We examine the stability of solid-solid interfaces when the shear modulus is slightly different in two phases. In a deep quench condition, the elastic energy is minimized when harder regions are elastically isotropic. As simple examples, we derive dynamic equations for disturbances on spherical interfaces of a growing precipitate as well as on planar surfaces separating two uniaxially deformed phases. They show how the Mullins-Sekerka instability is modified by the elastic misfit. A new instability is predicted in the planar interface case.

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A simple formula is presented for the lateral velocity v of a small sphere of radius r₀ sedimenting with a velocity U in a viscous fluid at a distance l from a vertical cylindrical wall on the assumption that κ=r₀⁄l<<1, Re=Ul⁄ν<<1 and ε=l⁄r<<1. Here r is the radius of curvature at the nearest wall from the particle. We have v=U=(3⁄32)κRe(1+(1⁄4)ε+O(ε²)) for the normal velocity leaving off the wall, where ε should be negative if the wall is convex to the fluid.

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High-frequency, high-power microwave radiations by a virtual cathode oscillator have been observed using the “point pinch diode” which can produce a high electron beam density. The peak power of microwave pulses is typically 350 MW in the frequency region of 20–22 GHz. The radiation frequency increases almost linearly from 20 to 35 GHz with decreasing anode-cathode gap spacing. The mechanism for microwave emission is ascribed to the oscillation of the virtual cathode.

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The effects of simple shear flow on concentration fluctuations in polymer solutions are investigated as a function of S, T, c, and N by the flow light scattering method. Here, S is the shear rate, T the temperature, c the polymer concentration, and N the degree of polymerization of the polymer. Over the range of the concentration studied in this experiment (a semidilute regime covering c⁄c^*=4 to 20, where c^* is the overlap concentration), strong shear-enhanced concentration fluctuations were observed above a certain critical shear rate S_c. For S>S_c, the integrated scattered intensity (Remark: Graphics omitted.) in the direction perpendicular to the flow increases at least by two orders of magnitude compared to that of the homogeneous solution. The scattering patterns observed for S>S_c have two main chracteristics: (i) they are very diffuse, extending up to high scattering vectors and (ii) they have a sharp and strong destructive interference in the direction perpendicular to the flow.

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We have studied the propagation properties of a focused acoustic beam in superfluid ⁴He at 300 mK under several pressures and observed new nonlinear phenomena under pressures higher than 18 atm. Under these high pressures (normal dispersion region), the received power is increased in proportion to the power input for the low-power region, but it is depleted rapidly after the saturation for higher power input. It exhibits several sharp dips for further increased power. This nonlinear phenomenon is a completely new one, so there is as yet no explanatory theory. We propose a possible mechanism to explain it which consists of two nonlinear processes.

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Transmission gaps were found in third-sound waves propagating on a periodic substrate which was a glass plate with aluminum strips arrayed on its surface. Experimental results agreed with Condat and Kirkpatrick’s theory [Phys. Rev. B32 (1985) 4392]. Third-sound scattering from a boundary of two different materials were confirmed experimentally for the first time. This will offer a new experimental opportunity to study modern wave phenomena such as “wave localization”.

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Transmission spectra were experimentally studied in third sound that was propagated through a Fibonacci lattice. Thin aluminum films were used to configure the Fibonacci lattice on a glass substrate. Many dips were observed in the spectrum and such structures as self-similarity and nesting were experimentally confirmed. A quantitative analysis of the dip positions was given.

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The two-dimensional Hubbard model has been studied in the region of low electron density based on the t-matrix approximation. This can take proper account of the singular behaviors of the forward scattering whose importance was indicated by Anderson. By performing first the angular integrations in the irreducible particle-particle correlation function, we can prove analytically that all of the poles of the t-matrix lie on the real axis. Hence the t-matrix and then the self-energy of the retarded Green function, Σ(k, z), are analytic in the upper half-plane of the energy variable, z. This, together with Im Σ(k_F, ε+iδ)∝ε² ln |ε|, leads to the conclusion that the electrons described by the two-dimensional Hubbard model are Fermi liquid, at least in the region of low electron density.

