The g-factors of the [πg_9⁄2²]8⁺ states of ⁹⁰Zr(t_1⁄2=130 nsec) and ⁹²Mo(t_1⁄2=190 nsec) have been determined to be 1.355±0.018 and 1.409±0.016, respectively, by the time-differential spin rotation method in (α, 2n) reactions. The results together with the known g-factors in the A=88 region are compared with theoretical values derived from the M1 spin polarization and the mesonic exchange current. It turns out from the analysis that (1) the difference between the observed g-factors of the two 8⁺ states is well accounted for by the M1 spin polarization mechanism and that (2) the mesonic effect of Δg_l=0.10 and Δg_s<0 explains the absolute values of the observed moments in this region.

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Cross section for second harmonic generation in Compton scattering is obtained, both quantum-mechanically and classically, for radiation field of general nature in terms of fourth order coherence functions. Strong dependence of this cross-section on the nature of incident radiation is shown by studying the special cases of coherent and chaotic beams of radiation having various polarizations, and some cases of beams of radiation having stabilized amplitude. It is shown that the results reported in literature for this phenomenon hold only for coherent radiation and that those reported for unpolarized radiation are not correct. It is also shown that fourth order coherence functions can be determined from the measurements of the intensity of second harmonic scattered radiation in different directions and the coherent states of radiation can be distinguished from the generalized coherent states.

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The screening effect is included into the Klauder-Yonezawa model of impurity band conduction at zero temperature. It is shown that the binding energy of impurity potential goes to zero smoothly with the increase of the concentration of impurities, which differs from the result of Li, Love and Miller and coincides with the suggestion of Krieger. The screening effect on the vallue of the mobility is in good agreement with experiments on InSb at comparatively low concentrations. It is also shown that this model is not good at high concentrations, which is demonstrated by the calculation of the dielectric function and by the comparison of the mobility with experiments on InSb. Effective mass of the impurity band is defined by the frequency dependent conductivity.

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Pressure dependence of the band structure of HgTe is calculated by the use of the pseudopotential method. The pseudopotential used in the calculation is Animalu-Heine’s model potential which is angular-momentum dependent. Effect of the valence electron is taken into account by screening the ionic potential with Penn’s dielectric function. To calculate the effect of the pressure the band structure, the angular-momentum dependence of the pseudopotential is found to be essential. Pressure dependence of effective masses for HgTe are calculated. The energy gaps of Hg_1−xCd_xTe (0<x<0.15) is obtained to have similar behavior to that of HgTe.

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Theory for the Urbach-Martienssen (U–M) rule on the low energy tail of the fundamental absorption edge of insulators is proposed. The exciton propagator solved for an adiabatic lattice is averaged for lattice vibrations at finite temperature, and the self-energy of exciton is obtained. It describes two characters of exciton in the lattice; the one is the mobile nature of exciton in the undeformed lattice, and the other is the localized nature of exciton trapped momentarily by the lattice deformation due to thermal vibrations. The interplay of the two natures results in the U–M tail below the exciton absorption peak. The result can be interpreted in terms of the Franck-Condon principle where the mobile nature is incorporated in the giant oscillator strength of the momentarily trapped exciton. Emission from this trapped state is discussed in connection with the U–M rule.

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The influence of the electron-phonon interaction of the paramagnetic susceptibilities for transition metals is discussed. While the electronic specific heat is influenced by this interaction, the Pauli spin paramagnetic susceptibility and the orbital paramagnetic susceptibility are not influenced. In the case where the spin-orbit interaction exists, however, the spin paramagnetic susceptibility χ_s, the orbital paramagnetic susceptibility χ_orb and the mixed contribution due to the spin and orbital angular momentums χ_so are influenced. In f. c. c. 4d and 5d and h. c. p. 5d transition metals the modifications of χ_s, χ_orb and χ_so due to the electron-phonon interaction are conceivable, but in other transition metals these modifications are very small. Finally, some discussions of this effect on the diamagnetic susceptibilities are given.

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The absorption coefficient for magnon side-bands is obtained in the whole temperature region by the two-time Green function method in the simple RPA description. The Hamiltonian is composed of excitons and spins, exciton operators being spin-dependent. It is shown that the magnon side-bands have the following behaviors. (1) For T∼0, only one band exists and its expression agrees with the result obtained by the simple spin wave approximation. (2) For 0<T<T_N, additional hot bands appear and the total intensity of absorption increases gradually as T increases. (3) For T∼T_N, all bands come together to from a single band at frequency ω=E₀ where E₀ is the orbital excitation energy. The total intensity is considerably temperature-dependent near and above T_N. (4) For T>>T_N, the total intensity tends to a constant value.

