A new hierarchy of braid group representations is derived from a generalization of solvable vertex models associated with SU(n) symmetry. A family of link polynomials is obtained based on the Markov traces on the braid group representations. The hierarchy includes both the Alexander-Conway polynomial and the Jones polynomial as special cases. The link polynomials are one-variable realizations of the HOMFLY polynomial.

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The distribution of pore size and the fractal dimension of irregular macroscopic precipitation patterns formed in initially homogeneous, supercooled solutions containing get materials of a sparingly soluble salt (PbI₂) were measured as a function of initial concentration and ambient temperature. We find, by image analysis, a log-normal shape of the size distribution with a peak at typically 0.5 to 3 mm and an average fractal dimension of 1.56 (range: 1.43 to 1.64) over 1 decade. The observations suggest that the structures arise from competitive territorial growth kinetics in a polydisperse crystal system and imply a spacing law in close analogy to the Liesegang precipitation bands.

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The nucleation and the growth process of turbulent areas in the electrohydrodynamic convection in nematic liquid crystals is investigated. During the transition from one turbulent state (DSM1) to another (DSM2), this fully dissipative system shows, on the qualitative level, a great similarity to classical nucleation phenomena. We found good agreement between the experimentally observed nucleation rates and those from classical nucleation theory. The main difference between the two turbulent states is the density of disclinations in the director field.

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The amount of an end-loss flux of warm electrons and its energy spectrum are studied by using an electrostatic energy analyser over a wide range of energy up to 10 keV in the GAMMA 10 tandem mirror. The outgoing electron flux is found to be much larger than the associated ion flux during the strong end-loss plugging under the fundamental electron cyclotron resonance heating. The observed energy spectrum reveals a high-energy tail component (T_eH∼3 keV) in addition to the already reported bulk warm component (T_eL∼700 eV). The new spectrum is successfully applied to evaluate the secondary electron flux from end plates so as to account for the charge balance of the net flux of electrons and the ion flux on the floating plates.

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An unexpected reduction of the X-ray diffraction intensity was found at 80°C in the ferroelectric phase of LiH₃(SeO₃)₂. It follows from the crystal structure analysis that no crystal structure change takes place at 80°C. It is concluded that this phenomenon is the irreversible transformation from the crystalline state to the amorphous state. The transformation is undergone selectively from the surface with an extremely long characteristic time. It is very likely that the previously reported superionic character originates in this transformation.

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Thin films of In have been found to decorate the domains in the commensurate ferroelectric phase of K₂ZnCl₄. A sample which was annealed in the incommensurate phase and quenched to room temperature exhibits light and dark strips running parallel to the b-axis on the a-face. These strips having the average width of 1.3 μm correspond to domains of different polarities. The average width increased to 3.2 μm after the sample had been annealed at 100°C for three days. In addition, patterns of vortices have been observed where six domain walls meet at a point.

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The one-dimensional periodic Anderson model with six sites is diagonalized numerically for various electron numbers and for various magnetizations. Detailed comparison with the perturbation theory in the half-filled case shows that both the RKKY- and the Kondo-type couplings are important to stabilize the nonmagnetic ground state, and that as the magnetization increases, the RKKY interactions dominate the behavior of the system.

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The Hall effect was studied in β-(BEDT–TTF)₂I₃ in order to survey the problem of the low-T_c and the high-T_c states and the general interest to the Fermi surface of this material. i) Our measurement revealed that this material is a metal with almost constant hole numbers down to 20 K. By the estimate of R_H=1⁄nec, the hole number seems to be less than one per unit cell. ii) In the temperature dependence of R_H in detail, we found a pronounced stepwise decrease by 8% in Hall voltage when temperature is lowered through 175 K but not through 110 K. iii) Further, below 20 K, Hall voltage was found to decrease. Possible reasons for such phenomena are discussed.