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The random exchange potential at the interfaces between magnetic and nonmagnetic layers is proposed to be an origin of the giant magnetoresistance in metallic superlattices. The material dependence of the potential is calculated for transition metal elements. An analysis using the Boltzmann equation shows that the theoretical results of the potential explain the giant magnetoresistance observed.

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Cooper pairing in two dimensions is discussed with emphasis on the effect of the mode-mode coupling of the pair fluctuations. Extending the Nozières and Schmitt-Rink theory so as to take into account the repulsion among pair fluctuations, the transition temperature T_c and the chemical potential μ are determined self-consistently, giving the solution T_c=0 and μ\simeqε_F in the limit of weak attraction among constituent fermions. It is essential to take into account the screening effect of the long-range repulsive interaction among the pair fluctuations.

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The uniaxial stress effect on the superconductivity of grain-aligned samples of La_2−xSr_xCuO₄ prepared by a “magnetic-field-induced alignment” method has been investigated. The T_c decreases with increasing uniaxial stress along the “c-axis”. The result indicates that the in-plane O–O or Cu–O bond length should significantly affect its superconductivity.

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Magnetic inelastic scattering of neutrons from a Heisenberg magnet RbMn_0.15Mg_0.85F₃, whose Mn concentration is far below the percolation threshold, has been studied. The observed incoherent inelastics spectrum reveals five peaks which correspond to the intracluster transition energies of isolated two-spin cluster.

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We investigate the S=1 bilinear-biquadratic model. In some region, the trimerized variational state is a good candidate for the ground state. This explains why the Sutherland model (J₁>0 and J₂⁄J₁=−1) has soft modes at q=0, ±2π⁄3. Moreover, the full phase diagram of this model is discussed. It is found that at the pure biquadratic ferromagnetic point, the ground state is extremely degenerate.

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Neutron scattering shows that two magnetic phase transitions occur in the triangular lattice antiferromagnet RbNiCl₃, in which only one phase transition has been observed. Ordering of magnetic moments parallel and perpendicular to the c-axis occurs at 11.25 K and 11.11 K, respectively, as commonly seen in Ising-like Heisenberg antiferromagnets on triangular lattices. The β exponents of the parallel and perpendicular sublattice magnetizations are precisely determined to be β_⁄⁄=0.27±0.01 and β_⊥=0.28±0.01. They do not correspond to the theoretical prediction β_⁄⁄=β_⊥=0.345 supporting the three-dimensional XY universality, which suggests that the observed β exponents are modified by a crossover effect from either the three-dimensional SO(3) universality or the three-dimensional S₁×S₁ one.

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In an amorphous CeCu₆ alloy, the electronic specific coefficient increases with the decrease in temperature, T, indicating the electron-mass-enhancement at low temperatures. With decreasing T, however, the magnetic susceptibility obeys the Curie law down to 4.2 K and the electrical resistivity increases gradually below 250 K and markedly below 25 K. These results imply that the random atomic configuration of Cu and Ce suppresses the occurence of the singlet state and/or the magnetic ordering and masks the Fermi liquid degeneracy of 4f electrons.

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Cu-NMR measurements have been performed on oxidized and reduced Nd_2−xCe_xCuO_y (0.10<x<0.18, y∼4). The electric field gradient at the Cu site was found to be quite small compared to Nd₂CuO₄, suggesting that the local electronic state of the Cu site changes drastically with carrier doping, in contrast to the hole-doped systems. A magnetically ordered state was observed in the metalliclike Nd_1.85Ce_0.15CuO_y (oxidized) specimen. The atomic hyperfine field in this ordered state was found to be rather small compared to those of the parent compound of cuprate superconductors. This indicates a small hyperfine coupling constant or the reduction of the averaged spin moment in the metalliclike specimen.

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The effects of uniaxial stress σ_yy on the incommensurate (INC) phase transition of quartz have been investigated by light scattering spectroscopy. The 1q INC phase is induced between β and the 3q INC phase and its region becomes wider with the increase of stress. Anomalies of the central peak in the Rayleigh-Brillouin spectra are observed at three temperatures, corresponding to T_i1 (β to 1q INC phase), T_i3 (1q to 3q INC phase) and T_c (3q to α phase). Only at T_i1, is the central peak found to have a dynamical component.

