We calculate semiclassically the energy-averaged local probability density of a wave function inside a weakly-open quantum dot in Coulomb blockade regime. We assume that the a clean cavity is connected to a large reservoir of electrons via one tunneling barrier. We show that scars should be observed at points on/near classical periodic orbits that are well coupled to the tunneling barrier. In particular, for a sufficiently small variation of systems parameters, scarring of a periodic orbit should recur, with a recurrence period corresponding to the properties of the periodic orbit.

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Self-diffusion of a polymer chain in a melt is studied by Monte Carlo simulations using the bond fluctuation model, where only the excluded volume interaction is taken into account. Polymer chains, each of which consists of N segments, are located on an L×L×L simple cubic lattice under periodic boundary conditions, where each segment occupies 2×2×2 unit cells. The results for N=32, 48, 64, 96, 128, 192, 256, 384 and 512 at the volume fraction φ\\simeq0.5 are reported, where L=128 for N≤256 and L=192 for N≥384. The N-dependence of the self-diffusion constant D is examined. Here, D is estimated from the mean square displacements of the center of mass of a single polymer chain at times longer than the longest relaxation time. From the data for N=256, 384 and 512, the apparent exponent x_d, which describes the apparent power law dependence of D on N as D∝N^−x_d, is estimated to be x_d\\simeq2.4. The ratio Dτ⁄⟨R_e²⟩ seems to be a constant for N=192,256,384 and 512, where τ and ⟨R_e²⟩ denote the longest relaxation time and the mean square end-to-end distance, respectively.

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An order–disorder transformation in a single decagonal quasicrystal of Al₇₂Ni₂₀Co₈ is studied in detail. In X-ray diffraction, the anomalous attenuation of intensities of Bragg reflections was found around the transformation temperature, T_c. The intensity attenuation at high temperature is explained by the anomalous Debye–Waller factor in thermal lattice dynamics. In particular, the intensity ratio above T_c and below T_c depends on |G^|||² values. In addition, the intensity ratio between room temperature and high temperature shows |G^⊥|² dependence. The results correspond to the in situ observation of a local vibrational anomaly related to an atomic flip by electron microscopy [Abe et al.: Nature 421 (2003) 347]. By X-ray diffraction, dynamic fluctuations as observed in electron microscopy are also realized even on a macroscopic scale at high temperature.

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Segregation and phase inversion are investigated through a simple granular system which consists of only two inelastic hard spheres in a square box with an energy source. With the variation of the coefficient of restitution, the mass ratio between two spheres or the box size, we show that two types of segregated states and crossover between them are realized in this small simple system.

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A series of phase-slip events in a clean mesoscopic charge-density-wave (CDW) system is studied by numerical simulations based on a Monte Carlo technique. Phase slips are classified into the winding phase slip (PS₊) after which a wavefront is added to the CDW, and the unwinding phase slip (PS₋) after which a wavefront is removed. Particular attention is focused on the time correlation of PS₊ and PS₋ events. It is shown that at relatively low bias voltages, a PS_\\mp event very likely occurs just after the appearance of a PS_± event to reduce CDW strain. It is also shown that this synchronization of phase-slip events becomes pronounced with decreasing sample length.

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A two-dimensional t–J model on a frustrating lattice is studied using mean-field variational theories with Gutzwiller approximation.We find that a superconducting state with broken time-reversal symmetry (d+id state) is realized in the parameter region close to the triangular lattice. The frustration enlarges the region of superconductivitywhen t<0 for the hole-doped case, which is equivalent to t>0 for electron doping. We also discuss SU(2) degeneracy at half-filling. The d+id state probably corresponds to the spin gap state at half-filling.

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The impurity effects on the transition temperature T_c and the isotope effect are examined in multiband superconductors with magnetic and nonmagnetic impurities, where the effect of Coulomb repulsion is considered. It is shown that an internal transition of the superconducting state is induced by impurity doping, and that the transition is accompanied by a jump of the isotope-effect coefficient α. In particular, the transition is illustrated in a system with two electron bands. In some special cases, extended Abrikosov and Gor’kov (AG) equations for T_c and the expressions of the isotope-effect coefficient α are obtained. Possible relevance of the present mechanism to the experimental results of Sr₂RuO₄ is discussed.