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We propose a probable pairing mechanism for high-T_c superconductors. The strong correlation between intra-atomic Cu–d holes, U, is treated exactly. We assume holes introduced by doping occupy O–p_π as well as O–p_σ orbits, and p_π holes become itinerant. Strong intra-atomic correlation V, between p_π- and p_σ-holes, and the Hubbard U can lead to an attractive force between O–p_π itinerant holes.

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The anisotropy of the upper critical field H_c2 has been measured at ambient pressure on a layered organic superconductor β-(BEDT–TTF)₂I₃ both in the states before and after annealing at 109 K for 120 hours. By annealing, the critical temperature T_c increases from 1.4 to 2.08 K, while the H_c2⊥plane increases and the anisotropy, H_{c2⁄⁄plane}⁄H_c2⊥plane, decreases. The angular dependences of H_c2 for both states are explained in terms of the effective mass model. It is clarified that the enhanced T_c which is ascribed to the annealing-induced configurational orderings of ethylene groups is closely related to the enhanced effective mass in the basal plane.

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Neutron powder diffraction studies have been performed to study the unusual magnetic ordering in half-metallic UNiSn with the cubic MgAgAs-type structure. The result indicates that the magnetic structure of UNiSn is a type-I antiferromagnetic structure with the ordered uranium moment of 1.55±0.10 μ_B. The Néel temperature is 46±2 K, which coincides with the transition temperature from semiconductor to metal in electrical conductivity. We therefore propose that the development of the type-I antiferromagnetism UNiSn strongly suppresses antiferromagnetic spin fluctuations and leads to disappearance of the semiconducting energy gap.

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The thermal expansion of bcc Cr Mn alloys containing 41, 60 and 66% Mn have been measured from 2 to 100 K. The 41% alloy shows an unusually large positive coefficient of expansion at low temperatures, the 66% alloy has a giant negative coefficient and the intermediate alloy changes rapidly from a large negative coefficient (T<20 K) to a large positive coefficient above 20 K. The unusual magnitudes and temperature dependences are discussed briefly in terms of magnetovolume and spin fluctuation effects.

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The development of the short-range ordering in Mn(HCOO)₂·2(NH₂)₂CO has been observed by the measurements of magnetic heat capacity and susceptibility. The experimental results are well reproduced by the high-temperature series expansion for the two-dimensional Heisenberg antiferromagnet with the exchange constant J⁄k_B=−0.34±0.02 K in the temperature region T>1.2 T_SK (T_SK; the Stanley-Kaplan temperature). The critical temperature T_N=3.77±0.02 K\simeq1.1 T_SK nearly coincides with that of Mn(HCOO)₂·2H₂O. It is suggested that the long-range ordering is responsible for the small Ising-like anisotropy in the exchange interaction. A two-dimensional spin structure with the canceled Weiss field from the adjacent layers, as in K₂NiF₄, is conjectured.

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Cu NMR signals have been observed in superconducting Nd_1.85Th_0.15CuO_4−y, Pr_1.85Th_0.15CuO_4−y and the parent compound, Nd₂CuO_4−y. In Nd₂CuO_4−y, the antiferromagnetic ordering appears at low temperatures. The related zero-field NMR of Cu was observed around 109–130 MHz. From the analysis of the spectrum, the internal field at Cu is estimated as 103 kOe and the electric quadrupole interaction as ν_Q=14.0 MHz for ⁶³Cu and ν_Q=12.9 MHz for ⁶⁵Cu. In the superconducting (Nd, Pr)_1.85Th_0.15CuO_4−y, two kinds of Cu signals were observed. One was a broad signal distributed around 20–70 MHz under zero external magnetic field. The other was a paramagnetic signal having an extremely small electric field gradient.

