An infinite number of linear differential equations whose solutions satisfy multi-dimensional Toda lattice (MDTL) equation are found. The coefficients of any of these linear equations are given by a solution of MDTL equation, thus the equation provides a kind of linear Bäcklund transformation of the NDTL equation.

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The S^x-S^x correlation function of S=1 XXZ chain is calculated at low temperatures by means of the transfer matrix with use of the Trotter formula. Critical properties of the correlation function, such as critical indices γ, η and ν and the mass identified by the inverse correlation length at T=0, are obtained. We conclude that a groundstate with an excitation gap appears for the anisotropy parameter Δ<Δ₁\simeq−0.3 including the isotropic antiferromagnetic point (Δ=−1). We have obtained η\simeq1⁄4 at Δ=Δ₁ in accord with the theoretical prediction by Haldane and den Nijs. Our result, however, shows the monotonic increase of the excitation gap with decreasing Δ for Δ<Δ₁ contrary to Haldane’s prediction.

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The non-linear three-dimensional thermoconvective instability of a second-order fluid layer between two parallel semi-infinite walls is analyzed under the fixed-heat flux boundary condition. In the analysis, the Boussinesq approximation is used to account for density changes in the system. It is shown that the non-linear time-dependent equation that governs the convective motion is of the same form as those obtained by Chapman and Proctor in the two-dimensional case and by Proctor (for infinitely thickwalls) in the three-dimensional case for Newtonian fluids. This result shows that the theorems of Tanner and Giesekus for planar, creeping flow of incompressible second-order fluids can be extended to three-dimensional, non-linear, time-dependent thermoconvective phenomena.

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An exact solution of the Navier-Stokes equations is presented for an incompressible circulatory flow about an infinite circular cylinder with uniform suction or injection. An asymptotic evaluation of the solution for large time shows that, starting from a typical initial state, the flow ultimately becomes irrotational for R≤1; for 1<R≤2, the initial vorticity distribution remains unchanged in the final state of flow; but for R>2, the initial vorticity distribution changes with the circulation at infinity remaining constant: Here R=Va⁄ν, with V, a and ν being the suction velocity, radius of the cylinder and the kinematic viscosity, respectively. The torque on the cylinder has been evaluated for both small and large times.

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MHD relaxation phenomena have been studied for a toroidal plasma in a safety factor q<1 regime. Ultra low-q(ULQ) equilibria with (n+1)⁻¹<q<n⁻¹ (n≥1) are set-up through MHD relaxation, and are sustained quasistatically. A ULQ equilibrium has a q profile with dq⁄dr<0 (r: minor radius) for a major region in the plasma, so that it is stable against global MHD modes. In the time-scale of the classical field-diffusion, the ULQ equilibrium deforms to take a peaked-current profile and destabilizes a global mode. Then a catastrophic transition to a higher q(lower n) state is observed.

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The low-temperature form of CeCu₆ has been determined from the Rietveld analysis on high-resolution TOF neutron diffraction data at 65 K. The crystal system is monoclinic with lattice parameters a=0.5080 nm, b=1.0121 nm, c=0.8067 nm and β=91.36°. The space group is P2₁⁄c and the unit cell contains four formula units. The structure is a derivative of the high-temperature orthorhombic form associated with a monoclinic deformation and minor shifts of the atomic positions.

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A calculation is presented of the relaxation rate T₁⁻¹ between the lower two branches of the atomic hyperfine states in spin-polarized atomic hydrogen H↓ below the Bose-Einstein condensation temperature T₀. We find that T₁⁻¹ has a maximum between T=0 and T₀, which is due to appearance of additional relaxation processes mediated by atoms in the condensed state. Theoretical estimation of T₁ is of the order of a minute with a magnetic field ∼100 kG and with density of H↓∼10¹⁸ atoms/cm³.

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Ultraviolet (UPS) and X-ray (XPS) photoemission spectra of quasi-two dimensional metal Ag₂F are presented. Three prominent bands are found at about 2.0 eV, 4.6 eV and 6.0 eV from the Fermi level in the UPS spectrum. They are assigned to the F 2p state, the Ag 4d state and the mixture of the two states, respectively. The comparison of the photoemission spectra with a recent LAPW band calculation shows that the calculated 4d band is shifted toward the lower binding energy by about 1 eV relative to that of the experiment. This discrepancy suggests that the 16th band which forms a small ellipsoidal Fermi surface in the LAPW calculation may be above the Fermi level.

