The effect of the J=2, T=0, π–π interaction on the π–N invariant amplitude B⁽⁺⁾ is analyzed. It was found that the π–N scattering data is inconsistent with a J=2, T=0, π–π phase, due to δ₂⁰, which rises To above 13° around 650 MeV. From the data it is impossible to say whether the results correspond to a resonant phase or only a sharp peak in the corresponding absorptive part of the amplitude.

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The interference effects in the production of bremsstrahlung in a silicon single crystal have been studied by using 720 MeV electrons. The energy spectrum of the bremsstrahlung has exhibited interference maxima of the first five orders. The intensity variation of the 150 MeV photons with the rotation of the crystal has shown also three interference Maxima on each side of the central minimum. The observed interference conditions for the photon energy and angles of incidence of electrons relative to crystal axes are in good agreement with the theory.

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X-ray reflection intensities were measured with a diffractometer on Powder specimens of NiO, CoO and MnO, of particle size less than about 5 μ with MoKα ,CuKα FeKα and CrKα. By a scaling procedure, the absolute values of the experimental structure factors were derived. The temperature factors of individual ions were estimated by three dimensional difference Fourier syntheses. The factors obtained were B_Ni=0.63 Ų and B_O=0.41 Ų for NiO, B_Co=0.52 Ų and B_O=0.48 Ų for CoO and B_Mn=0.88 Ų and B_O=0.66 Ų for MnO. It is found that the electron Distribution in the three oxides is very similar to each other, and that the electron density near the center of [111] direction is smaller beyond the limit of experimental errors than that of the theoretical calculations for the spherical free ion.

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Contributions of anharmonic vibration to the Debye-Waller factor and the intensity of X-ray diffuse scattering were calculated for polyatomic crystal by the quantum statistics. Applying the anharmonic parameters which were obtained in the theory of specific heat, the contribution to the temperature factor and the intensity of diffuse scattering were estimated numerically for ionic crystals. From the comparison between the results of calculation and experiments, it was made clear that most parts of anharmonic effect arise from the thermal expansion, although cubic And quartic anharmonic contributions are noticeable for KCl at high temperatures. The effect of anharmonicity was investigated at absolute zero degree in ionic crystals.

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The changes of resistivity during isothermal aging after quenching were measured in Al-0.72wt%Ag, Al-3.0wt%Ag binary alloys, Al-3.0wt%Ag-0.10wt%Ge, Al-3.0wt%Ag-0.01wt%In and Al-3.0wt%Ag-0.01wt%Sn ternary alloys and the interaction between a vacancy and an Ag atom was studied. General features of clustering in these ternary alloys were not different from those in Al-3.0wt%Ag binary alloy. Therefore, the binding energy between a vacancy and an Ag atom could be obtained by taking the ratio of time, t_Mt, required to reach the maximum of electrical resistivity in ternary alloys with that time, t_Mb, in binary alloy and using the already known binding energy between a vacancy and a second solute atom. Binding energy between a vacancy and an Ag atom was estimated to be 0.25±0.05 eV.

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The absorption spectrum of anthracene single crystal was measured in the range from 3950 A to 4400 A, i. e., the long wave-length tail of A_1g–B_2u transition. For the change of temperature from −180°C to 80°C, the absorption increases markedly both for a- and b-polarized light. The contour in the absorption tail can be separated into two parts. The one is the absorption obeyed to the Urbach rule, and the other is the absorption due to the transition from the hot level in the ground state to the first excited state. In the former absorption at a temperature Range above −80°C, the constant values of σ in the Urbach formula are obtained; 1.68 in a-polarized light and 0.88 in b-polarized light. In the latter absorption, the peaks at 4125 A and 4145 A were observed with a- and b-polarized light, respectively. The common thermal activation energy of 0.16 eV is obtained.

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The specific heat of InSb was measured over the temperature range Between 6 and 100°K. The Debye characteristic temperature curve shows a minimum at about 13°K in agreement with the prediction of Fray et al. Analysis by the method of Thirring-like expansion gives Θ_∞=250±5°K which is much smaller than the equivalent temperature 283°K of the maximum frequency of lattice vibration (197 cm⁻¹, in wave number unit), compared with the cases of Ge and Si. It is pointed out that the anharmonic effect is relatively large even in low temperature region.

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By using a network model, the effects on the band structure of two-dimensional graphite due to localized perturbations are studied. The density of states near the Fermi energy is considerably modified by such perturbations. In the case of attractive perturbation, the density of states above the Fermi energy is increased and the density of states below the Fermi energy is slightly decreased. In the case of repulsive perturbation, the reverse is the case.