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Nuclear quadrupole resonance (NQR) measurements were performed on superconducting La_2−xCuO_4−y (T_C∼30 K) synthesized by high-temperature and high-pressure oxygen enrichment. At liquid ⁴He temperature, the existence of a weak and broad line has been found around 6.35 MHz which is the resonance frequency expected in stoichiometric La₂CuO₄ when an internal magnetic field is absent. The spin-echo intensity of this new signal increases in weak magnetic field (∼100 Oe) which is characteristic of the resonance in the mixed state of the superconductors. On the other hand, the dominant lines corresponding to the magnetic phase do not show any significant changes in contrast with the case of the Sr-doped samples. These results indicate that superconductivity occurs in the regions where antiferromagnetic ordering is suppressed sufficiently by the carrier doping.

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The primary step of firefly D-(−)-luciferin (Ln) chemiluminescence in the O₂-bubbled dimethyl sulfoxide (DMSO) dissolving t-BuOK was investigated by the ESR rapid-freezing technique. It was discovered that superoxide anion radical (O₂⁻) is generated and is stably present in the DMSO solution of t-BuOK at room temperature and is consumed on mixing with the solution containing Ln to produce light emission. Thus it was concluded that O₂⁻ is clearly related to the primary step of Ln chemiluminescence.

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N double pole solution for the modified Korteweg-de Vries equation is conjectured from 2N soliton solution by using the Hirota’s method.

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We consider a 2+1d nonlinear Klein-Gordon equation, which has a nonlinear part λφ³+μφ². We have found many higher-order solutions corresponding to specific initial values. The characteristic feature of this system is that the space integral of the “potential” energy λφ⁴⁄4+μφ³⁄3 vanishes for all these higher-order solutions.

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This paper deals with how a classical mechanics relates to the quantum mechanics, comparing the stationary distribution function on a constant energy in a coarse-grained classical system with the Husimi function ρ_H of the eigenstate of quantum system. In the domain of a torus with one degree of freedom, these two functions are quite similar to each other. On the other hand, around a hyperbolic fixed-point the functions satisfy the equations of the similar type. However the solutions admissible for classical and quantum distribution functions have very different forms. In this paper we discuss the necessity for the problem of the correspondence between classical and quantum mechanics to investigate not only the similarity of the equations but also the geometrical structure of the solutions.

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The terrace-step-kink (TSK) model is the simplest model to describe the crystal surface. In ordinary TSK models, step is always regarded as one-dimensional interface with in-plane solid-on-solid (SOS) condition. In the present article we introduce an extended TSK model where the non-SOS type step excitations are allowed and investigate the crystal surface profile. The model is shown to have the two universal properties at the facet edge: the Gruber-Mullins-Pokrovsky-Talapov behavior and the universal Gaussian curvature jump.

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Pattern formation processes and the associated defect motion are experimentally studied for various rectangular cells in the electrohydrodynamic instability. Wavenumber selection arises from the competition between the growth of the most rapidly growing mode and the finally stable mode in the Williams domain (WD) state. Defect motion is associated with such a competitive growth into the final stage. The fluctuating WD (FWD) is strongly related to the oscillatory gliding motion of defects. Temporally nonperiodic change of the number of defects is observed in the FWD state with a power spectrum of 1⁄f type (defect chaos). A large hysteresis is observed near the onset of FWD. A detailed phase diagram of stable convective patterns in the plane spanned by the threshold voltage and the applied frequency is presented with the characteristic behavior of defect motions.

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A super-hypernucleus is a nucleus which consists of many strange quarks as well as up and down quarks. An important part of the results of our recent investigation on the mass spectrum and other properties of super-hypernuclei in the quark-shell model is reported. It is expected that not only certain exotic nuclei such as the “dideltas” (Dδ⁺⁺⁺⁺ and Dδ⁻⁻) but also certain super-hypernuclei such as the “hexalambda” (Hλ) and the “vigintiquattuoralambda” (Vqλ) may appear as quasi-stable nuclei. However, in the quark-shell model, there is no qualitative reason why the “dihyperon” or “H dibaryon” (H) should be quasi-stable or even stable. Many other predictions including a sudden increase of the K/π ratio due to the production of super-hypernuclei in heavy-ion collisions at high energies are also made.

