The differential cross-sections for the elastic scattering of protons from ²⁶Mg were measured over the energy range of incident protons from 1.2 to 3.0 MeV. Measurements were made at three c.m. angles of 90.0°, 125.3° and 165.6° with energy step of 1.5 keV. Isotopically pure ²⁶MgO on a carbon backing foil was used as a target. Overall energy resolution was estimated to be 2 to 3 keV. Thirty-four resonances were observed and an attempt was made to fit these resonances by using the multi-level resonance formula. The experimental results are discussed in terms of the rotational model based on the potential model including isobaric spin term.

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The (α, α′) reaction has been investigated on ⁴⁰Ar at 21.5 and 22.2 MeV of incident energies. Spin and parity assignments have been made on the basis of Blair’s phase rule and the distorted wave Born approximation. The energy levels and their spins and parities found in this experiment are compared with results of previous experiments and theoretical considerations. Spin and parity of 2⁺ for the 2.529 MeV level are considered decisive, while spin and parity of (1⁻) are proposed for the 3.21 MeV level.

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The depolarization parameter D(θ) in elastic scattering of 1.36 MeV neutrons was measured at θ₂=30°, 38°, 80°, 120° and 150° for ²⁷Al, ⁵⁹Co, ^63,65Cu, ²⁰⁹Bi and Ni nuclei. The departure of D(θ) from unity for Al, Co, Cu and Bi was observed particularly at backward angles, but not observed for Ni. This fact shows that the spin flip of incident neutrons takes place along the normal to the scattering plane in the elastic scattering process for non-zero spin targets. These results are discussed in the light of different nuclear reaction mechanisms.

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The diagram technique, which was developed to solve a hierarchy of equations of motion for the reduced density matrices, is applied in order to solve a hierarchy of the equations of motion for the two-time Green’s functions. The diagrammatical representations of the two-time Green’s functions are obtained either in terms of the equilibrium one- and many-particle reduced density matrices or in terms only of the equilibrium one-particle reduced density matrix. The latter representation for the one-particle two-time Green’s function and the formula by which the reduced density matrix is calculated from the Green’s function give us a set of coupled equations which determines both the reduced density matrix and the two-time Green’s function. The calculation with the aid of the present technique is illustrated for an example of Hubbard’s calculation for the “Hubbard Hamiltonian”.

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The energy bands of MgO, the oxygen 2s-band, the oxygen 2p-bands and the conduction bands, are evaluated by the Green’s function method with the Hartree-Fock-Slater self-consistent potential. The charge distribution of electrons in the 2p-bands is determined. It is well localized in the oxygen sphere and the ionic character of the MgO crystal seems to be evident. The atomic 2p-wave function of the hypothetical doubly charged oxygen negative ion is derived from the wave functions of the three states, Γ₁₅, X′₄ and X′₅.

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The band structure of h.c.p. cobalt is calculated self-consistently by using Green’s function method. The calculation gives the density-of-state curve for the paramagnetic state, the Fermi energy for both spin bands, the shape of Fermi surfaces. The exchange splitting energy ΔE is estimated to be 1.71 eV from the density-of-states and the Bohr magneton number, but it is estimated as about 1.1 eV from the other properties, particularly from the photoemission data. This difference is presumably due to uncertainties in the potential which, when corrected, should cause the s-band to be lower in energy by about 0.5 eV.

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Static magnetic susceptibilities of simplified model vibronic systems where non-Kramers paramagnetic ions in triplet ground state interact either with localized tetragonal modes of vibration with sharp frequency spectrum at ω (localized model), or with tetragonal modes composed of the superposition of phonons with continuous frequency spectrum (Debye model) are calculated in a rigorous way.
The susceptibility is simply expressed in terms of a temperature dependent reduction factor γ_L(T) for the localized model, or γ_D(T) for the Debye model, which diminishes the effective Curie constant and makes the susceptibility deviate from the Curie-Weiss law.
The theory explains the characteristic features of the susceptibilities of dilute solid solutions of UO₂ in ThO₂ measured by Slowinski and Elliott and by Comly, for example, the convex curvature of reciprocal susceptibility vs. temperature plot. The values of parameters determined to fit the observed susceptibilities are reasonable in orders of magnitude.