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Valence of Ce in the Chevrel compound CeMo₆S₈ was investigated by XPS and lattice constant measurements at room temperature. The concentration dependence of lattice constant in the system Ce_xLa_1−xMo₆S₈ follows the Vegard’s law in a whole concentration region of Ce. The Ce 3d and 4d XPS spectra show strong peaks with the initial state of Ce³⁺ and no peaks due to Ce⁴⁺. The mixing rate of Ce⁴⁺/Ce³⁺ was estimated to be less than 2%, assuming the noise level of the XPS spectrum to be the upper limit of the Ce⁴⁺ peaks.

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A new magnetic field effect on the blue color of liquid oxygen is found in pulsed high magnetic field up to 500 kOe. It is clearly shown that the color is reduced and the transparency increases by applying the magnetic field. The effect is explained by introducing the model that the bimolecular absorption transition 2(³Σ_g⁻)−2(¹Δ_g), which is responsible to the blue color of liquid oxygen, is reduced in high magnetic field because of the spin polarization of paramagnetic O₂ molecules.

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Solar neutron fluences from large gamma-ray flares are deduced from accelerated proton spectra and numbers derived from the gamma-ray observations. The deduced solar neutron fluences range from 1 to 200 neutrons cm⁻². The present result indicates a possibility that high sensitivity ground-based neutron monitors can detect solar neutron events, just as detected by the Jungfraujoch and Rome neutron monitors.

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The stochastic system of Schlögl’s bimolecular reaction model has only a trivial stationary distribution in very far away from equilibrium and has been considered not to cause nonequilibrium transition. However in the same manner there exist a class of stochastic systems which have only a trivial stationary distribution too in very far away from equilibrium. This has its origin in strong dependency of stationary distribution on both the size of system and the distance from equilibrium. Then it is pointed out that reasonable results are obtained by the joint infinite limit under a relation between the size of system and the distance from equilibrium.

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The transfer matrix formalism for an assembly of physisorbed atoms on an anisotropic rectangular lattice is developed. In this formalism, statistical mechanics of the assembly is reduced to a quantum mechanical problem of interacting Fermions in a one-dimensional lattice. The Kosterlitz-Thouless dislocations are neglected. This simplified model is analyzed by means of RPA. A complete phase diagram of this model is given. It is found that there are two commensurate phases C₁ and C₂ and also two incommensurate (or fluid) phases IC₁ and IC₂. Critical phenomena around the phase boundaries are investigated.

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Partial cross sections σ_L and σ_m for respective formation of H(2p) and H(2s) atoms in charge-transfer collisions of H¹ with Cs, Rb, K and Na atoms have been measured over the energy range from 0.06 to 5.0 keV. The measurement of σ_L was made by the use of crossed-beam method together with detection of H(2p) atoms by Lyman-α photons emitted in spontaneous decay of those atoms. The measurement of σ_m was made by the use of beam-target-cell method together with detection of H(2s) atoms by Lyman-α photons emitted when an electric field was applied on them. Almost all of cross-section curves obtained show oscillatory structures arising from secondary effects. The aspect of the structure changes remarkably with target atom, suggesting that the long-range sharing process between charge-exchange channels in Cs and Rb cases is replaced by a different secondary effect in K and Na cases.

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An effective Hamiltonian method is developed to evaluate the distribution function of r_α (α=1, 2), which are the positions of the α-th particle at the time t_α. By using this method the Lagrangian auto-velocity correlation function is expressed in terms of the Eulerian one. The spectrum of the Lagrangian one clearly shows ω⁻² form under a specific model Eulerian correlation function which realizes the Kolmogorov spectrum.

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The initial-boundary value problem is solved for acoustic disturbance caused by a source in the uniform bubbly liquid flow without the velocity slip. The solution shows the transient and final characteristics of four modes of unusual acoustic wave, resulting from the interaction between the volume oscillation of bubbles and the wave motion in the flowing medium. The solution also shows that the energy distributed for each mode is different depending on the frequency of the source and on Mach number of the main stream. For high frequency, the ratio of propagation mode to cutoff mode is very small at low Mach number but large at high Mach number. There is a possibility that the energy of cutoff modes is expended to break up bubbles.

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This paper is concerned with existence conditions for large amplitude shock waves in a plasma with negative ions. It is shown that the large amplitude shock waves with negative potential well in front can exist in the plasma, if there are electron or negative ion beams behind the shock.

