinger, J.. (1948a). Phys. Rev., 7J1, 416 (1948). 9.7. Seagrave, J. D. (1953). Phys. Rev., 22, 1222 (1953). Segel, R. E.., Schwartz, C. D.., and Owen, G. E. (1954). Rev.. Sci. Inst., 2i, 140 (1954). Sharp, W. T.., Kennedy, J..M., Sears, B. J., and Hoyle, M. G. (1953). "Tables of Coefficients for Angular Distribution Analysis", Atomic Energy of Canada Ltd., CRT-556 (1953). Sherwood, J. E.., Stephenson, T. E., and Bernstein, S. (1954). Phys. Rev.., 26, 1546 (1954).-Shulf, C.C. , Cha5C,C.T. , a.nd M y e r s , F. E.(194-3). Phys.Rev., £3 2 ? (191-3). Shull, C. G. (1951).- Phys. Rev., 81, 626 (1951). Simon, A., Rose, M. E.., and Jauch, J. M.. (1951). Phys.. Rev. 8£, 1155 (1951). Simon, A. and Welton, T. A. (1953). Phys. Rev., 22, 1036 (1953). Simon, A. and Welton, T. A. (1954). Phys.. Rev., 24, 943 (1954). Snyder, H. S., Pasternak, S.., and Hornbostel, J., (1948). Phys. Rev., 12, 44P (1948). Steenberg, N. R.. (1952). Proc. Phys. Soc., A£5, 791 (1952). Steenberg, N. R. (1953a). Can. Journ. Phys., 21* 204 (1953). Steenberg, N. R. (1953bj. Proc.. Phys. Soc., A66, 391 (1953). Stump, R. (1952). Phys. Rev., 86, 249 (1952). Sutton, R. B.,, Hall, T., Anderson, E. E., Bridge, H. S., DeWire, J. W., Lavatelli, L. S., Long, E. A., Snyder, T., and Williams, R. W. (1947). Phys. Rev., 2g, 1147 (1947). Tolhoek, H. A., and de Groot, S. R.. (1951). Physica, 12, 81 (1951). Van Patter, D. M., Buechner, W. W,, and Sperduto, A. (1951). Phys. Rev., 82, 248 (1951). Vlasov, N. A., and Dzhelepov, B. S.. (1949). Dokl. Akad. Nauk., SSSE, 62, 777 (1949). Watson, G. N.. (1945). "Theory of Bessel Functions", (Second Edition), - Macmillan (1945). West, H. I. and Mann, L. G.. (1954). Rev. Sci. Inst., 25, 129 (1954). ?8r Whitehead, W. D.. and Snowdon, S. 0. (1953). Bays. Rev., 22, 114 (1953). Wick, G. C. (1951). Phys. Rev., 81, 467 (1951). Wightman, A. (1948). Phys. Rev., 2L, 1813 (1948). Wilkinson, D. H. (1952). Phil. Mag., -42, 659 (1952). Willaxd, H. B., Bair, J. K.., and Kington, J. D. (1954). Phys. Rev., 2 5 , 1359 (1954). Wolfenstein, L. (1949). Phys.. Rev., 7i, 342- (1949). Wouters, L. F.. (1951). Phys. Rev., 84, 1069 (1951). Wu, C. S. and Shaknov, I.. (1950). Phys. Rev., 22, 136 (1950). Yang, C. N.. (1950). Phys. Rev., JJ, 722 (1950). Zinnes, I.. (1950)Phys. Rev., 80, 386 (1950) \ 


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