Using 5.7 Mev protons from the cyclotron, we have studied the angular distributions of protons elastically scattered from Ni and Cu by means of nuclear emulsion technique. The angular distributions were measured from 14° to 161° at an interval of 5° in the laboratory system. The differential cross sections, in the ratio to the Rutherford cross section, have a minimum at about 85° in both cases, but at large scattering angles the cross section for Ni increases linearly, while there is a maximum at about 130° in the case of Cu. The results are in essential agreement with those of Bromley and Wall.

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Geometrical theory of convex molecules in uniform gases (T. Kihara, Revs. Modern Physics, 25 (1953) 831, 27 (1955) 412) is generalized to that in non-uniform gases when molecules are represented by rigid convex bodies without any additional intermolecular force. For this representation collisions between heavy molecules and light spherical molecules are treated exactly. Shape and size of several molecules are determined from diffusion coefficient. A “geometrical approximation” is suggested for more general cases.

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A general type of fluctuation-dissipation theorem is discussed to show that the physical quantities such as complex susceptibility of magnetic or electric polarization and complex conductivity for electric conduction are rigorously expressed in terms of time-fluctuation of dynamical variables associated with such irreversible processes. This is a generalization of statistical mechanics which affords exact formulation as the basis of calculation of such irreversible quantities from atomistic theory. The general formalism of this statistical-mechanical theory is examined in detail. The response, relaxation, and correlation functions are defined in quantummechanical way and their relations are investigated. The formalism is illustrated by simple examples of magnetic and conduction problems. Certain sum rules are discussed for these examples. Finally it is pointed out that this theory may be looked as a generalization of the Einstein relation.

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It is shown that an electron gas exhibits the Meissner-Ochsenfeld effect if a special type of electron-electron interaction, e²s₁·s₂⁄r, is assumed and if the motion of an electron is considered to obey Dirac’s relativistic equation. (s₁ and s₂ are the spin operators belonging respectively to each interacting electron.) The perturbation method of statistical mechanics, when applied to this system, leads to the London equation though the coefficient is different from London’s original one. The theory talks in principle about the feature at the absolute zero of temperature in the sense that the electron-phonon interaction is not taken into account. The penetration depth of the field calculated according to the present model is quantitatively in good agreement with experiment. The known type of electron-electron interaction due to Breit, does not lead to superconductivity even in the relativistic treatment. The proposed interaction is discussed in connection with some experimental facts, i.e. the existance of an impurity effect for the penetration depth and the smaller Knight shift in the superconducting than the normal state.

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The temperature independent diffuse scattering of X-ray by a diamond lattice, in which a few carbon atoms are missing or have been replaced by foreign atoms of valency four is investigated. By the method given by Matsubara the intensity of diffuse scattering is calculated in terms of the force constants which are related to changes in bond length and of bond angle. The diffuse patterns observed by Lonsdale and Smith in natural diamonds are of streak or spike type but ours are of lemniscate type. Our patterns may be observed in radiation damaged diamond crystals.

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The effect of inelastic scattering on electron diffraction by crystals is theoretically studied. It is proved that the effect of inelastic scattering gives rise to an additional complex term to Fourier coefficient of the inner potential. The imaginary part of the additional term explains qualitatively the observation that two components of a doubly refracted electron beam are subjected to different degrees of absorption (Honjo and Mihama, J. Phys. Soc. Japan 9 (1954) 184). The real part of the additional term gives a correction of about 6∼7 % to the calculated value of mean inner potential at accelerating voltages of 30∼40 kv. This explains the systematic difference between the mean inner potential experimentally obtained by electron diffraction and that calculated by the use of diamagnetic susceptibility (Miyake, Proc. Physico-Math. Soc. Japan 22 (1940) 666).