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The principal magnetic susceptibilities and anisotropy of single crystals of DyCl₃ and HoCl₃ are computed in the temperature range 70–300°K, considering that a trigonal electric field of C_3h symmetry exists about the free ion. The anisotropy is found to increase with the decrease of temperature. Furthermore, the variation of mean magnetic moment with temperature is studied which remains constant over a wide range of temperature in both the compounds. The computed value of the magnetic moment at room temperature is 10.63 B. M. for DyCl₃ and 10.87 B. M. for HoCl₃ which are in good agreement with free ion values 10.62 B. M. and 10.60 B. M. respectively. Following crystal field parameters are used in these calculations.
(Remark: Graphics omitted.)

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The magnetic susceptibility and solute resistivity of Cr impurity in Pd_1−cRh_c (c=0, 0.01, 0.04, 0.05, 0.08 and 0.10) and Pt were measured. The residual resistance of Cr solute impurity showed the maximum at the Rh concentration that the exchange enhancement of host alloy becomes largest. At the temperature below 10°K the solute resistivity obeys T² and the coefficients of T² term also show the maximum at about the same Rh concentration. A large decrease of the magnetic susceptibility of Pd_1−cRh_c alloys by addition of Cr impurity was observed and such a decrease and temperature dependence are interpreted by the negative polarization of neighbouring Pd atoms.

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The NMR spin-echo spectra of Ni and Co in disordered and annealed Ni₃Co alloys are almost identical, indicating that long-range crystallographic order does not occur in this alloy.

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The effect of the magnon-phonon interaction on the specific heat of an antiferromagnet is calculated on the basis of a simple model. We treat a Hamiltonian which includes terms of quasi-magnons, phonons and magnon-phonon interaction. The Hamiltonian is diagonalized and two branches representing coupled modes are obtained. The specific heat of the coupled system is calculated. It is shown that for weak interaction the contribution from the magnon-phonon interaction is very small, and for strong interaction it increases rapidly with decreasing temperature and it gives a large correction to the total specific heat at low temperatures.

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Some empirical relations between the bond angle (of M–O²⁻–M) and the asymptotic Curie temperature (Θ) or Néel temperature (T_N) are derived from data for oxides containing Cr³⁺, Mn²⁺, Fe³⁺ or Ni²⁺ ions. Further, these relations seem to be explained through assuming the presence of two types of exchange interactions; one is a 90° superexchange interaction which obeys the rule proposed by Kanamori and Goodenough, the other a direct exchange interaction which is sensitive to the overlap between neighboring two dε orbitals. In oxides containing Cr³⁺ or Mn²⁺ the above two types of exchange are effective, while in oxides containing Fe³⁺ or Ni²⁺ only the former (superexchange) effective.

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Nuclear magnetic resonances of Mo⁹⁵, Mo⁹⁷ and Fe⁵⁷ in Ba₂(FeMo)O₆, Sr₂(FeMo)O₆ and Ca₂(FeMo)O₆ with ordered perovskite structure were studied in their ferrimagnetic state by spin echo method. The Mo⁹⁵ and Mo⁹⁷ spin echo signals at 4.2°K were observed between 33.0 MHz to 65.6 MHz, 30.5 MHz to 81.2 MHz and 31.5 MHz to 79.6 MHz, respectively. The Mo⁹⁵ spin echo peak frequencies of these compounds (54.4 MHz, 67.6 MHz and 63.4 MHz, respectively) are higher in the compound with higher ferrimagnetic Néel temperature. In Ba₂(FeMo)O₆, the Mo⁹⁵ spin echo peak shifts to higher frequencies with increasing external static magnetic field. The measured hyperfine fields of the Mo⁵⁺ ions in these compounds are far smaller than the value of the orbital hyperfine field which is expected when the magnitude of the effective orbital angular momentum is 1. The Fe⁵⁷ spin echo signal in Ba₂(FeMo)O₆ at 4.2°K was found at 79 MHz.

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The temperature dependence of Cu⁶³ N.M.R. signal intensity in Cu-380 ppM Fe dilute alloy was observed between 1.4°K and 4.2°K. The wipeout number of each Fe impurity was 1000 at 4.2°K and temperature dependent. From the tail end of N.M.R. signal, the local field of Cu nuclei, which are situated about the 1000 neighbouring nuclei of the impurity, was estimated. The local field which was calculated by R. K. K. Y. theory was found to coincide with the experimentally obtained value.