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The multi-orbital Hubbard model in one dimension is studied using the numerical diagonalization method. Due to the effect of crystal-field splitting Δ, the fully polarized ferromagnetism, which is observed in the strong coupling regime, becomes unstable against the partially polarized ferromagnetism when Hund’s rule coupling J is smaller than a certain critical value of order of Δ. In the vicinity of the partially polarized ferromagnetism, the orbital fluctuation develops due to the competition between Hund’s rule coupling and crystal-field splitting. The superconducting phase with the Luttinger liquid parameter K_ρ>1 is observed for the singlet ground state in this region.

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We examine the isotope effect of superconductivity in systems with coexisting interactions of phonon and nonphonon mechanisms in addition to the direct Coulomb interaction. The interaction mediated by the spin fluctuations is discussed as an example of the nonphonon interaction. Extended formulas for the transition temperature T_c and the isotope-effect coefficient α are derived for cases (a) ω_np<ω_D and (b) ω_np>ω_D, where ω_np is an effective cutoff frequency of the nonphonon interaction that corresponds to the Debye frequency ω_D in the phonon interaction. In case (a), it is found that the nonphonon interaction does not change the condition for the inverse isotope effect, i.e., μ^*>λ_ph⁄2, but it modifies the magnitude of α markedly. In particular, it is found that a giant isotope shift occurs when the phonon and nonphonon interactions cancel each other largely. For instance, strong critical spin fluctuations may give rise to the giant isotope effect. In case (b), it is found that the inverse isotope effect occurs only when the nonphonon interaction and the repulsive Coulomb interaction, in total effect, work as repulsive interactions against the superconductivity. We discuss the relevance of the present result to some organic superconductors, such as κ-(ET)₂Cu(NCS)₂, and Sr₂RuO₄ superconductor, in which inverse isotope effects have been observed, and briefly to high-T_c cuprates, in which giant isotope effects have been observed.

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The effect of pressure on magnetic and transport properties of pyrochlore molybdates has been studied using single-crystal specimens of (Sm_1−xTb_x)₂Mo₂O₇, which show ferromagnetic metallic behavior for x<x_c (=0.7–0.8) at ambient pressure. It is found that a spin-glass-like metallic state is stabilized under hydrostatic pressure (p) through measurements for the specimens near x_c for p<1.5 GPa. The application of pressure reveals that there is no correlation between ferromagnetism and metallic behavior in pyrochlore molybdates, in contrast to a double-exchange system.

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Possible order parameters of the phase IV in Ce_xLa_1−xB₆ are discussed with special attention to the lattice distortion recently observed. A Γ_5u-type octupole order with a finite wave number is proposed as the origin of the distortion along the [111] direction. The Γ₈ crystalline electric field (CEF) level splits into three levels by a mean field with the Γ_5u symmetry. The ground and highest singlets have the same quadrupole moment, while the intermediate doublet has an opposite sign. It is shown that any collinear order of the Γ_5u-type octupole moment accompanies the Γ_5g-type ferro-quadrupole order, and the coupling of the quadrupole moment with the lattice induces the distortion. The cusp in the magnetization at the phase transition is reproduced, but the internal magnetic field due to the octupole moment is smaller than the observed one by an order of magnitude.

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We have performed spectrally resolved degenerate four-wave mixing (FWM) spectroscopy on exciton systems in β-ZnP₂ using a femtosecond laser. The FWM signal clearly exhibits a periodic ultrafast modulation as a function of the delay time between two excitation pulses, which indicates the quantum beats due to the interference of two closely spaced transitions. From FWM and reflection spectra, the transitions are assigned to the 1s free exciton and the bound exciton. Dephasing times of the 1s exciton polariton are measured at various energies between the longitudinal and transverse excitons. The dephasing time is found to be longer as the polariton energy is lower, which suggests that the scatterings by acoustic phonons mainly govern the polariton dephasing. The difference in the modulation behavior of the quantum beats for the free and bound excitons is briefly discussed based on a simple model with a three-level system.