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The conduction mechanism of α, α′-diphenyl-β-picrylhydrazyl (DPPH) single crystal is studied by measuring electric conductivity, magneto-resistance, ESR etc. Moreover, the electric conductivity is theoretically given by the following equation,
σ=A_θn(e²d²J⁄hkT)exp(−E_J⁄kT)
which is based on the hopping of unpaired electrons in DPPH molecule, and the theoretical value shows good agreement with the experimental value.

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A new method of investigating energy band structure is proposed which makes use of the angular dependence of two-photon absorption coefficient of polarized beams. The angular dependences of the allowed transitions are calculated and tabulated for 32 crystal point groups. The exciton as well as interband transitions are discussed, and the method will be explained for the cases of NaCl–, CsCl–, ZnS– and diamond-type crystals how to determine the points of extremum vertical energy separation in the Brillouin zone with the help of associated tables and figures.

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The part of absorption coefficients of X-rays arising from the phonon excitations is calculated quantum mechanically. When the polarization vectors of the incident X-rays are in the diffraction plane, and are parallel to the direction of diffracted wave, the cross terms of the direct phonon and the photoelectric excitations mainly contribute to the h-wave absorption coefficient (i.e. h-component of the absorption coefficient in the two-wave approximation). It is also concluded that the direct phonon excitation could be significant near the absorption edges.

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It is evidently shown by neutron diffraction that the alloy Cu₂NiZn forms the long range order after prolonged annealing at 300°C. The observed structure factors of the superlattice reflections with mixed indices are evaluated to be between 0.29 and 0.33×10⁻¹² cm. Three structure models, whose unit cells are based upon the original face centered cubic cell containing four atoms, are proposed to interpret the experimental results. A good agreement between the observed and calculated structure factors is found in the following model, i. e., a nickel atom is at the origin, and a zinc and two copper atoms are statistically distributed at the three positions (1/2, 1/2, 0, (Remark: Graphics omitted.)). Possibility of other two models is also discussed on the basis of the present investigation as well as other physical properties.

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By making use of the result obtained in Part I, the numerical calculation of A in ω=A·M_d(T) of Fe⁵⁷ in ferromagnetic iron has been carried out and the calculated value of A is found to become 1.4₇∼1.9₄×10⁵ gauss⁻¹ sec⁻¹, corresponding to the assumed values, ranging 2 to 1 of η, i.e., the amount in percentage of the admixture effect which is generally expected to be a few percent or less. The comparison with the observed value, i.e., A=1.67×10⁵ gauss⁻¹ sec⁻¹ at T=0 for Fe⁵⁷ in ferromagnetic iron seems to be quite satisfactory. It shoud be remarked that the more or less spreaded, atomic orbitals of 3d-electron within the crystal compared with the Hartree-data of an isolated Fe atom may give favourable results for the nuclear magnetic resonance frequency of Fe crystal. The hyperfine field felt by Fe⁵⁷ nucleus within the ferromagnetic Fe has also been calculated to become H_hy=−3.0∼−3.9×10⁵ Oe at T=0, which agree remarkably well with the observed values of −3.39×10⁵ Oe by the nuclear magnetic resonance method and of −3.33×10⁵ Oe by the Mössbauer-type experiment.

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A calculation on the temperature variation of the magnetization for Ni metals performed by the Stoner theory, by making use of the density of states curve which was determined from low temperature specific heat data. The effective exchange energy is expanded as a power series of the magnetization, M, and the values of coefficients are estimated from the comparison between calculated and experimental results of the M vs T curve. In order to explain the experimental results for the temperature variation of M in Ni metal, the terms of the higher power of M than the quadratic term in the exchange energy must be taken into account. Our density of states curve is not similar to the normal band used by Stoner and the rectangular band used by Wrohlfarth, nevertheless the calculated results for the temperature variation of M are similar to each other. It is shown that there is a Possibility that a first order transition of magnetization occurs.

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Very narrow lines and abroad band have been observed in emission with the excitation into the band to band region or the exciton absorption band. Narrow emissions consist of a strong 3901 Å, a weak 3870 Å and a very weak 3785 Å lines at 4°K. They are attributed to the n=1 Stokes, n=1 and n′=1 resonance exciton emissions, respectively. n=1 and n′=1 are the first members of the sharp and the diffuse absorption line-series. A broad emission consists of two bands peaking at 4030 and 4250 Å. The former emission band has an asymmetric shape and is ascribed to the annihilation of a trapped exciton. From the temperature dependence of the emission intensity and the photoconductivity, the discussion is given on the emission processes.