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The measurements of the extended X-ray absorption fine structure and the photoacoustic spectroscopy have been carried out for Se chains confined in the channels of synthetic mordenite with about 6.7 A diameter. The first-nearest Se–Se distance in mordenite channels is 2.32 A, shorter than that in crystalline Se. The absorption edge for Se adsorbed in the mordenite channels lies at shorter wavelength than that for amorphous Se. This suggests that the covalent bonds along the Se chain become stronger when the coupling between adjacent Se chains is reduced. It is found that the isolated Se chains in the mordenite channels are strongly photo-sensitive.

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The quasicrystalline (qc.) phase with the icosahedral symmetry in melt-spun Al_100−xMn_x (x=14, 17, 20) has been investigated by X-ray diffraction, TEM and DSC. Nearly single phase quasicrystal is obtainable for Al₈₀Mn₂₀ when the quenching rate is sufficiently fast, while slower quenching rate produces an alternative metastable phase called T phase. On heating, the qc. phase in Al₈₀Mn₂₀ changes to T phase at around 300°C and then at around 600°C to the stable hexagonal Al₄Mn, whereas the qc. phase in Al₈₆Mn₁₄ crystallizes directly to the stable orthorhombic Al₆Mn. Heat evolution of the latter reaction is 0.40 kcal/mol, while those of the qc. phase to T phase and T phase to the hex.-Al₄Mn in Al₈₀Mn₂₀ are 0.12 and 0.17 kcal/mol, respectively. Atomic model of the qc. phase with a stoichiometric composition of Al_78.35Mn_21.65 is proposed.

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Ultrasonic attenuation due to electron-phonon interaction has been calculated in the intermetallic compound CeAl₃ in low temperature region between 0.5 K and 40 K. The resistivity of the substance is very large as compared to metals. Even in the low temperature region the ultrasonic attenuation due to electron-phonon interaction is very small, and as the temperature increases the variation of attenuation is of the same nature as common metals.

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Internal friction and the period of vibration of an orderable alloy Cu₃Au are measured as functions of temperature between about 310 K and 870 K both in heating and in cooling runs with a fully automatic inverted torsion pendulum. Two distinct internal friction peaks P₂ and P_G located at about 680 K and 800 K are identified with the Zener peak and the grain boundary peak, respectively. Around the order-disorder transition temperature the period of vibration changes stepwise with a temperature hysteresis of about 15 K, while no peculiar change in internal friction is observed associated with it. The effects of heat treatments and deformation on all these phenomena are investigated.

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The phonon dispersion, frequency distribution, Debye θ and the elastic constants of Ta–W alloys have been investigated using the deLauney angular force (DAF) model. The central force constants have been considered up to third neighbours while the angular force constants are operative up to two neighbours. It has been found that the third neighbour interaction is very weak in Ta–W alloys. The angular forces are quite important for the second neighbours. The phonon frequencies, Debye θ and the elastic constants exhibit a good agreement with the experimental values.

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Stage stability and stage transition in SbCl₅-graphite intercalation compounds have been investigated by use of the in situ X-ray diffraction technique. A precise isotherm of stage n has been determined for stages up to 6. The stage-stability range in chemical potential Δμ(n) is evaluated from the isotherm. A comparison of Δμ(n) with the theoretical results of the electrostatic interlayer interaction model gives the ionicity of 1⁄4<f<1⁄2 for SbCl₅-graphite intercalation compounds. A very narrow two-phase region is observed in the stage transition region, in which two single-stage phases coexist in thermal equilibrium.

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A constitutive model of helium II is perturbed by a pulsating body force and a pulsating fluid source, both having arbitrary anisotropic distributions. The model is compressible, viscous and heat conducting. The general solution has complex wave-numbers, anisotropic amplitudes and some isotropic features. Long-range decays are spherical and partially-but-dominantly exponential. Viscosity waves form one wave-species found only in the velocity perturbation. Waves of two other species propagate with all perturbations; they each implicate both ordinary and second sounds; those propagating with the velocity perturbation and a generalised velocity perturbation are irrotational waves. When specific heats nearly coincide, those other two wave-species separately approximate ordinary sound and second sound; also, a nonfree perturbation system supports viscosity waves and ordinary sound and weakly supports second sound, while a freelike perturbation system weakly supports ordinary and second sounds; both systems are weakly coupled. Uncoupling occurs with coincidence of specific heats.

