The ESR spectra of the powder samples of cubic ZnS:Mn, hexagonal ZnS:Mn, and CdS:Mn are treated theoretically for the case where the exchange interaction exists between the Mn²⁺ ions. The comparison of the calculation with experiments indicates that, for a pair of Mn²⁺ ions, the resonance spectra are well described by the spin Hamiltonian in which the Zeeman, hyperfine, and isotropic exchange terms are included, but anisotropic interaction terms are neglected; the g-factor and the hyperfine constant are isotropic and the same for each of exchange-coupled Mn²⁺ ions, and the cxchange interaction is of the Heisenberg type. Also, a discussion is given on the case of a cluster of three or more Mn²⁺ ions.

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The degree of self-compensation in heavily doped binary semiconductors is calculated by assuming the existence of both doubly ionizable vacancies and impurity-vacancy complexes. It is found that the compensation by the complexes results in limitation in the concentration of effective donors. A tentative explanation is proposed for the observed limit in n-type conductivity in ZnTe.

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The pair distribution function for a cell-model liquid has been derived by Lund in an earlier work in the form of an integral equation which depends upon the cell-center distribution function and the cell model. From this integral equation an approximate integral equation is obtained by substituting a function, linearly dependent upon the molecular pair distribution function and a variable parameter λ, for the cell-center distribution function. This approximate integral equation is solved for the molecular pair distribution and λ is shown to depend upon the difference between temperature and the critical temperature. Although the exact numerical solution of the molecular pair distribution is not practical because of a great number of arbitrary constants of integration, the stability of phase can be noted above and below the critical point. The solution for the molecular pair distribution function is shown to agree with the Ornstein-Zernike theory in the neighborhood of the critical point.

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The composition dependence of the Hall coefficient and the electrical resistivity on dilute alloys of zinc, magnesium, germanium and silicon in aluminium have been measured at 500°C. The Hall coefficient, plotted against the electron concentration (e/a), shows two distinct features: one is a “valley” at 3.00 in e/a, and the other is a “step variation” at about 2.95 in e/a. The former seems to be explained fairly well by the scattering mechanism suggested by Takano. The latter may be related to an electronic effect.

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The magnetic susceptibilities of the Pd–Cd, Pd–Sb, and Pt–Cu binary alloy systems have been measured from room to liquid helium temperatures. The various contributions to the susceptibility have been caluculated and the spin paramagnetic susceptibility has been discussed in terms of the rigid-band model of alloying.

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The observed dielectric constants of silver show clearly a contribution from the interband transition. Making use of the same values for various parameters as in a previous analysis for optical absorptions, analysis of the dielectric constants is made on the basis of the mechanism of direct transition. It is found that the mechanism of the direct transition from the d-band to the conduction band under the calculated band structure is able to explain consistently the optical absorption and the dielectric constant. By calculating the energy decrease for an excited state of the system resulting from the fact that conduction electrons screen a d-hole, it is shown that the discrepancy in the gap energy between our band structure taken consistently with the optical data and the band structure calculated by Segall can be explained by the many body effect.
For sodium, it is shown that the contribution to the dielectric constant from the excitation of conduction electrons into the nearest higher band is negligibly small.

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Within the frame of the random phase approximation, the equation of motion for normal modes in an electron gas is solved by the iteration method and dispersion relations of a plasmon for the paramagnetic and ferromagnetic electron gases are obtained. The dispersion relation in the paramagnetic state agrees with that given by Kanazawa et al.. It is shown that there is no difference between the constant terms in the dispersion relation with respect to the momentum of plasmon in the paramagnetic and ferromagnetic states, but coefficients of the terms proportional to the square of the momentum in the dispersion relation are different in the paramagnetic and ferromagnetic states. This difference is roughly estimated for the real ferromagnetic metals, iron, cobalt and nickel, and a possibility of the observation of this difference is discussed.

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From measurement of magnetic resonance under forced strain, two magnetoelastic coupling constants of αFe₂O₃ were obtained separately. The trigonal magnetoelastic coupling constant B₁₅ is dominant and it explains quantitatively the in-plane anisotropy field in the (111) plane observed in resonance experiment, confirming the theory of the coupling proposed by Iida and Tasaki formerly.

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The expressions of the coefficients appearing in the interaction (Remark: Graphics omitted.) between unpaired spins have been derived together with the expressions for the ordinary superexchange integral J_ij. The latter expressions include some new terms which have been overlooked in previous derivations. Consideration of the former interaciton seems to solve, at least qualitatively, the difficulties encountered before. The results were also applied in the derivation of the expressions of the coupling constant in the interaction between a paramagnetic ion pair and an electric field.
Finally, an attempt is made to calculate the superexchange integral in the three center four electron problem by using the values obtained in the calculation on KMnF₃. The relation between Anderson’s recent theory and the older based upon Heitler-London model is studied. Numerical results are given and analyzed from both points of view.