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Based on the density functional theory, we investigate and discuss what possible stable configurations hydrogen might assume, once found inside/between graphite layers stacked in an AB configuration. Our calculation results show that the reconstruction of the constituent carbon atoms is crucial in determining the final configuration of hydrogen. When a hydrogen atom impinges directly above one of the carbon atoms on the surface, that carbon atom relaxes 0.26–0.33 Å towards the incoming hydrogen atom. Similarly, when a hydrogen atom is positioned between two graphite layers such that there are carbon atoms immediately above and below it, one of these two carbon atoms relaxes 0.26–0.33 Å towards the hydrogen atom, while the other carbon atom hardly moves. The hydrogen atom finally takes a position 1.11–1.15 Å from one of the carbon atoms and 1.87–1.98 Å from the other. Note that, without the hydrogen atom, the distance between successive layers is 3.35 Å. Our calculation results indicate agreement with the results of recent neutron diffraction and thermal desorption studies on deuterated nanographite. Our calculation results also suggest that, due to the reconstruction of the carbon atoms, it is more likely to find hydrogen as atomic hydrogen rather than as molecular hydrogen between the graphite layers.

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We derive a nonlinear evolution equation which describes the development of a solid surface due to the mechanism of evaporation–condensation under a temperature gradient. The existence of stationary grain boundary grooves is shown and the stationary shapes are evaluated.

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Presented are solutions of the Yang–Yang integral equation for a one-dimensional system of bosons with repulsive δ-function interaction at zero temperature. By use of a method proposed in the previous paper, the first few terms of the asymptotic expansions of the excitation spectrum for both strong and weak coupling cases are calculated explicitly.

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A method of solving noncommutative linear algebraic equations plays a key role in the extension of the \\bar∂-dressing method on the noncommutative space-time manifold. In this paper, a solution–generating method of noncommutative linear algebraic equations is proposed. By use of the proposed method, a class of multi-line soliton solutions of noncommutative KP (ncKP) equation is constructed explicitly. The method is expected to be of use for constructions of noncommutative soliton equations. The significance of the noncommutativity of coordinates is investigated. It is found that the noncommutativity of the space-time coordinate has a role to split the spatial waveform of the classical multi-line solitons and reform it to a new configuration.

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New exact solutions are obtained by means of the modified mapping method to a new Hamiltonian amplitude equation introduced by Wadati et al. [J. Phys. Soc. Jpn. 61 (1992) 1187]. The new periodic wave solutions are the linear combination of two different Jacobi elliptic waves. Limit cases are studied, and new solitary wave solution and triangular periodic wave solution are got.

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Classical dynamics of the hydrogen molecular ion H₂⁺ is investigated, and electron dynamics involved in nonadiabatic (non-Born–Oppenheimer) processes is clarified in the framework of nonlinear dynamics. When the electron motion is described by the action variables, J_ξ and J_η, of the system with a fixed internuclear distance R, the electron dynamics coupled with the R motion is governed by nonlinear resonances between the ξ and η degrees of freedom. As a result, the system possesses an approximate constant of motion of the form nJ_ξ+mJ_η, where the integers, n and m, depend on the initial condition of the trajectory. In consequence, the electronic degrees of freedom consists of (1) one degree of freedom conserved approximately and (2) the other degree of freedom corresponding to the nonadiabatic process. The latter degree of freedom exhibits stochastic-like time evolution, which is ascribable to the Arnol’d diffusion along the resonance lines.

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Quantum mechanical decoherence process is studied with the use of a boson detector model. Generalizing the previous method, thermal effect is taken into account: Coherence of an incident particle is destroyed in interaction with its surroundings at finite temperature. Vanishing of off-diagonal elements of a reduced density matrix is rigorously shown when the detector (surroundings) is composed of a large number of constituents and/or its temperature is very high. The temperature effect reveals itself through a renormalization of interaction strength between an incident particle and the detector. Time evolution of the von Neumann entropy is explicitly determined.