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By means of ultrasonic attenuation measurements in megacycle range, the frictional force on a fast moving dislocation is studied in pure Cu and Cu–Mn, Cu–Ni, Cu–Ge, Cu–Pd and Cu–Pt dilute alloys from 4.2°K to 273°K. The magnitude of the damping constant, B, deduced from asymptotic behavior of the attenuation at high ultrasonic frequencies, is found to depend on the solute concentration and the atomic size of the solute atom, but rarely depend on the difference of the electronic state, the stacking fault energy or the mass of the solute atom. Empirical formulae for B in these alloys in the temperature from 54°K to 273°K are given, where B is expressed as a function of the misfit parameter. A tentative explanation of the impurity effect is given as an elastic interaction between an impurity atom and the dislocation. The explanation seems to give a right order of magnitude of the damping constant.

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The line shape of the giant quantum attenuation of sound waves in bismuth is studied on the basis of current theories and compared with our measurements. By taking into account the energy and magnetic field dependences of the level broadening and the hot electron effect, we may understand the symmetry of the line shape with regard to each peak field and the tendency to saturation of the attenuation peaks observed in a high field region. The minimum value of the life time of the electron Landau level touching the Fermi level is 2.5×10⁻¹⁰ sec; this is obtained for the magnetic field parallel to a bisectrix axis at liquid helium temperature and is about two orders of magnitude larger than the value derived from the de Haas-van Alphen effect by Bhargava. The remarkable change of the experimental line shape under conditions such that the electrons and holes simultaneously satisfy resonance can be qualitatively explained by taking into account the magnetic field dependence of the Fermi energy.

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Specific heats of sodium trihydrogen selenite, NaH₃(SeO₃)₂, and its deuterated crystal were measured in their transition temperature regions. The entropy changes in NaH₃(SeO₃)₂ associated with the upper and lower phase transitions are found respectively to be (1.03±0.05) and ∼0.5 cal·mol⁻¹·deg⁻¹, resulting in the total entropy change, ∼1.53 cal·mol⁻¹·deg⁻¹. The entropy change for the lower transition is the value estimated roughly with the help of differential thermal analysis. The entropy change associated with the phase transition in NaD₃(SeO₃)₂, which undergoes one phase transition in contrast with the two in NaH₃(SeO₃)₂, is found to be (1.58±0.09) cal·mol⁻¹·deg⁻¹.
The number of configurations of hydrogens which can be assumed to form the layer structure is calculated by taking full correlations into account. The entropy change between ordered and disordered states is calculated to be 1.59 cal·mol⁻¹·deg⁻¹, which is in good agreement with the experimental results. Another calculation for the entropy change by Pauling’s method gives 2.18 cal·mol⁻¹·deg⁻¹, which is too large when it is compared with the experimental values.

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A study was made on absorption and emission spectra of Ag⁻ centers in KCl crystals. By inspecting the excitation spectra for emission, two new bands were found at 3.11 and 3.27 eV in addition to the previously known 4.36 eV absorption band. These three bands, named A, B, and C, are ascribed to transitions ¹S₀→³P₁, ³P₂ and ¹P₁ respectively. Besides the 2.93 eV emission, another emission band was discovered at 4.08 eV. They are attributed to transitions ³P₁ and ¹P₁→¹S₀. Energy parameters and electron-lattice coupling constants specifying the configuration-coordinate surfaces were determined from the peak energies, second moments, and Stokes shifts of the observed spectra. Data on the degree of polarization suggest that a trigonal lattice deformation is dominantly realized in each of the relaxed ¹P₁ and ³P₁ states. The shape of the C band and the ratio of life times for the ¹P₁ and ³P₁ states are in reasonable agreement with theory.

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Thermal formation and destruction of M centers in fictitious KCl crystals have been studied and compared with the experimental results in real crystals. In fictitious crystals an idealized F-center distribution is introduced. Half of F centers are distributed uniformly and their positions are fixed and the other half are distributed to make pairs with each F center distributed uniformly. Such pairs with various inter F-center distances are handled as H₂ molecules in a dielectric medium and their concentrations are computed statistically. By moving F centers belonging to the latter half under an attractive force, the variation of the concentration of F-center pairs sitting at the nearest negative ion sites (M centers) are computed statistically and compared with the experimental results in real crystals. It is shown that the variations computed in fictitious crystals explain nicely the variation of M-center concentration in real crystals. It is also shown that a potential in short range is effective enough for the thermal M-center formation.

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The accurate pulse shapes of luminescence of anthracene single crystal in the time region of about 50 nsec from the rise-portion of pulse excited by UV light pulse, α-, β-particle and γ-ray were obtained. The pure decay constants of scintillation excited by high energy radiation, and of fluorescence by UV light pulse were determined to be (10±1) nsec and (6.5±0.5) nsec respectively without the self-absorption effect. The differences of decay constants and rise times between scintillation and fluorescence pulses were discussed on the basis of the fact that the life time of ions generated in anthracene crystal by high energy radiation is longer than that of the lowest singlet excitons.