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By using the variational adiabatic method, the energy values and the equilibrium internuclear separations of the H₂⁺ ion in π_g state in strong magnetic fields are calculated and compared with those obtained from the adiabatic method and the Monte Carlo method and our conclusion through the Monte Carlo Method are confirmed, that is, the antibonding state π_g in the absence of external magnetic field changes to a bonding state with an increasing magnetic field.

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Maxwell’s equations are transformed into a new set of equations for the general class of electromagnetic waves with parallel electric (E) and magnetic (H) fields in free space. From these equations various methods for obtaining new forms of such electromagnetic waves are derived. In particular, a prescription is given by which one can construct electromagnetic waves with parallel E and H fields from any known waves with non-parallel E and H fields. Some examples of non-transverse electromagnetic waves thus obtained are shown.

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The scattering cross section has been numerically calculated for longitudinal (L) and transverse (T) elastic waves in a solid medium scattered by a spherical particle. The scattering due to the difference of mechanical properties between the particle and the medium was considered. The cross section is a function of ak (a: particle radius, k: wave number), and the calculation has been extended to the region of large ak values for several combinations of the particle and the medium materials. As ak is increased, the cross section for the L-wave rapidly increases, approaches a saturation, and then slowly fluctuates. The cross section for the T-wave gradually increases with rapid fluctuation and sharp peaks, and the magnitude of the cross section is very large when the particle is hard and the medium is soft elastically. The origin of the strong scattering was considered to be the resonance scattering of the T-wave by the induced particle vibrations,

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The N-breather solutions to the Boussinesq (-Type) equation: u_tt−pu_xx−6q(u²)_xx−qu_xxxx=0, where p=±1, q=±1 and their existence conditions are presented. It is shown that they are linearly unstable by using the growing-mode solutions, which affect only the phase shift to the breathers as time approaches infinitely.

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Generation of the highly charged ions such as C⁺∼C⁴⁺ using the Mather type plasma focus is carried out. Measurement of the energy distribution with a Thomson parabola analyzer shows that the maximum energy per charge state extends to ∼1.5 MeV/Z, for each species approximately. Generation of such huge electric field to accelerate ions is reasonably explained by an anomalous plasma resistivity induced in the collapsed plasma column. The discrepancy between the induced voltage and the observed one across the collector plates is discussed taking the capacitance of the coaxial electrode into account. A microchannel plate which is extremely useful for the time dependent ion measurement is calibrated for energetic ions of C⁺∼C⁴⁺ by the produced ion beams.

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We investigated the phase separation process in the binary mixture of the semi-rigid thermotropic liquid crystalline polymer and the flexible polymer. By raising temperature, an initially homogeneous mixture undergoes the phase separation. Utilizing the nematic property of one component, we were able to observe this segregation process by means of a polarizing microscope under crossed polarizers. We found a new mechanism to explain the coalescence of droplets in the latest stage.

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The occupation probability of impurity atoms, Co, Fe or Ni, on each site of β-Mn structure has been determined by means of neutron diffraction with the single crystal specimens. Almost 90% of the impurity atoms occupy the site I. In the β-Mn(Co) alloy, an atomic long range order of Co impurities on the site I has been discovered below 500 K. The ordered structure is analyzed by introducing the scalar basis functions based on the group theoretical treatment and is discussed on the relation to the icosahedral packing sequence.

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The crystal structure of the title oxide was studied by means of the X-ray and neutron single crystal diffraction measurements. At room temperature, the tetragonal crystal structure is P4₂/ncm-type (No. 138), which is one of the subgroup of the space group I4/mmm. The lattice parameters of a sample annealed and slowly cooled in oxygen atmosphere from 673 K are a=b=5.4640(1) Å and c=12.6719(2) Å, while the oxygen content, x=0.10(4), was determined from obtained neutron data. The title oxide undergoes a tetragonal (P4₂/ncm)/tetragonal (I4/mmm) phase transition at about 560 K. The transition temperature is almost identical both in the annealed and as-grown crystals.