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The velocity distribution function of the steady-state Boltzmann equation for hard-core molecules in the presence of a temperature gradient has been obtained explicitly to second order in density and the temperature gradient. Some thermodynamical quantities are calculated from the velocity distribution function for hard-core molecules and compared with those for Maxwell molecules and the steady-state Bhatnagar–Gross–Krook (BGK) equation. We have found qualitative differences between hard-core molecules and Maxwell molecules in the thermodynamical quantities, and also confirmed that the steady-state BGK equation belongs to the same universality class as Maxwell molecules.

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In order to study complete and incomplete fusion in heavy ion induced reactions the experiment has been carried out for measuring excitation functions (EF’s) for several reactions in the system ¹²C+¹²⁸Te, in the energy range ≈42–82 MeV, using activation technique. To the best of our knowledge EF’s for presently measured reactions are being reported for the first time. The measured EF’s have been compared with those calculated theoretically using codes CASCADE and ALICE-91. Effect of variation of parameters, of the codes, on calculated EF’s has also been studied. The analysis of the present data indicates presence of contributions from incomplete fusion in some cases. In general, theoretical calculations agree well with the experimental data.

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A novel formulation of the formally exact density functional theory is constructed on the basis of a constrained search formulation in a local-scaling density functional theory. In the formulation, a new type infinitesimal local-scaling transformation is proposed. A formally exact expression for the exchange–correlation potential with an exchange–correlation charge density is derived as well as a general method to derive an explicit form of a local-scaling potential. The present expression of the exchange–correlation potential is equivalent to that of Holas and March [Phys. Rev. A 51 (1995) 2040]. The density-dependence of the pair correlation function is also discussed.

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Saturated absorption spectra of the 1s₃–2p₂ (Paschen notation) line of metastable argon (Ar^*) atoms in a 1 mm thick glow discharge cell have been observed at room temperature. We examined the pressure dependence of the spectra from 0.025 to 0.5 torr. The profiles of the spectra were compared with the velocity-changing collision kernels of the Ar^*(1s₃)–Ar collisions. The results suggest that the saturated absorption spectroscopy with the thin cell is useful to detect collision kernels of metastable atoms.

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Velocity distributions of the 1s₃ (Paschen notation) metastable argon atoms (Ar^*) in a 1 mm thick glow discharge cell have been examined by a Monte Carlo simulation model including Ar^*(1s₃)–Ar elastic collisions and collisional quenching of Ar^* atoms at the cell surface. In order to describe the elastic collisions, the differential cross sections, the collision kernels and the collision rate coefficients were calculated from Ar^*(1s₃)–Ar potentials. The calculated velocity distributions with the model were in good agreement with the absorption spectra of the Ar^* (1s₃) atoms measured by single beam absorption spectroscopy with the thin cell.

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Fractal basin structure in the two-dimensional dissipative circle map is examined in detail. Numerically obtained basin appears to be riddling in the parameter region where two periodic orbits co-exist near a boundary crisis, but it is shown to consist of layers of thin bands.

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In geophysical flows, coherent vortex structures persist for long time and their interactions dominate the dynamics of geophysical turbulence. Miyazaki et al. derived a Hamiltonian dynamical system describing the interactions of N ellipsoidal vortices, where each coherent vortex was modeled by an ellipsoid of uniform potential vorticity embedded in a locally uniform 3D shear field. In this paper, the interaction of counter-rotating vortex pair (dipole) is investigated. According to the ellipsoidal moment model, the inclination from the vertical axis approaches π⁄2 and one of the principal axis of the ellipsoid grows exponentially with time, if two slender vortices are placed within a critical distance initially. Direct numerical simulations, based on the Contour Advective Semi-Lagrangian algorithm, are performed in order to assess the validity of the model. The CASL computaion tells that the vortices keep the dipole structure quite robustly. They survive from tilting down by emittimg thin filaments from their top and bottom, even if they are placed very close.

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Hydrodynamic equations are solved numerically to investigate convection in vibrating beds of cohesionless granular materials. Crucial influence of boundary conditions on the flow pattern is demonstrated. In addition, the dynamic transition of the roll pattern turns out to originate in different mechanisms of convection. Rolls upwards along sidewalls are thermally activated, while downward modes are driven by sidewalls. A key role of frictional heat in determining the roll pattern is also clarified.