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The electron spin resonance of Eu⁺⁺ in SrF₂ have been studied from 4°K to 800°K. The experiment showed that the hyperfine coupling constant A decreased in magnitude by approximately 3.5% over that temperature range. The calculation of the temperature dependence of A is made by using the mechanism proposed by Šimánek and Orbach with the introduction of the “modified Debye temperature.” The contribution due to acoustic phonons and optical phonons are calculated separately, the theoretical prediction agrees well with the experimental values. The zero-point contribution to the hyperfine coupling constant is −1.73×10⁻⁵ cm⁻¹ and the hyperfine coupling constant in the “rigid lattice” at T=0°K is −34.42×10⁻⁴cm⁻¹.

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The probability of relaxation between two excited levels, ⁵D₃ and ⁵D₄, of Tb³⁺ ion is obtained experimentally in glassy calcium meta-phosphate. Effects of coexisting other rare earth ions on this relaxation process are studied. It is clarified that energy transfer due to resonance between Tb³⁺ ions or to other rare earth ions strongly accelerates this relaxation process, and that the mechanism governing this energy transfer is electric multipole interaction.

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The precise temperature dependence of the ralaxation time of the polarization in NaNO₂ has been given through a new approach, in which the relaxation time is derived from the imaginary part of the complex dielectric constant in the low frequency region. On the way of this experimental procedure, it was found that the measurement of the static electric susceptibility should be made at around 1 MHz, because another dielectric dispersion occurs below this frequency. The critical index for the static susceptibility is determined as γ=1.11±0.05. Throughout the paraelectric and sinusoidal antiferroelectric phases, the temperature dependence of the relaxation time has been explained qualitatively by simple equations in molecular field approximation for the kinematical Ising model. The critical index of the kinematical slowing down is found to be positive and smaller than 0.20. This value is consistent with that expected theoretically.

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The ferroelectric properties of a single crystal of Pb(Zn_1⁄3Nb_2⁄3)O₃ were investigated in the ferroelectric and paraelectric temperature regions. The crystal undergoes a ferroelectric phase transition in a wide temperature range, changing from cubic perovskite structure to rhombohedral one. A broad peak was observed in the dielectric constant vs temperature curve, being characteristic of the disordered perovskite ferroelectrics. The spontaneous polarizations were obtained from the hysteresis loop and the pyroelectric current, and there was found a discrepancy in both measurements. Without applying an electric field the optical anisotropy was not detected. But with the field the domain and the birefringence were observed. The effects of the d.c. field on the dielectric constant and the birefringence were observed over the wide temperature range. A brief explanation of the character of the phase transition as well as dielectric and optical properties were given.

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Magnetic field dependence has been calculated in detail for the attenuation of microwave phonons by neutral donors in Ge. Magnetic fields give rise to a considerable change in the attenuation. The aspect of the change depends on whether the product of the phonon angular frequency (ω_qt) and the relaxation time (τ) is larger or smaller than 1: roughly speaking, the attenuation increases with magnetic fields when ω_qtτ>>1, while it decreases when ω_qtτ\lesssim1. The magnitude of the change depends on the strength and the direction of magnetic fields and also on the level width of triplet states when ω_qtτ\lesssim1. Besides the ultrasonic spin resonance, a resonant absorption of phonons in the triplet states can occur when the energy splitting of triplet states becomes equal to the phonon energy and the splitting becomes larger than the level width of triplet states.

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The restricted Hartree-Fock molecular orbital calculations are carried out on the ground state of the (MnF₆)⁴⁻ system and the covalency parameters are evaluated. The molecular orbitals are constructed from the manganese 4s and 3d and the fluorine 2s and 2p atomic Hartree-Fock wave functions, and they are determined by solving the Hartree-Fock equations. All the many center integrals are evaluated rigorously. The agreements of the calculated parameters with experiments are not very good, but the value of 10Dq is greatly improved compared to the previous calculation. From the results it is concluded that the effect of the manganese 4s orbital and the four center integrals on the total energies and the spin densities are not so large, but the four center integrals cannot be ignored in calculating 10Dq. It is also indicated that the core electrons cannot be treated as point-charges.

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The aim of this paper is to show that for a neutral diatomic molecule one can obtain an approximate analytical solution of the TF equation by making use of an equivalent variational principle.