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A variety of Fibonacci lattices, which are locally isomorphic each other and satisfy Conway’s theorem, is found to exist through the projection method by changing the location of the window in the square lattice. The structure of each system, described by a (semi-infinite) series of the Fibonacci generations, is characterized by its own cycle, i.e. its own self-similarity. On the wave function at E=0 in an off-diagonal model (for example), the family yields a variety of multi-fractal distributions.

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Dielectric, dilatometric and AC calorimetric properties of (CH₃NH₃)NaSO₄·6H₂O in addition to a preliminary X-ray examination were investigated. The crystal at room temperature belongs to 6mm with the unit cell parameters: a=7.25 Å, c=12.93 Å and Z=2. It was found that the crystal undergoes a phase transition of the second order at −133.8°C (T_c). The dielectric constant along the a axis shows an anomalous break at T_c, while the dielectric constant along the c axis does not show a remarkable anomaly near T_c. Both the anomalous linear thermal expansion coefficient and the relative specific heat observed in the critical temperature region were discussed shortly.

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It is shown that some systematic series of exactly solvable models become canonical in the CAM theory, namely that generalized cactus trees play a role of systematic mean-field approximations in the CAM to study the true critical behaviour of the corresponding regular system. A confluent transfer-matrix method is introduced to solve such fractal systems. On the basis of this formulation, the spontaneous broken symmetry of effective Hamiltonians is clarified. Some simple applications of this general formulation are given explicitly to estimate critical exponents using the CAM theory.

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Phonons and rotons in liquid helium II eject ⁴He atoms in evaporation through a single-quantum process. We investigate this phenomenon based on the concept of the “dressed-boson” introduced in the previous work. It is explained why one phonon (or roton) can eject only one helium atom. We discuss the reverse process and find that a beam of helium atoms branches to three refracting beams at a liquid-gas boundary. The values of the transmission rates to the three beams are calculated. Next, we investigate reflection of a phonon (or roton) at a boundary between liquid helium II and solid. In the phenomena, a beam composed of phonons (or rotons) is also expected to branch into three beams after reflection.

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It is known experimentally that Heusler alloys, Ni₂MnGa and Co₂NbSn undergo the cubic-to-tetragonal lattice transformation, in a ferromagnetic state and a paramagnetic one, respectively. We calculated electronic structures of Co₂NbSn and Ni₂MnGa for both cubic and tetragonal structures by KKR method. Comparing the density-of-state of the cubic and tetragonal structures for each alloy, it is expected that the band Jahn-Teller effect cause the lattice transformation in both alloys.

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Spectral densities of local single-particle, magnetic and charge excitations are calculated for the impurity Anderson Hamiltonian based on the renormalization group approach. Calculation is made in wide range of energy and for various magnitude of f-f Coulomb interaction constant, U_f, and for degeneracy factor from 2 to 5. The width of the peak at the Fermi level in the single-particle spectrum has always comparable scale to the magnetic excitation energy, and is never larger than the hybridization width. In the BIS side of this sharp peak a broad satellite with large intensity appears as a shoulder when U_f is large and the f-electron number is intermediate larger than 1. The band-like peak in BIS of U-compounds, which has much larger width than that of the usual band theory, is interpreted by this broad satellite.

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The electronic states of the stage-2 hydrogen-potassium-graphite ternary intercalation compounds C₈KH_x (x=0.5, 1.0) are investigated. The band structures of these compounds are determined in a local density functional formalism using the self-consistent numerical-basis-set LCAO (linear combination of atomic orbitals) method. We estimate the amount of the charge transfer among the individual atoms and show that the hydrogen atom acts as an acceptor to graphite, while the potassium atom acts as a donor. The charge transfer to the hydrogen atoms is imperfect and therefore the hydrogen 1s state forms a partially occupied metallic band. This hydrogen-1s-like band coexists with the graphite-π^*-like bands at the Fermi level. These results indicate that C₈KH_x has a feature of the metallic hydrogen. Our results are consistent with recent experimental results of electrical conductivity, thermoelectric power, ESR and NMR.