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Two-dimensional vortex sheet suffers an unstable deformation from the Kelvin–Helmholtz instability and a curvature singularity which develops in a finite time. In this paper, long time computations of the two-dimensional vortex sheet are performed by a robust and efficient numerical method with high accuracy. To handle the rapid and non-uniform stretching of the interface, we adopt the adaptive point insertion and redistribution procedures. Computational results show highly refined structures of a complex and chaotic pattern for the vortex sheet up to very long time.

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An Alfvèn ion cyclotron (AIC) wave spontaneously excited in the central cell of the GAMMA 10 tandem mirror has strong effects on electrons. The end loss electron flux, the electron temperature and the field aligned loss power carried by these electrons increase with excitation of the AIC wave. Since electrons escape to the machine end with a good memory of the processes having in the plasma, the action of the AIC wave on electrons has been studied through measurement of end loss electrons. Response of electrons to the AIC wave is dominated by Landau damping. Electrons are accelerated by the parallel electric field of the AIC wave only when the electron thermal velocity is nearly equal to the parallel phase velocity of the excited wave. No strong action of the AIC wave on electrons is observed if this condition does not hold. A simplified calculation shows that the temporal variation of the electron temperature is the result of balance between the absorbed power through Landau damping and the field-aligned loss power.

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We have presented a new model for the direct correlation function, DCF, of monatomic fluids. In this model the core of DCF has been assumed as Precus–Yevik function for the DCF of hard sphere and its tail has been considered a Mayer f-function type. In this way, an effective pair potential in a non-linear form has related the DCF to the interatomic interactions of system. We have compared our results with other known theoretical models, which are available in the literatures, by prediction of low-angle structure of factor, S(k), via this model. In the critical region, the model is also able to predict the divergence of S(0) which is related to fluctuation phenomena. Our results show a better agreement with the experimental data at high temperature and low density where the contribution of three-body interaction is not considerable. The model is successful in presentation of the Ornestine–Zernike behaviour of S(k) in the small-k region and shows a new regularity that the minimum of S(k) and its k-position varies linearly with density, which is correct just for insulator fluids.

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Macroscopic basic equations for analyzing nolinear and nonequilibrium phenomena in anharmonic crystal lattices at finite temperatures are derived explicitly from the previously obtained microscopic basic equations by adopting the continuum approximation. The macroscopic basic equations are valid in a wide temperature range including the melting point. The equations may also be regarded as new equations for finite deformation continuum theory incorporating microscopic thermal vibration of constituent atoms. By using both two systems of microscopic and macroscopic basic equations extensively, the analyses of the nonequilibrium phenomena will be made in the following papers of the present series.

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Phonon dispersion in a two-dimensional electron–lattice system described by a two-dimensional square-lattice version of Su–Schrieffer–Heeger’s model and having the half-filled electronic band is studied theoretically at temperatures higher than the mean field critical temperature of the Peierls transition. When the temperature is lowered from the higher region down to the critical one, softening of multiple phonon modes which have wave vectors equal to the nesting vector Q=(π⁄a,π⁄a) with a the lattice constant or parallel to Q is observed. Although both of the transverse and longitudinal modes are softened at the critical temperature in the case of the wave vector equal to Q, only the transverse modes are softened for other wave vectors parallel to Q. This behavior is consistent with the Peierls distortions at lower temperatures.

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We investigate an influence of edge diffusion on island formation in molecular beam epitaxy. Edge diffusion not only yields compact islands but also results in small clusters such as dimers and trimers mobile. We find that both the morphology of islands and the mobility of small clusters yield nontrivial effects on the power–law behavior of the monomer and island densities and the scaling functions of the island size distributions. When dimers and trimers are stable, an influence of the morphology of islands on the power–law behavior is found to be negligible. On the other hand, when dimers and trimers are subject to diffuse, the scaling powers and the scaling functions vary depending on the degrees of the mobility for both the fractal growth and the compact growth models. The morphology of islands in this case influences the power–law behavior of only the monomer density.