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The orbital paramagnetic susceptibilities for vanadium, chromium, and both paramagnetic ferromagnetic irons are calculated by means of the Kubo and Obata formula. Band structures and wave functions which were obtained self-consistently by a combined method of the modified tight-binding and orthogonalized-plane-wave methods are used. The temperature variation of the orbital paramagnetic susceptibility and the high-field susceptibility are also calculated and the comparisons with experiments are discussed for vanadium and ferromagnetic iron.

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An application of the coherent potential approximation (CPA) to ferromagnetic alloys is discussed on the basis of a nondegenerate tight-binding model. The intraatomic coulomb interaction is taken into account self-consistently within the framework of the Hartree-Fock approximation. Numerical calculations are carried out for the case of Ni_1−xFe_x. The results are in good agreement with the experimental data of the magnetic moments of Ni and Fe in concentrated alloys and also with the data of the electronic specific heat. The instability of the nonmagnetic state at a finite temperature is discussed by calculating the susceptibility in CPA. Possible experiments to check the calculated electronic structure are discussed. An extention to a degenerate (multiband) tight-binding model is also presented.

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A theory for the two-magnon bound state problem is developed for the Heisenberg Hamiltonian with arbitrary spin S and arbitrary dimensionality. The present theory can be applied not only to a ferromagnet but also to an antiferromagnet. It is much simpler and straightforward compared with the many previous theories for the case of ferromagnetism. In the case of antiferromagnetism, the spin-wave approximation must be used. The detailed calculations were carried out for the total wave number K=0, π⁄2 and π in a one-dimensional antiferromagnet. It was first found that bound states exist outside of the two-magnon band. It is very interesting that the energies of the bound states at K=0 and π are lower than the ground-state energy obtained by the spin-wave theory. This indicates that the antiferromagnetic order is not stable in a one-dimensional lattice.

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The nonlocal pseudopotentials in the OPW formalism are determined for sodium and potassium from the experimental data in the radial distortion of the Fermi surfaces, by taking the core shift in the pseudopotential as an only adjustable parameter to fit the data. It is found that the exchange interaction between core and conduction electrons should be treated properly without using the approximate form like the slater exchange to find a reasonable value for the core shift parameter. The exchange and correlation effects among conduction electrons are taken into account in the approximate form proposed recently by Kleinman and are found to be also important. The nonlocality of the determined pseudopotentials is quite significant; the validity of the local pseudopotential approximation seems rather limited. The reason why the analysis of the Fermi surface distortion by using the local pseudopotential has been quite successful for Na but not for K is discussed.

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The band structures of alloy system Hg_1−xCd_xTe are calculated at high symmetry points Γ, X, L, K and on symmetry lines Δ, Λ, Σ by the use of the model potential of Animalu and Heine screened by Penn’s dielectric function. The parameter E_g in Penn’s dielectric function is adjusted so as to make the resulting band structure be in agreement with certain known optical transition energies. The band structures of the alloy system change from the inverted band structure to the normal one as mole fraction of CdTe increases from 0 to 1. The critical mole fraction at which the semimetal-semiconductor transition occurs is obtained as x₀=0.146 at 77K. The agreement with experiment is excellent. The detailed band structure in the vicinity of Γ point is also calculated and is found to be well described by Kane’s expression. The effective masses at the extrema of the bands are evaluated in the full range of mole fraction. The values calculated are about twice the experimental values.

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Radial distortions of the Fermi surface are evaluated for K and Rb by APW method. The Hartree-Fock-Slater potential, the Wigner-Seitz potential, and the Hedin potential, which were used to evaluate the radial distortion of the Fermi surface of K and Rb in a previous paper, are now modified to be l-dependent in order to obtain a good agreement between the calculated and the observed Fermi surface. It is found that very slight modification of the potential is sufficient to have an excellent agreement.

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The correction of dipole fields due to lattice deformation in the NaCl and the CsCl crystals is carried out. The photoelastic effect of these crystals is discussed by taking account of the lattice deformation. It is found that this effect cannot be explained well enough by considering only the contribution of the lattice deformation to the local field acting on the ions which have isotropic electronic polarizability. Then the anisotropy of the electronic polarizability is calculated in the case of NaCl crystal.