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Based on the effective Hamiltonian for a CuO₂ layer of high T_c oxides, we have examined the case of a single Cu spin and a single hole in a Bloch band, whose structure is determined not only by direct transfer integrals between oxygens but also by the indirect one via Cu sites. It is found that the singlet state is strongly stabilized because of the particular feature of the band structure and that the triplet state is also possible below the hole band.

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The angular dependence of the de Haas-van Alphen (dHvA) frequency has been studied in the Kondo lattice compound CeB₆. The Fermi surface of CeB₆ is quite similar to that of PrB₆ or LaB₆, with an electron pocket of almost the same size as that in PrB₆. We have also determined the field dependence of the heavy cyclotron mass for the main belly orbit in CeB₆ and have confirmed a discrepancy between the present mass and the one estimated from the low temperature specific heat coefficient.

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We have measured the magnetoresistance and de Haas-van Alphen (dHvA) effect in CeNi in the field up to 150 kOe and at temperature down to 0.4 K. This material is found to be a compensated metal with equal carrier concentration of electrons and holes. The open orbits exist along the b- and c-axes. Four dHvA branches have been found in the field along the b-axis. The dHvA frequencies and the cyclotron masses are 3.60×10⁷ Oe (10.3 m₀), 1.25×10⁷ Oe (8.91 m₀), 6.58×10⁶ Oe (3.05 m₀) and 2.15×10⁶ Oe (2.58 m₀).

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Some exact properties of local current distribution are investigated theoretically in two dimensional systems in high magnetic fields. In the high-field limit and when each Landau level is completely filled, the local current becomes the sum of that induced by an external electric field and that due to random potential fluctuations. The latter becomes the same as that in the absence of a field and the former becomes uniform and exactly the same as that in the absence of impurity potentials. When the magnetic field becomes weaker, there exists a correction to the local current from the quantized value in contrast to the global current which is always quantized.

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Optically detected cyclotron resonance (ODCR) in pure-Ge has been observed. Experimental results are (1) hole resonance has been observed stronger at ODCR than at usual cyclotron resonance (CR), (2) effective mass dependence of signal intensity of electron resonance at ODCR is different from one at CR, and (3) both free carrier-exciton and free carrier-exciton-electron hole droplet coexisting systems are not expressed by a single carrier temperature when free carriers are rather hot through microwave absorption. By means of kinetic equations it is shown that the origin of ODCR observation is the impact ionization of excitons by free carriers in the free carrier-exciton coexisting system.

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Energy band structures of short period superlattices (GaAs)_m/(AlAs)₅ with m ranged from 1 to 11 are calculated by using the tight-binding approximation, where the second-nearest neighbor interactions are included in addition to the nearest neighbor interactions. The calculated lowest direct and indirect energy gaps are found to depend on the valence band discontinuity. Momentum matrix elements are also calculated for the transitions between the top valence bands and several lowest conduction bands in order to clarify the optical transition, allowed or forbidden. It is found that the transition for the lowest direct gap in the superlattices with m<5 is forbidden, reflecting the band folding eflect. The present calculations show a good agreement with the previous experimental observation, where (GaAs)_m/(AlAs)₅ superlattices are indirect gap material for m<7 and direct gap material for m>7.

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Two-dimensional Antiferromagnetic Heisenberg model is investigated by a mean field theory, where order parameter corresponding to the resonating valence bond (RVB) state is retained. The spin is expressed by Schwinger bosons. As has been shown before, this method gives long-range Néel order at T=0 [D. Yoshioka: J. Phys. Soc. Jpn. 58 (1989) 32], and gives reasonable results at finite temperatures [A. Auerbach and D. P. Arovas: Phys. Rev. Lett. 61 (1988) 617]. In the present paper phase diagram in a magnetic field is given. Exact expressions for the specific heat, uniform susceptibility, and correlation length at low temperatures are given, too, which improve the results by Auerbach and Arovas. The results are compared with those by computer simulations, and good agreement is obtained.