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The effect of edge and corner diffusions on the morphology and on the density of islands nucleated irreversibly on a flat substrate surface is studied. Without edge and corner diffusion, islands are fractal. As an edge diffusion constant D_e increases, islands tend to take a cross shape with four needles in the ⟨10⟩ direction. Additional corner diffusion with a diffusion constant D_c yields square islands. When D_e is small relative to the surface diffusion constant D_s, the square corner shows the Berg instability to produce hopper growth in the ⟨11⟩ direction. The corner diffusion influences the island number density n. At a deposition flux F with a small D_c, mainly monomers are mobile and n∝(F⁄D_s)^1⁄3. At large D_c, dimers and trimers are also mobile and n∝F^3⁄7D_s^−5⁄21D_c^−4⁄21. The F dependence is in good agreement to the rate equation analysis, but the dependence on D_c cannot be explained by the theory.

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A constructive method to find flat bands is demonstrated for a model describing tight-binding electrons on the hexagonal lattice in which each atomic site has three orbitals. The system may represent σ-electrons of an sp²-hybridized material but we assume transfer integrals between orbitals to be free parameters for general discussion. Finding highly degenerate eigenfunctions of each flat band is identified as finding a localized eigenfunction, which is determined as a basis function of an irreducible representation of, for example, a point group C_6v. This approach yields not only flat bands on all over the k-space but also some partial flat bands only on a partial k-space. In the former case, if the flat band locates at the bottom (or the top) of a band structure, it is shown that Mielke’s condition holds, allowing occurrence of the flat band ferromagnetism.

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A weak distortion of a [FeO₆] octahedron was observed in hexagonal BaFeO_2.91 at around 180 K by neutron powder diffraction. The occurrence of a weak distortion is consistent with the results of Mössbauer measurements, which indicated a decrease in the Fe⁴⁺ concentration below 170 K. We strongly suggest that the weak distortion of a [FeO₆] octahedron results from a charge-disproportionation phenomenon, 2Fe⁴⁺ → Fe^⟨4+τ⟩+ + Fe^{⟨4−τ⟩+}, where 0<τ≤1. Below 130 K, BaFeO_2.91 orders antiferromagnetically and the propagation vector is ⟨00 0.45c^∗⟩ at 50 K.

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The charge and spin states of transition-metal atoms in a hemoprotein are studied based on the extended Haldane–Anderson model in which exchange interaction between localized d electrons and orbital dependence of p–d hybridization are taken into account. It is shown that both multiple charge states and transition between high-spin and low-spin states can be described properly in this model.

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We invastigate the general properties of the hybridization gap in Ce compounds focusing on the case with orthorhombic structure. In the study we use the periodic Anderson model possessing Kramers doublets in f level and mainly discuss the hybridization between one of Kramers doublets and a conduction band. In higher symmetry such as cubic, tetragonal and hexagonal structure, the f-state with J_z=±1⁄2 component becomes insulating state with a real energy gap near the f-level. In lower symmetry such as orthorhombic structure, although f-states contain the component of J_z=±1⁄2, semimetallic states with pseudogap or metallic states with a peak are realized in specific f states.

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The ground-state properties of the Hubbard model on the square lattice with nearest-neighbor and next-nearest-neighbor hoppings at half filling are studied by the path-integral-renormalization-group method. The nonmagnetic-insulator phase sandwiched by the paramagnetic-metal phase and the antiferromagnetic-insulator phase shows evidence against translational symmetry breaking of the dimerized state, plaquette singlet state, staggered flux state, and charge ordered state. These results support that the genuine Mott insulator which cannot be adiabatically continued to the band insulator is realized generically by Umklapp scattering through the effects of geometrical frustration and quantum fluctuation in the two-dimensional system.

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In EuPd₂Si₂, the valence transition of Eu atoms between the Eu²⁺ state and the Eu³⁺ state takes place when the temperature of the sample changes. In the present study, we prepared Eu_xY_1−xPd₂Si₂ and Eu_xLa_1−xPd₂Si₂, in which the Eu atoms of EuPd₂Si₂ are systematically substituted by non-magnetic Y or La atoms, and we have measured the magnetic susceptibility χ, the electric resistivity ρ and the thermoelectric power S. We found that the temperature of the valence transition of Eu ions is only very weakly dependent on the alloying concentration x of Eu atoms. In addition, the notable structures of the S(T) curves were observed for these samples, which we understand in term of the anomalies of the relaxation time of conduction electrons interacting with the Eu 4f⁷ virtual bound state. In this respect, the valence transition of Eu ions in this study makes a contrast with the Kondo problems of the Ce compounds, where the anomalies of the state density of conduction electrons are their central issue.