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The self correlation function G_s(r, t) and its spacetime transform S_s(k, w) are calculated in the non-Gaussian approximation by using a model for a liquid which molecules move by Langevin diffusion between random binary collisions and also incorporating the solid like oscillatory behaviour into account according to the model of Rehman, Singwi and Sjölander. Similar calculations for G_s(r, t) in the non-Gaussian approximation were previously done by Gibbs and Ferziger. But in their model these authors did not incorporate the oscillatory motion characteristic of liquids. Hence the present model shows an improvement over GF. The non-Gaussian corrections have been estimated for liquid Argon by comparing the best fit of the calculated S_s(k, w) for different values of α⁄(α+β) with the computer experimental non-Gaussian S_s(k, w) of Nijboer and Rahman at K=2Å⁻¹. Here α and β are the binary collision rate and the Langevin friction coefficients respectively. From the results it appears that in liquid Argon (to the extent that it is described by the present model) the binary collision rate is about four times the Langevin friction coefficient.

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Manganese-rich γ-phase alloys of Mn–Ni, Mn–Zn, Mn–Ga and Mn–Ge have been investigated with X-ray and neutron diffraction and specific heat measurements. The Mn–Zn, Mn–Ga and Mn–Ge alloys exhibit antiferromagnetism below the transition temperature, at which the cubic lattice is transformed to the tetragonal lattice (the axial ratio c⁄a<1). The Mn–Ni alloys containing less than 15 at. % Ni become tetragonal (c⁄a<1) at the Néel temperature, while those containing more than 15 at. % Ni are cubic even below the Néel temperature and become tetragonal (c⁄a>1) at a lower temperature. The magnetic structure for the axial ratio c⁄a>1 is different from that for the axial ratio c⁄a<1. The integrated values of the anomalous specific heat are less than the values predicted by the localized moment model of antiferromagnetism.

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The magnetocrystalline anisotropy of the heavy rare earth impurities doped in gadolinium metal was measured by a torque method in a temperature range from 4.2°K to about 200°K. The large contribution from the heavy rare earth impurities to the anisotropy is well explained by the crystal field theory. The temperature dependence of the anisotropy constant can be explained fairly well by assuming that impurity moments behave paramagnetically in the exchange field produced by the host gadolinium. Anomalous bents were observed in torque curves at low temperatures for all the alloys except for Tm–Gd.

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Magnetic properties of a single crystal of almost pure Ulvöspinel Fe_2.05Ti_0.95O_4.00 have been investigated by neutron diffraction and magnetic studies. Fe₂TiO₄ is a perfect inverse spinel with oxygen parameter of u=0.386±0.001 at room temperature. The crystal becomes weakly ferromagnetic below 142°K. The magnetic structure is of the Néel type with the sublattice magnetic moments of 4.2±0.2μ_B on both octahedral and tetrahedral sites at 4.2°K. The moment on the octahedral site decreases with increasing temperature faster than that on the tetrahedral site. The spontaneous weak ferromagnetic moment is induced in one of the ⟨100⟩ direction perpendicular to spins. The spins tend to orient to the direction of the field, only when the magnetic field is applied in the [100] direction. The crystal is suggested to distort tetragonally at low temperatures with the spin along the long axis. The average \baru parameter at 4.2°K is also 0.386±0.001.

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The crystal distortion of a single crystal of Fe₂TiO₄ has been studied as a function of temperature (77°K to 300°K), magnetic field (up to 30 kOe) and field direction, by means of strain gauge as well as X-ray analysis. The distortion is close to tetragonal with tetragonality of (c−a)⁄a=7.1±0.4×10⁻³ at 77°K. The distortion is found to be due to the magnetostriction with λ₁₀₀=4.7±0.3×10⁻³ and λ₁₁₁=1.3±0.4×10⁻³. The magnetoelastic coupling constant B₁ is determined to be 520 cm⁻¹ per molecule. The crystal elongates in the field direction only when the field is applied in the [100] direction. The saturated values of the distortion at 30 kOe are about 70% of the intrinsic distortion in zero field. These phenomena have been explained by assuming the canted spin structure, the cubic anisotropy due to the magnetostriction and the uniaxial anisotropy originated from the internal stress. The cubic anisotropy constant K₁ of the ferromagnetic component is 5.8×10⁵ erg/cc at 77°K.

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The temperature dependence of elastic constants c₁₁−c₁₂ and c₄₄ of Fe_2.05Ti_0.95O_4.00 is measured by the ultrasonic pulse echo method, using a small (110) platelet with approximate dimension of 5×7×1.364 mm, for the temperature range of 77°∼300°K. c₁₁−c₁₂ decreases anomalously with decreasing temperature in the paramagnetic phase, whereas c₄₄ increases. An extraordinarily large attenuation is observed around the Curie temperature in the 1\bar10 shear mode which couples to c₁₁−c₁₂. The elastic constants obtained, c₁₁−c₁₂=0.265×10¹² dyne/cm² and c₄₄=0.396×10¹² dyne/cm² at room temperature, are almost an order of magnitude smaller than those of magnetite and spinel, and provide a reasonable explanation for the giant magnetostriction observed in the crystal. The soft mode in the crystal is interpreted to be due to the Jahn-Teller relaxation effect of Fe²⁺ ions in the tetrahedral site.