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Magnetization measurements are made on a Heisenberg spin glass Co_0.1TiS₂. The field dependence of irreversibility-onset temperature T_ir is determined from the difference between field-cooled and zero-field-cooled magnetizations. The field dependence of temperature T_cr of susceptibility anomaly is determined. Many features of the present data are consistent with the mean-field predictions of Kotliar and Sompolinsky for Heisenberg spin glasses with random anisotropy.

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Numerical results obtained from Monte Carlo simulation in the ground state and at finite temperatures as well as the exact diagonalization and the transfer matrix method are reported. Efficiency of the Monte Carlo method in the ground state is examined. Spin, charge and superconducting correlations are investigated for the Hubbard and the t-J model in one and two dimensions. The momentum distribution in the one-dimensional Hubbard model shows fermi-liquid-like behavior at least in two orders of magnitude smaller energy scale than the band width. The short-range incommensurate spin correlation is observed and analyzed in the doped Hubbard and the t-J model both in one and two dimensions. In the ground state, the superconducting correlation shows the absence of system size dependence in two dimensions at the filling smaller than 0.8 and in one dimension at any filling. The binding energy of two fermions and the spin and charge distortion around an itinerant fermion are also discussed in the t-J and the coupled spin-fermion model.

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Angular dependence of Fe³⁺ ESR spectra in hexagonal BaTiO₃ has been measured around the phase transition temperature of 222 K (T₀). The ESR lines split in three lines respectively in the ab-plane below T₀, and the intensities change with uniaxial stress. These splittings can be explained by the formation of domains. The spin Hamiltonian parameters D and a are −0.059 cm⁻¹ and 0.005 cm⁻¹, respectively, in the both phases. The parameter E is nearly zero above 222 K and increases with decreasing the temperature. The principal axis Z rotates in the bc-plane below T₀. Analysis due to the superposition model indicates that Fe³⁺ substitutes for Ti site in Ti₂O₉ cluster and shifts along the b-axis with decreasing the temperature below T₀.

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Anomalously long nuclear spin-lattice relaxation time was observed at low temperatures below 0.5 K in small metallic particles of copper with diameters smaller than 100 A by a new method for setting the nuclear magnetization to zero. The observed anomaly is in accordance with what is expected for very small metals in which the spacing of energy levels of conduction electrons is much larger than the life time broadening of the levels. The new method was indispensable to observe the intrinsic relaxation time in copper particles where the electric quadrupole broadening of the nuclear magnetic resonance was huge.

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The dielectric dispersion associated with the ferroelectric phase transition in Li₂Ge₇O₁₅ has been measured in the frequency range from 21 MHz to 7 GHz around the Curie point, T_c=10.4°C. The Debye type dispersion which showed a critical slowing-down of dielectric response was observed, its relaxation frequency being about 1 GHz at T_c. The relation between the observed critical slowing-down and the softening of the optical phonon reported previously is discussed.

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The first order Raman scattering processes due to phonons are considered in a continuum model for t–(CH)_x when there is a nonlinear excitation as a soliton or a polaron. The formulation by Ono and Ito is generalized to incorporate the amplitude mode formalism, proposed by Horovitz and later developed further by Mele and Hicks. The transition amplitudes are calculated for the two states, one with a soliton and the other with a polaron. Difference Raman spectra between these states and the perfectly dimerized state have three prominent dips due to bleaching of extended optical phonons. There is one small peak at the lower shift frequency side of each dip for the soliton. The intensity of the peak is about one tenth of the dip for the system with one soliton over 100 lattice sites. The difference spectrum between the states with and without a polaron has two or three small peaks at the lower shift frequency side. If these small peaks are observable, we should be able to determine whether the photoconduction is carried out by solitons or polarons.

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