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We calculate the effective pairing interaction in the Hubbard model on the two-dimensional square lattice, by applying perturbation expansion up to the fourth order in the on-site repulsion U. We evaluate transition temperature as functions of the repulsion U. We consider only the following two typical cases (I) and (II): (I) The system is near the half-filled state, and the Fermi surface nesting yields the strong antiferromagnetic fluctuations. (II) The system is away from the half-filled state. This case is intended to reproduce the single main band of the spin–triplet superconductor Sr₂RuO₄. In the both cases, the Fermi level is set close to the Van Hove singularity. In the case (I), each order of the perturbation expansion for the pairing interaction gives a similar momentum dependence, and in addition the perturbation expansion for the pairing interaction converges relatively well even for moderately strong U. On the other hand, in the case (II), the perturbation expansion does not converge well. While the third order terms give the momentum dependence much favorable for the p-wave pairing, there are strong fourth order contributions which have the momentum dependence similar to that of the third order contributions but are introduced with the opposite sign. We can prepare a natural remedy for this bad convergence of the expansion, and obtain reasonably the momentum dependence favorable for the p-wave pairing. Consequently, we find that the d_x²−y²-wave and highly anisotropic p-wave states are obtained for the cases (I) and (II), respectively.

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We estimate the effect of the superconducting gap anisotropy in the dispersive gap mode of phonons, which is observed by the neutron scattering on borocarbide superconductors. We numerically analyze the phonon spectrum considering the electron–phonon coupling, and examine contributions coming from the gap suppression and the sign change of the pairing function on the Fermi surface. When the sign of the pairing function is changed by the nesting translation, the gap mode does not appear. We also discuss the suppression of the phonon softening of the Kohn anomaly due to the onset of superconductivity. We demonstrate that observation of the gap dispersive mode is useful for sorting out the underlying superconducting pairing function.

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We propose the pf+pd mixing model for CeSb to explain the stability of the ferromagnetic double layer structure in the magnetic ordering. The pd mixing causes the saddle type singular points, neighboring the Δ axis, for the bands which gain energy through the pf hybridization with the occupied f state. The peak of the density of states due to this combined effect of the pf mixing and the pd mixing enhances the stability of the double layer structure. The same combined effect also causes the saddle type singular points in the joint density of states of the optical transition. The peak structure of the magneto-optical spectra which has been observed in experiments is explained by the present model.

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The element specific magnetic susceptibilities of some rare-earth compounds are estimated by measuring magnetic circular dichroism at rare-earth M_4,5 absorption edges. The temperature dependences of the rare-earth 4f local magnetic susceptibilities in dense Kondo materials, CeNi, CeSn₃ and CeRu₄Sb₁₂, are remarkably different from those of the bulk magnetic susceptibilities measured by a conventional magnetometer, although the 4f electron is regarded to mainly hold the magnetic moment in these compounds. In contrast, the rare-earth 4f local magnetic susceptibility of ferromagnetic NdFe₄P₁₂ shows almost as similar behavior as the bulk one.

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The jarosite-type compounds, KFe₃(OH)₆(SO₄)₂ and KCr₃(OH)₆(SO₄)₂, are model materials of the frustrated antiferromagnet on the kagomé lattice. We have synthesized new Cr-jarosites, ACr₃(OH)₆(SO₄)₂, with other monovalent cations A⁺ [A = Rb, NH₄, Na] and have measured the magnetization between 2 K and 300 K. The measured susceptibilities above 20 K agree well with the calculation based on the high-temperature expansion and with the Monte Carlo simulation for the two-dimensional Heisenberg antiferromagnet on the kagomé lattice, which indicates that the new Cr-jarosites are good examples of the Heisenberg kagomé lattice antiferromagnets with S=3⁄2. The exchange interactions for these Cr-jarosites are estimated to be about 5 K. The susceptibilities of the Cr-jarosites with K, Rb, and NH₄ increase steeply below about 4 or 8 K, although they are antiferromagnets. The susceptibilities after zero-field-cooling and those after field-cooling are different below this temperature, and the magnetization curves at 2.0 K show small hysteresis loops, which indicates the existence of small ferromagnetic components. The anomalies are considered to be due to the magnetic ordering and not to the spin-glass-like freezing. The weak ferromagnetic moment is caused by the canted 120° spin structure in the ordered state.