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The nuclear magnetic resonance of Pt¹⁹⁵ in dilute magnetic PtCr alloys was observed at the temperature of 4.2 K and 1.5 K. The linear decrease of the nagative Knight shift of Pt¹⁹⁵ versus Cr impurity concentration was observed and found to be slightly temperature dependent. The nagative host polarization by addition of Cr impurity was found by the magnetic susceptibility measurement and this negative polarization due to Cr impurity slightly increases with the decrease of temperature. These results were qualilatively interpreted by the decrease of the effective s conduction electron density and the relation of the reduction of s conduction electron density to the formation of s-d bound state was examined. Also the magnetic susceptibility of PtMo alloy is reported in connection with the Pt¹⁹⁵ Knight shifts in this alloy which were previously reported by Weissman and Knight. The results of thermo-electric power of PtCr alloy are also given.

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The effects of magnetic impurities on superconductors La_3−xGd_xAl containing up to 2 at. % Gd have been studied extensively mainly by specific heat measurements. In the investigated range of temperature and impurity concentration, the superconducting transition temperature T_c as a function of impurity concentration agrees well with the theoretical curve of Abrikosov and Gor’kov. The magnetic ordering temperature T_M observed as the temperature at which the specific heat reaches maximum is lower than T_c in the present study. Absence of the departure from Abrikosov and Gor’kov curve results in the fact that the magnetic ordering has no effect on T_c in the temperature range above T_M. Generally the upper critical field H_c2 decreases linearly with increasing Gd content. The examination of the behaviors of H_c2 gives the possible presence of the magnetic ordering on H_c2 below the studied temperature range. The nature of the magnetic ordering is discussed.

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Crystal structures of palladium-manganese alloys with compositions in the neighborhood of 25 at.%Mn have been studied, and it has been confirmed that the alloys with manganese less than about 24 at.% have the disordered F.C.C. lattice and those with the manganese contents ranging from about 24 to 30 at.% the one-dimensional long period ordered structure with M=2.
Refinement of the structure analysis of the long period ordered alloy Pd₃Mn by X-ray diffraction has been made using single crystals, and periodic atom displacements of the heavy and light atoms have been found to occur with displacement directions similar to those in Cu₃Pd(α″), the magnitude of displacements being as small as 0.01Å for both the kinds of atom. These atom displacements are discussed in relation to the electron-atom ratio of the alloy. Neutron diffraction powder patterns have been observed, in order to see whether the nuclei in Pd₃Mn are displaced together with the electron clouds belonging to them or not, but no definite conclusion has been drawn.

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A phenomenological theory is given for ferroelectric domain switching. It takes into account the initial size of a reversed nucleus and also the shape of domains. It is shown that the Avrami theorem can be easily derived if we utilize Kolmogorov’s method. We solved the problems under two assumptions: one is the constant nucleation rate throughout the switching period and the order is the assumption of latent nuclei of a given definite number and no further nucleations. The i_maxt_max⁄P_s values of several ferroelectrics reported so far summarized and discussed in the light of the present theory.

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The electric spin resonance of donor electrons was investigated in the temperature range from 1.4 K to 4.2 K in several types of CdS, i.e. the undoped crystals grown from the vapour phase and grown by the melt, the crystals doped with chlorine, iodine, oxygen, and both chlorine and neodymium. In Cl-doped CdS and also I-doped CdS, the variation of the line width with the excess donor concentration and the temperature indicated that the motional narrowing effect due to the hopping motion of the donor electron occurred on the line width in a certain donor concentration range. In Cl-doped CdS the additional line broadening due to the shortening of the relaxation time occurred at the concentrations above 7×16¹⁶cm⁻³. The hyperfine splitting of the donors Cl and I was estimated by the line width extraporated to the lower limit of their concentration. In other crystals, the nature of the donor is discussed on the basis of the results of ESR measurements and optical emission ones. The electric field effect on the donor resonance was examined at 1.4 K, but no change in the resonance line was observed in the static electric field up to 3.29 kV/cm.