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Line broadening of cyclotron resonance is treated theoretically assuming the radius of cyclotron orbit to be smaller than the force range of impurity potential. The impurity potential causes adiabatic change of The cyclotron frequency and non-adiabatic transitions. The modulation of the frequency due to electron motion is treated for the case of slow modulation as well as for that of rapid modulation. The validity of statistical theory and impact theory Is discussed. The non-adiabatic effect is shown to be small in the case under consideration.

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A Markoff chain model to describe the structure of semi-crystalline Polymers is presented. It consists of a random walk on a square lattice. The crystalline region is characterized by a preferred walk whereas the amorphous region by a random walk. The steps of the walk are identified with the bond vectors of the chain and its progress is governed by a transition probability matrix. Expression for the expected square of the end-to-end distance is derived in terms of two probability parameters p and α. The mathematical methods of Markoff chains are used. The Extension of the model to account for the modern ideas of chain folding In the single crystals of polymers is suggested. The problem of excluded volume is excluded.

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A simple and uniform treatment is presented for eliminating the angular variables from the n-particle Schrödinger equation and for deriving the Hamiltonian of polyatomic molecules in a form suitable for a perturbation calculation. The Hamiltonian is first set up conveniently in a special set of rotating axes. Introduction of three pseudo-momenta, which correspond to no coordinates, greatly simplifies the calculation and makes it unnecessary to evaluate the Jacobian of the transformation, The Hamiltonian so obtained can be directly used to eliminate the angular variables. For the molecular problem it is found necessary to pass on to some other rotating frame in which the coupling between rotation and vibration becomes sufficiently small. A method for doing this is discussed in the last section.

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Approximate formulas for some basic quantities concerning the transition between a discrete state and the continuum in collision problems are given with some estimate of the error. As to the matrix of the interaction it is assumed that only the elements corresponding to the transition between the discrete state and the continuum have non-zero values.

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The magnetic hyperfine structure of the J=3, K=2 line in the inversion spectrum of N¹⁴H₃ has been studied by means of a molecular beam maser spectrometer. The results are analyzed by assuming (I·J) type interactions of the protons and nitrogen spins, and by taking the coupling scheme of angular momenta F₂=I+J,F=I_N+F₂. The observed hyperfine structure shows two satellite lines on each side of the central line, corresponding to the transitions with ΔF₂=0, ΔF=±1, and ΔF₂=ΔF=±1. From the frequency measurements of these satellite lines the coupling constants of the (I·J) interactions are determined to be −17.67±0.3 kc for the protons, and 6.73±0.04 kc for the nitrogen nucleus. The theory predicts that the hyperfine components with ΔF₂=0, ΔF=±1 consist of two groups of lines separated by abut 7 kc, while the experiments show that the separation is smaller than 4.5±0.5 kc. Effects of other types of interactions are taken into consideraction, but they give no appropriate interpretation of the discrepancy.

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Plasma ion oscillations have been studied in a plasma produced by hot-cathode, mercury-vapour discharge, at a pressure of about 1 μHg. A super-heterodyne detector and a movable probe were employed to observe frequency spectra at different points in a small tube having plane electrodes.
The frequencies of the self-sustained plasma ion oscillations were markedly dependent on the position in the tube, and the frequencies of the ion oscillations on the inside of a beam were lower than that on the outside.
In order to explain our observation, a simple theory of plasma ion oscillation in a plasma-beam system is proposed.

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A theoretical investigation is made on the steady axisymmetric flow of an incompressible viscous fluid through a taperared tube. The velocity field is expanded into inverse powers of r, the distance from the virtual vertex of the conical tube, and the equations for the coefficient functions are solved successively. Distributions of the velocity, the pressure and the stress are determined to the second approximation, the first being the results obtained with the Stokes approximation. The flux of the flow per unit time is also calculated and shown to agree with that obtained with the Stokes approximation.

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The flow of viscous fluid past a tangential flat plate is studied to Oseen’s approximation with special reference to the flow around the trailing edge of the plate. Bairstow-Cave-Lang integral equation is solved asymptotically for large Reynolds numbers and for the trailing edge region by making use of singular perturbation technique. The analysis confirmed the uniform validity of the classical solution of Piercy-Winny over whole region including the trailing edge.

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