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The magnetic properties of the compound (CePd₃)₈Ge have been studied by means of neutron diffraction and specific heat measurement at ambient pressure and also of measurements of susceptibility and electrical resistivity under hydrostatic pressure. The magnetic modulation vector, q, of the antiferromagnetic phase is {001} and the spin polarization is parallel to q. With increasing the applied pressure up to 6 GPa, the Néel temperature keeps increasing, which indicates a strongly localized nature of the 4f-electrons of the compound.

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The discovery of ferromagnetism in CaB₆ doped with La was surprising, because there is no magnetic element in the compound nevertheless the system involved a ferromagnetic Curie temperature as high as 600 K. In order to resolve the origin of the ferromagnetism, we have made magnetization measurements and chemical analysis of CaB₆ and LaB₆ samples synthesized under various conditions. We have found that the ferromagnetism disappears almost completely by the acid etching, and that there is strong correlation between the magnitude of reduced magnetization and the iron concentration involved in the acid. Therefore we conclude that the ferromagnetism is of extrinsic origin and can be ascribed to iron impurity phases, probably FeB and Fe₂B that have nearly the same Curie temperature as CaB₆. We suggest that these iron impurities originate from the crucible used in the synthesis. Furthermore we have measured the thermoelectric power at high temperatures including the Curie temperature. There seems to be no relation between the appearance of the ferromagnetism and the transport properties, and no evidence for the bulk ferromagnetism has been observed.

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Dielectric constant of binary mixtures of Di-isobutylketone (DIBK) with some carboxylic acid viz. acetic acid, propionic acid and butyric acid is measured at 303.16 K and 455 kHz. The data are used to compute the mutual correlation factor g_ab, excess molar polarization ΔP and Gibb’s free energy ΔG of mixing to study the molecular interaction. The study reveals that interaction is maximum in DIBK + butyric acid system and micro heterogeneous β-clusters with antiparallel orientation of dissimilar molecules predominate in it.

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The coexisting phases of Clathrate Hydrate (CH) and low concentration aqueous solution of tetrahydrofuran (THF) or ice I_h has been studied using low frequency Raman spectroscopy. Observed low frequency Raman spectra were found to be reproducible by the linear combination of the Raman spectrum of pure CH and that of low concentration aqueous solution of THF or that of ice I_h. Moreover, the coexisting curve can be constructed from the analysis of spectra. In case of liquid phase, however, Raman spectra were not reproducible by the spectrum of pure water and that of pure THF. To reconstruct observed low frequency Raman spectra of THF aqueous solution of any concentration, we found that the additional vibrational mode was required in addition to that of pure water and that of pure THF. For low concentration range, low frequency Raman spectra of the liquid phase can be reconstructed by the linear combination of the Raman spectrum of pure water and that of 0.1 molar fraction aqueous solution of THF.

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The structure of copper ion clusters in dehydrated N-isopropylacrylamide/sodium acrylate (NIPA/SA) gel has been studied by means of small angle X-ray scattering (SAXS) method. In order to distinguish the intensity scattered by Cu ions, the X-ray anomalous dispersion effect around the Cu K absorption edge has been coupled with SAXS. It is found that the dispersion effect dependent on the incident X-ray energy is remarkable only at the momentum transfer q=0.031 Å⁻¹, where a SAXS peak is observed. The results indicate that copper ions form clusters in the dehydrated gel, and that the mean size of clusters is the same as that of SA clusters produced by microphase separation.It is therefore naturally presumed that copper ions are adsorbed into the SA molecules. On the basis of the presumption, a mechanism is proposed for microphase-separation and clustering of Cu ions.

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