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A new formulation of the theory of X-ray diffraction by a crystal using techniques of quantum field theory has been developed. The classical field amplitudes of previous theories are replaced, in the present work, by scattering amplitudes for the transmitted and diffracted beams which are obtained from a photon Green’s function. The case of a single-Bragg reflection for a parallel sided crystal has been treated in detail. The scattering amplitudes for this case give results which are essentially those of the semi-classical dynamical theory with absorption. The application of the theory to the diffraction of a beam of finite width for the Laue geometry provides an alternate demonstration that the beam emerges from the exit surface of the crystal at a point given by the direction of energy flow.

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The intensity variations in the Compton and thermal scatterings with the change in diffraction condition were measured using a double crystal spectrometer of parallel setting for Si and Ge single crystals with Cu Kαand Mo Kα radiations. For comparison, the fluorescent emission was also measured for Ge with Mo Kα. A large dip was observed in the intensity cures of the Compton and thermal scatterings for all the cases, like in the fluorescent scattering observed by Batterman. The asymmetric profile of the intensity curve varies with the specimen, radiation and reflecting plane used. The various asymmetric profiles are explained qualitatively by the difference in mechanism of the scattering, i.e. by taking into consideration that the Compton scattering is caused mainly by the outer electrons, the thermal scattering by the whole electrons and the fluorescent emission by the inner electrons.

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For the study of the temperature effect on X-ray diffraction for a perfect crystal, precise measurements of the rocking curves were made at room and high temperatures by a triple-crystal spectrometer. The Bragg case diffraction was studied for the 111 and 333 reflections from Ge with Cu Kα and the Laue case diffraction for the 220 reflection from Si with Cu Kα (μd=13.85) and Mo Kα (μd=1.03) where μ is the mean absorption coefficient and d the effective thickness of the specimen. The experimental results on the reflection width, peak value, integrated intensity and profiles were in fairly good agreement with the calculated ones in which both the real and imaginary parts of the structure factor were multiplied by the Debye factor exp(−M).

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A structural model of the hydrated electron in the radiation chemistry of water and aqueous solutions is proposed. The energy levels of the hydrated electron have been calculated. The binding energy is estimated at 2.4eV. The excitation energy is estimated at 0.80eV, which is comparable with the experimental data, 1.7eV. The oscillator strength of this transition is calculated at 0.26.

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Optical activities of macromolecules, characteristic lengths of which are larger than or comparable to the wavelength of the incident light, are discussed. Long helical polymers are treated in detail. No special length dependent phenomena are found to be expected. The effectiveness of the small (compared with the wavelength) molecule treatment of long helical polymers is thus assured.

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The optical mixing process, in which two incident light beams with frequencies ω₁ and ω₂ produce light of frequency 2ω₁−ω₂ through the third order nonlinear polarization in the electric field, has been experimentally studied in crystalline quartz. A ruby laser, a Nd glass laser and several liquid Raman lasers were used as light sources. Making use of the symmetry properties of the nonlinear susceptibilities, it was confirmed that the observed phenomenon is not the combined effect of two processes due to the second order nonlinear polarization in the electric field. The dispersive property of the associated nonlinear susceptibility χ₃ was measured as a function of ω₁−ω₂. The value of χ₃ showed no appreciable change in the frequency range (ω₁−ω₂)−ω_v=100∼4000 cm⁻¹ where ω_v is the typical lattice vibrational frequency. The results are discussed in connection with the energy level structure of quartz.

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Rayleigh problem in which a plane wall bounding infinite mass of a gas is set impulsively into uniform motion in its own plane is considered using the B-G-K model of the Boltzmann equation. The velocity U of the wall is assumed to be small, but nonlinear terms of order U² in addition to linear ones are taken into account in this analysis. Normal stress on the wall at the initial stage is seen to increase gradually from the initial equilibrium value. The corresponding continuum theory exhibits, however, a sudden jump of the normal stress at the initial moment.

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The Stokes equations for creeping flow are used to obtain steady flow of an incompressible, viscous fluid of infinite extent past a liquid drop which deviates slightly from a sphere and includes fully circulating flow. The flow fields, both external and internal to the drop, are determined up to the first order in a parameter which characterizes the departure of the drop surface from a sphere. Further, the condition relating the normal components of viscous stress at the drop boundary to the surface tension force is examined. It is shown that this condition, when connected with the creeping flow solution obtained, leads to the expression of drag force experienced by the drop, but does not permit to specify the drop shape, assumed at the beginning, in terms of known parameters such as Reynolds number, Weber number, etc.

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