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Fundamental absorption spectra have been measured in layer compounds InSe and GaSe under hydrostatic pressure up to 4 GPa. The first and the second direct edges exhibit extremely nonlinear behaviors: The energy gap at the former edge decreases first, takes a minimum at 0.5 GPa in InSe and at 1.1 GPa in GaSe, and then increases with pressure, while that of the latter increases monotonically over the whole pressure range examined. Hydrostatic deformation potentials for respective absorption edges have been deduced on the basis of these results. Such anomalous behaviors of energy gaps have been found to arise from competitions between the nonlinear variation of the van der Waals gap and linear variations of intralayer bondings. Several essential aspects of the band structure have been clarified in terms of the hydrostatic deformation potenticals thus deduced.

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Hot electron transport in a semiconductor is analyzed through a thermodynamic treatment. Analytic solution of the Boltzmann transport equation is obtained assuming extremely high electron-electron scattering condition. Particle and energy balance equations are solved using rigorous particle and thermal energy flow expressions derived from the transport equation. Obtained velocity-field relationship for electrons in silicon with electrode distance longer than 10 μm is in good agreement with the experimental data. It is found that saturation velocity increases for shorter samples due to electron cooling through electrodes. Moreover, for samples with length between 0.1 μm to 1 μm, particle and thermal energy currents strongly couple. Because of this coupling, anomalous phenomena such as excess voltage and higher electron temperature will appear.

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The electrical conductivities of liquid Mn and Mn_xTe_100−x alloys were measured by using a high purity alumina cell in the temperature range up to about 1400°C. Their concentration dependence of conductivities exhibited a sharp minimum at the stoichiometric composition MnTe. It suggests that liquid MnTe has the ionic configuration of Mn²⁺ and Te²⁻ at the composition MnTe. The conductivity of liquid MnTe was about 20.7 ohm⁻¹·cm⁻¹ at the melting point and the temperature dependence of conductivity was found to be exponential with an energy gap of 1.84 eV. For liquid Mn, the resistivity ρ was 199.5 μΩ·cm at the melting point and its temperature dependence dρ⁄dT was about 0.022 μΩ·cm/K near the melting point.

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The parallel critical field H_c3 to the film surface is calculated including the effect of the mass anisotropy for dirty superconductors. It is shown that H_c3 is larger near the transition temperature T_c and smaller at low temperatures than the perpendicular critical field H_c2 to the film surface, if m_⊥<<m_⁄⁄ where m_⊥ and m_⁄⁄ are the effective mass perpendicular and parallel to the film surface.

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Heavy fermion aspects of strong electron-phonon coupling compounds are discussed on the basis of the idea that two-level systems (TLS) play a role of the localized spins in the dense Kondo system. Using the Vladar and Zawadowski’s results that, at low temperatures, a single TLS interacting with electrons can be transformed to spin-1/2 Kondo system, it is shown that a heavy fermion band is formed through the coherence among virtual bound states around each TLS. The effective interaction between thus obtained heavy fermions consists of on-site repulsion and intersite attraction; so that the Cooper pair becomes inevitably anisotropic. It is shown that the local-phonon model can be transformed to TLS when the adiabatic potential for an ion becomes double-well. For this, it is essential to take into account the term quadratic in ionic displacement in the local-phonon model.

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Random impurity effects in an antiferromagnetic Ising model with ferromagnetic next nearest neighbor interactions on the triangular lattice are studied by using a Monte Carlo method. It is shown that (i) the ferrimagnetic phase occurring in the pure case is destroyed by a small amount of impurities, whereas (ii) a KT-like phase is not affected much by impurities. A pin effect of impurities is also discussed.

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Magnetization of Fe₃Ga₄ is measured as a function of magnetic field and temperature. In weak fields, Fe₃Ga₄ is an antiferromagnetic with a Néel temperature of 392 K. In strong fields, it shows a metamagnetic transition and gives a saturation moment of 1.27 μ_B per Fe atom at 4.2 K and 70 kOe. Its Mössbauer spectrum is analyzed into four sextets, assigned to the crystal site Fe(1), Fe(2), Fe(3) and fe(4): each site has, respectively, an internal field of 225, 190, 150 and 171 kOe at 80 K. The magnetic phase diagram of Fe₃Ga₄ involving the metamagnetism can be explained by the Moriya-Usami theory.

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Low-temperature magnetic susceptibilities of the dense Kondo Ce compounds such as CeAl₃, CeCu₂Si₂, CeAl₂, CeB₆ are analyzed on the basis of the Coqblin-Schrieffer model with crystal-field splitting from the Yosida theory. It gives an estimate of the Kondo temperature, in good agreement with the quasielastic line width in the neutron experiments. It also gives important information about the crystal-field level structure: in particular, two candidates for the lowest doublet of CeCu₂Si₂ are obtained.