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Electrical conductivity and electron spin resonance of the metal free phthalocyanine doped with iodine were investigated.
The electrical resistivity and its activation energy of the phthalocyanine doped with iodine were largely decreased as compared with the undoped metal free phthalocyanine.
The change of the conductivity is attributed to the change of the activation energy. The activation energy of the doped phthalocyanine E is expressed by E=I−2P, where I is the ionization energy and P the polarization energy.
The phthalocyanine doped with iodine showed the strong electron spin resonance absorption at g=2.0036 with the line width of 5.03 gauss and its spin density D varied with temperature according to the following relation
(Remark: Graphics omitted.).

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The reflectivity spectra of NaBr and NaI have been measured in the range 5 eV to 11.8 eV at 85°K and particularly in the Γ(3/2, 1/2)-exciton region at several temperatures between 26°K and 302°K. Below about 150°K, a sideband is separated from the Γ(3/2, 1/2)-peak in its higher energy side, the peak-sideband separation being about two times of the LO-phonon energy. This results from the energy dependence of the broadening function hΓ and the sideband is identified as an LO-phonon sideband due to the simultaneous creation of a quasifree pair of an exciton and an LO-phonon. Above 150°K, this sideband merges in the higher energy tail main peak conforming the whole Γ(3/2, 1/2)-exciton line to a single asymmetric Lorentzian function (A. L. F.). hΓ(T) deviates from the coth-law above 70°K accompanying a rapid increase of hΓ due to the LO-phonon sideband. The Γ-exciton spectra of NaCl at temperatures up to 573°K can be well fitted with an A. L. F. regarding hΓ as an energy-independent quantity and assuming the coth-law on its temperature dependence. The reliability of the values deduced from the Kramers-Kronig analysis is also investigated.

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Some experimental investigations have been made in order to understand the nature of phase transitions in the perovskite-type crystal CsPbCl₃. Measurements of the birefringence and conoscopic observations confirm three phase transitions occurring at 37°C, 42°C and 47°C, respectively. The crystal system in each phase and the superstructure below 37°C are determined from the results of these measurements and an X-ray work. A dielectric measurement shows that CsPbCl₃ is neither ferroelectric nor antiferroelectric in any of the phases. The transition entropies estimated from the result of a specific heat measurement are considerably smaller than that reported by Møller. The elastic compliance measured by the method of composite oscillator shows anomaly at each transition point. Temperature-dependent Raman spectra demonstrate the existence of “soft” modes which are overdamped near the transition temperatures. The nature of these phase transitions is discussed on the basis of the experimental results.

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The cross section for X-ray inelastic scattering from crystals has been derived from first principles to explain the coexisting Compton and Raman scattering in solids. This derivation makes it possible to express the inelastic scattering cross section in terms of the current correlation of electrons in a crystal. The criterion for having a distinct Raman scattering is obtained through the dependence of the current correlation on the momentum transfer.

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A very sharp anisotropy of the angular correlation of annihilation radiation in a single crystal specimen was found and investigated. It proved to be attributed to the diffraction of the annihilation photons by the lattice planes of the crystal. The experiment was performed by the rotating specimen method as well as by the angular correlation method. The results showed that the diffraction of the annihilation photons makes a serious effect on the shape of the usual angular correlation curve and that the effect is very sensitive to the orientation of the crystal as expected. The integrated intensities of the diffraction peaks calculated by using the kinematical theory of X-ray diffraction were in a fairly good agreement with the experimental values.

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Associative ionization through slow collisions of an atom with a metastable atom is investigated theoretically, in which the excitation energy of an excited atom is larger than the ionization potential of the other atom. The process is dealt with by the local complex potential method, since in this case the initial discrete electronic state is a resonance state because of the coupling with a degenerate continuum. Cross section formulas are obtained for a molecular ion formation with specified rotational and vibrational quantum numbers (j, v) and a total associative ionization. As a demonstration the method is applied to the system He^*(2³S, 2¹S)+H. Population inversion with respect to vibrational levels is expected to occur fairly effectively in these processes.

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The electronic states in the Debye-Hückel potential, −(Ze²⁄r)exp(−r⁄D), are investigated and the critical screening radius D=D_c(n,l) is given by the simple formulae
(Remark: Graphics omitted.),
where n and l denote the principal and azimuthal quantum numbers, respectively, and a=h²⁄me². By a comparison with the results of numerical calculations, it is ascertained that these formulae hold with sufficient accuracy. The method is to connect the quasi-classical solution of the Schrödinger equation with the solution for the pure Coulomb potential in the region where both approximations are valid.

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Investigation has been made of the motion of vortex rings deformed from circular shape. A theoretical calculation of their shapes on the basis of the localized induction equation for a very thin vortex filament is made and is compared with observation of distorted smoke rings produced in the laboratory, using smoke of tobacco.
Observations are also reported of fusion of two smoke rings into and splitting of very much distorted smoke rings.

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