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Samples of cobalt of the α-modification (hexagonal close-packed lattice) and the β-modification (face centered cubic lattice) and their mixtures were prepared, and their crystal structures were examined by means of the X-ray diffraction method. Fine structures of the X-ray K absorption spectra of these cobalt samples were photographed by a bent crystal spectrograph and the mass absorption coefficients in the X-ray K absorption spectral region were measured by using the North American Philips Diffraction Unit and Wide Range Spectrometer modified to a tube spectrometer with a Geiger-Müller counter. By comparing these photometer curves of these spectrograms or the recorded curves, the fine structures of the absorption spectra of these cobalt samples were found to be very similar. The wavelength values and the mass absorption coefficient of the fine structures of the absorption spectra also nearly coincided within experimental errors, and thus the position and the form of the maximum and minimum of these structures were found to be the same. We conclude that this is due to the fact that atoms in the α-cobalt have the same immediate surroundings as those in the β-cobalt.

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Intensity of electron diffraction Debye-Scherrer rings was studied for evaporated films of Al, Ag, Au, NaCl, KCl and MgO of various thicknesses and crystal sizes. The observed intensity deviates from the value calculated by the kinematical theory of diffraction at crystal sizes less than 100 Å for all the materials examined. This result agrees with the conclusion of Blackman’s dynamical theory (Proc. Roy. Soc. 173 (1989) 68).
Yamzin & Pinsker’s conclusion (Dokl. Akad. Nauk 65 (1949) 645) that the kinematical theory can hold for films of thickness up to 500 Å, apparently contradicts the present result. It was pointed out that Yamzin & Pinsker’s conclusion resulted from the fact that they neglected the effect of the temperature factor.

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The electronic energy levels of typical triphenylmethane dyes, Döbner’s Violet and Rosaniline, are calculated through the simple LCAO MO method. The electron densities and the bond orders in the ground states are also computed. Then, with these values of electron densities and the bond orders, the differences of the coulomb and of the resonance integrals, Δα_i and Δβ_ij, respectively, as well as those between the carbon and the nitrogen atoms are taken into account and the electronic energy levels calculated above are modified by perturbation method. The differences of the coulomb integrals between the carbon and the nitrogen atoms cause profound effects to the absorption energy which amount to 23∼27 Kcal (40∼50 %), whereas those of different carbon atoms affect to the absorption only 4 Kcal (10 %). The energy levels of the various derivatives of Döbner’s Violet and Rosaniline, e.g. dimethyl and diethyl derivatives of Döbner’s Violet, Malachite Green, Brilliant Green, Hoffmann’s Violet. Crystal Violet, Ethyl Violet etc. are also calculated by the method of perturbation. The values of the coulomb integrals of attached end groups are estimated through the basicity of the groups. The calculated absorption energies for these derivatives are compared with the observed light absorptions and it is shown that the course of the calculations is reasonable.

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The number of nonequivalent directions of the z-axes of the field gradient in the crystal for every symmetry class is calculated. It is shown that we may discuss about the symmetry of the crystal and may determine the orientations of nonequivalent directions with respect to the axes of symmetry through the Zeeman analysis of nuclear quadrupole resonance line.

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Details of the universal quadrupole resonance crystal analyzer were described, and using this apparatus the crystal structure of SnBr was studied at room temperature (15°∼20°C). The SnBr₄ molecule is an almost exact tetrahedron, and each of the four resonance lines is assigned to each bromine atom situated at the apexes of the tetrahedron, and the value of asymmetry parameter of the field gradient at the bromine nucleus is less than 0.025. The crystal has monoclinic symmetry and one of the Sn-Br bond in one molecule is perpendicular to the b-axis and the other two orient at the same angle to the b-axis. All atoms including Sn in a molecule have nonequivalent general positions in the crystal, and the number of molecules in a unit-cell is equal to the maximum number of equivalent coordinates of the space-group. The existence of pair of two molecules is suggested, and the origin of the splitting of the spectrum is discussed. SnBr₄ may be assigned to the symmetry class C_2h. The crystal symmetry of the low temperature phase is assigned to the cubic or hexagonal class.

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This is the final report of a series of papers from this laboratory on the internal motion and the structure of methyl amine. Most of the observed lines including J=1←0, K=0←0 lines were analyzed in the frequency range between 4 and 50 kMc/sec. The barrier height of internal rotation has been determined to be 691.1 cm⁻¹ as well as the molecular structure, d_CN=1.474 A, ∠HNC=112°10′, ∠HNH=105°50′, ∠HCH=109°30′ and the angle between CN and methyl axis=3°30′ on the assumption that d_CH=1.093 A and d_NH=1.014 A. These results were compared with the barrier height and the structure of other CH₃ MH_n type molecules, methyl alcohol and methyl mercaptan.
The inversion doubling of the observed lines was also analyzed satisfactorily. The quadrupole coupling constant of N¹⁴ along the charge symmetry axis has been obtained as −3.6±0.3 Mc/sec, with the direction of the axis, 90°±8, from the methyl axis.