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The inelastic neutron scattering was studied in both PrCu₆ and the reference system LaCu₆ in order to isolate the magnetic CF-transitions in orthorombic PrCu₆. Ten CF-transitions could easily be resolved, leading to a CF-scheme with two singlets forming a nearly doubly degenerate groundstate (Δ≈0.02 meV) without any coupling through a magnetic dipole matrix element (this doublet shows no quasielastic scattering). The first excited state is found to be 1.48 meV above that quasi-doublet ground state and the overall splitting comes out to be 8.95 meV. The static susceptibility calculated from this CF-scheme is in good agreement with the measured one, which is also presented in this paper.

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We have investigated the spin-1/2 random Heisenberg model with infinite range interactions by a numerical method. Extrapolation of finite size (N≤16) properties to the infinite system has yielded the following results. The average ground state energy is lower than that of the SK model (Ising spin) by about 25%. In the ground state, a critical point between the spin glass and ferromagnetic (mixed) phases exists just around the critical point (\ ildeJ₀⁄\ ildeJ=1) of the corresponding classical random Heisenberg model. Quantum fluctuations are concluded not to change the ground state properties qualitatively.

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Pyroelectricity of magnetite along the triclinic a, b and c axes was measured over the temperature range from 4.2 K to 20 K. It was found that the pyroelectricity along the triclinic a axis begins to decrease at 6 K, as the temperature is increased, while the one along the b and c axes begins to increase at the same temperature.

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The cluster theory which is developed to describe the glassy phase of Rb_1−x(NH₄)_xH₂PO₄ is extended to explain the anomalous behaviour in the dielectric susceptibility χ of this phase. It is shown that χ begins to deviate from the normal value of the paraelectric phase at and below the glass transition temperature T_g, and the deficient part of the susceptibility below T_g is precisely proportional to the glass order parameter properly redefined.

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Temperature dependence of Raman spectra in 4Hb-TaSe₂ was studied. The high-frequency spectra of 4Hb-TaSe₂ consist of 1T-TaSe₂- and 2H-TaSe₂-like modes. In relation to the two charge-density-wave phase transitions occurring in the octahedral (OH) and the trigonal-prismatic (TP) layers, two kinds of soft modes were observed. Mode repulsion was observed in the A_g and E_2g soft modes which are related to the phase transition of the OH layer. The two-phonon overtone scattering of the Kohn-anomaly modes of the TP layer was observed. The frequency of the lower edge of this mode corresponds to twice the minimum frequency of the Kohn-anomaly mode. From this frequency, temperature dependence of the electronic susceptibility of the TP layer was estimated. An E_2g rigid-layer mode was observed at 16.5 cm⁻¹.

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Doppler-broadening lineshapes of positron annihilation in nearly perfect crystals of aluminum were measured as a function of temperature during cooling down from 650 K to room temperature with various cooling rates, 1.9–27.4 K/h. The lineshape parameter S reflected the existence of excess vacancies depending on the cooling rate, and exhibited a linear temperature dependence below about 500 K. Its associated temperature coefficient was larger than the corresponding quantity for the equilibrium measurements of S in the prevacancy region, and increased with the excess vacancy concentration. The results, in conjunction with the data for the quenched-state below 200 K, suggested that the temperature dependence of S for the vacancy-trapped state of the positron is approximately linear, over the range 100–500 K, with a temperature coefficient about twice that found for the free state.

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Photoemission experiment was carried out on a (100) surface of Fe₃O₄ at room temperature, for the incident photon energies between 30.5 and 140 eV, and the results were compared with the band structure calculated by APW method (J. Phys. Soc. Jpn. 53 (1984) 312). Peaks due to the Fe(3d)–O(2p) valence band, O(2s) band, Fe(3p) band and Auger electrons were observed. Valence band emission starts from the Fermi level indicating that Fe₃O₄ is a “metal”, not an “insulator with electron diffusion”. Several peaks are distinguished in angle-resolved normal emission spectra in the valence band region. Other peaks are broad and do not show any structure. As a whole, applicability of the calculated band structure is proved. Resonant enhancement of photoemission is observed near the Fe(3p) core excitation region. Two subsidiary peaks at 7.5 and 11 eV are tentatively assigned to satellites due to a singlet and a triplet hole pair, respectively. Correlation energy between 3d electrons is estimated from the satellite position and the kinetic energy of Auger electrons.

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