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An excess charge effect on the hydrogen bond O_A–H…O_B is examined with the valence bond method developed in the authors’ recent paper. It is shown that the potential energy curve of the proton becomes to have two minima and the stretching frequency of the proton decreases with the increase of excess charges (lack of electrons on the proton donor atom O_A and excess on the acceptor atom O_B). Hydrogen bonds of a guanine-cytosine (G–C) base pair, i.e., N₈^C–H…O₁₁^G and N₁^G–H…N₁^C, are also studied. It is shown that an N–H…N type H–bond is apt to have a stable secondminimum of the proton potential as compared with N–H…O and O–H…O bonds, and the reason is discussed.

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The situation where dimer formation and splitting is possible in irradiated RNA molecules is considered. The equilibrium distribution of dimers (i.e. the distribution after a long time) is obtained, in particular the average number of dimmers as a function of molecule length and reaction rates. The average equilibrium dimer density is obtained for long chains, and this exact result is compared with earlier approximations to the full problem.

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Asymptotic method of Krylov, Bogoliubov and Mitropolsky is applied to study the possibility of excitation of extra-ordinary waves in a cold plasma by small and periodic external electric field. Excitation conditions and maximum growth rate are deduced.

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Standing waves of longitudinal electron oscillation were observed in a beam-plasma system. By applying a density modulation to the beam, the amplitude of oscillation decreased to zero when the modulation frequency was near to those of the spontaneous oscillation. The modulation depth necessary for the oscillation to vanish was nearly proportional to the difference between the oscillation frequency and the modulation one. When the oscillation was suppressed, the oscillation having the same frequency as the modulation one was excited. These suppression and synchronization can be well explained by the assumption that the oscillation of electron density is described by the Van der Pol equation. Under this self-oscillator model the linear growth rate is evaluated and compared with the value calculated from the dispersion equation of the two-stream instability.

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Nonlinear perturbation method is applied to describe the behaviour of unsteaby magneto-acoustic waves of small but finite amplitude propagating in a cold plasma in the presence of effective electron-ion collisions.
It is shown under an assumption of small effective collision frequency that the original system of equations can be reduced to a single nonlinear equation which has a combined form of the Korteweg-de Vries and the Burgers equations. The dispersion term is just the same as that of collisionless case, whereas the dissipation term is found to be proportional to the magnetic viscosity. A qualitative discussion is given concerning the steady solutions of this equation.

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The magnetohydrodynamic effect of an axial magnetic field on the cylindrical shock is studied theoretically on the basis of the blast wave theory. The result shows the reduced velocity of the shock front due to the applied magnetic field. Experiments were also carried out by use of exploding wires with or without magnetic field. The differences in shock arrival times of these two cases are compared and these are in satisfactory agreement with the above theoretical result.

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Computer results for the shape of a bubble or a drop in equilibrium under the influence of both gravity and surface tension are shown. Axisymmetric configuration is exclusively studied for a wide range of a parameter.
In some cases of a pendent liquid drop from a flat wall, which is equivalent to a scandent gas bubble, a central portion shows a lumpy character and stretches itself.

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The effect of uniform rotation on the onset of thermal instability in a horizontal layer of fluid is studied by means of linear stability analysis, assuming that one of the bounding surfaces is free and the other rigid. As the agencies causing instability, both surface tension and buoyancy are taken into consideration. A Fourier series method is used to obtain the eigenvalue equation which is then computed numerically. It was found that the Coriolis force has an inhibiting effect on the onset of convection even if the surface tension effect is taken into consideration, and as the speed of rotation increases the coupling between the two agencies causing instability becomes weaker; further, that in a rapidly rotating layer, a discontinuous change in cell size occurs at a certain value of the Rayleigh number, as a result of a sudden changeover from convection dominated by one of the two agencies to that dominated by the other.

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Structure of plane steady detonation waves propagating with Chapman-Jouguet velocity is analysed in consideration of transport phenomena. For rich mixtures of oxyozone, only O₃+X→O₂+O+X and O+O₃→O₂+O₂ have to be considered in the analysis as associated elementary reactions, where numerical integrations can be carried out from hot boundary to cold boundary singularities since the hot boundary constitutes a nodal singularity due to the first-order character of reaction. Detonation solutions are found out for arbitrarily lean mixtures.
For lean mixtures, on the other hand, the inclusion of the recombination reaction O+O₂+X→O₃+X becomes necessary and consequently the reaction order near the hot boundary is raised from the first to the second. The examination of such hot boundary presents non-existence of the integration curve satisfying both boundary conditions.

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