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The microwave spectrum of normal methyl mercaptan has been studied in the frequency range from 14 to 29 kMc/sec. The potential barrier height hindering internal rotation has been determined as 444±10 cm⁻¹ from the analysis of the lines corresponding to the transitions involving both over-all and internal rotations. The fine structures of J=1←0, K=0←0 lines of the various isotopic species have also been analysed and discussed. The molecular structure of methyl mercaptan has been calculated to be d_SH=1.336±0.01 A, d_CS=1.819±0.005 A, d_CH=1.091±0.01 A, ∠CSH=96°30′±1°, ∠HCH=109°45′±30′ and the angle between CS bond and methyl axis, θ=2°0′±30′.

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Fluctuations in the amplification and absorption of waves by quantum processes are considered. Assuming for each quantum the probability (per unit time) a of producing another quantum, probability b of being absorbed, and assuming a probability c that a new quantum is introduced, a set of differential equations is obtained. By solving these equations, a complete expression for the probability of distribution of quanta is obtained, as well as expressions for the average values and fractional fluctuation.
The expressions developed are applied in particular to maser-type amplifiers, and certain fluctuations in the amplification of electromagnetic waves are pointed out which are important when their quantum character becomes significant. This condition can occur in maser-type amplifiers, where thermal and extraneous noises may be very small. For such an amplifier, a is proportional to the number of excited molecules, whereas b consists of a term proportional to the number of molecules in the ground state plus terms due to certain other losses. The noise temperature of a maser-type traveling-wave amplifier is the “effective temperature” a(a−b)⁻¹hν⁄k. In superregenerative and regenerative amplifiers using resonant cavities, the noise temperature is rather similar, if losses through the input coupling hole are excluded from b. In any case, the limiting noise for an ideal amplifier corresponds to a classical noise temperature of hν⁄k.

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The magnetic susceptibilities of various Fe-Ni alloys have been measured through their melting points up to 1600°C. The susceptibilities of the alloys with less than 60 % Ni increase discontinuously on melting, while those of the alloys with more than 60 % Ni decrease. The temperature variation of the susceptibilities is approximately expressed by the Curie-Weiss law in the liquid state as well as in the solid state, but the Curie constants and the paramagnetic Curie temperatures of liquids are in general different from those of solids.
These results can be explained by assuming that the atomic magnetic moments remain unaltered and that the magnetic interaction varies with the interatomic distance as indicated by the Bethe-Slater curve. The change of susceptibility at the melting point is solely due to the difference in interatomic distance between the liquid and the solid.
It is expected, in some cases, that the especially strong dependence of the magnetic interaction on the interatomic distance results in an appreciable change of interaction with temperature through the thermal expansion. It can account for the anomalously large Curie constants of pure γ-Fe and Fe-rich alloys in the solid state.

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The wave functions of the ground state and several lower excited states of O₂ and O₂⁺ are calculated non-empirically at R=2.3 a.u. by LCAO MO method, where all sixteen electrons are taken into consideration and Slater type 1s, 2s, and 2p atomic orbitals are used. For the ground state of O₂, various approximate treatments are investigated. Further for ¹Δ_g, ¹∑_g⁺, ¹∑_u⁻, ³∑_u⁺, and ³∑_u⁻ states improved calculations are performed by mixing several configurations. By using the wave functions thus obtained, dissociation energy D_e, excitation energies ΔE, molecular quadrupole moment Q, magnetic hyperfine structure parameters ⟨ψ²(0)⟩ and ⟨P₂⁄r³⟩, oscillator strengths f, diamagnetic second order Zeeman term χ_dia., and polarizabilities α_\varparallel and α_⊥ are calculated and compared with the observed values. The results are found to be improved appreciably by mixing a small number of configurations. Finally, several of the wave functions of the O₂ ground state are analyzed by the population analysis method developed by Mulliken.

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