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It is shown that a higher-order nonlinear Schrödinger equation which describes propagation of pulses in optical fiber is solvable by means of the inverse scattering transform. The soliton solution possesses a remarkable property that it can propagate steadily with two peaks of the same height.

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The survival probability σ(A) is studied for the one-dimensional contact process. An approximate function h⁽³⁾(A) for σ(A) is obtained; a partial stationary condition is used to determine h⁽³⁾(C_i) for small sets C_i’s and then it is extended to all finite subsets A of Z¹ by the Markov extension. It is proved that h⁽³⁾(A) gives an upper bound for σ(A) in the parameter region where the infection rate λ is greater than Griffeath’s lower bound for λ_c, i.e. (Remark: Graphics omitted.). The present result improves previous upper bounds.

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Upper bounds for order parameters are studied for the d-dimensional contact processes by using the Harris-FKG inequality. Particularly, in the one-dimensional system, it is proved that our improved upper bound ρ_1,λ⁽⁴⁾ is less than Griffeath’s bound for λ≥λ_c(1).

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In spin models exhibiting a transition between a low temperature phase with long range chiral order and a high temperature phase without such order, the thermal expectation value of the square of the fluctuation in the chiral order parameter is expected to diverge at the transition temperature. For the spin-1/2 XY antiferromagnet on the triangular lattice a space-type graph high temperature expansion is developed for the fluctuation in the square of the vector chirality operator. Padé approximant analysis of the first six terms of the series yields a pair of complex conjugate poles in the complex K=1⁄kT plane, but provides no evidence for a phase transition indicated by a singularity on the real K axis.

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It is shown that the Lee-Yang Ising system with an imaginary magnetic field βH=h=iπ⁄2 on the square lattice is equivalent to Villain’s fully-frustrated Ising systems. Thus, the present paper unifies the two streams of investigation on Lee-Yang complex-field systems and frustrated Ising systems. This observation suggests a new possibility to study frustrated systems using the corresponding equivalent Lee-Yang complex-field systems. An algebraic approach to dual transformations is given using the quantum σ−τ transformation.

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Diffraction-free beams of light have recently been studied by quite a few authors using the Helmholtz equation. The scalar theory of diffraction, however, is not a good approximation when the beam size is comparable to the wavelength. In this paper, Maxwell’s equations are solved exactly to obtain the vectorial components of the diffraction-free beam. Solutions for the plane-polarized-electric (or magnetic) waves, and the TE (or TM) modes are given and their relations are discusssed. The exact solution shows that the diffraction-free beam should have longitudinal components of the electric and/or magnetic fields and that no mode has the exact J₀ intensity distribution. Relation to the non-transverse cylindrically symmetric wave with parallel electric and magnetic fields is also found.

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Linear stability theory is applied to the problem of the stability of natural convection that occurs in an inclined fluid layer with uniformly distributed internal heat sources. It is assumed that one bounding plate is a thermally perfect insulator and the other bounding plate is maintained at constant temperature. The power series method is used to obtain the eigenvalue equation which is then solved numerically with the aid of the Muller method. The stability conditions are obtained for Prandtl numbers ranging from 0.001 to 100 and for angles of inclination ranging from −90° to 90°. It is found that the instability sets in as either transverse travelling wave modes or longitudinal stationary modes and that three-dimensional disturbances are not responsible for instability.

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A new complete set of equations for magnetic fluids is derived using the thermodynamical method and micropolar theory. The present constitutive equations, which take consideration of both viscoelasticity and internal freedom, satisfy the principle of material frame indifference. It is shown that the constitutive equations of magnetization is related to the magnetic field, its change in time and angular velocity of suspended particles. Furthermore, it is made clear that the electromagnetic pressure is independent of the dissipative parts of the magnetization and the electric polarization.

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The probability distribution of the sum of n independent random variables with finite mean and finite variance does not generally approach the normal distribution with variance proportional to n, contrary to the log-normal theory of turbulence in which the central limit theorem is applied in an easy manner. Although the expectations of all the moments of the sum agree with those of the limiting normal distribution in the leading order for n>>1, the moments of the exponential of the sum do not. Thus the log-normal theory is not so robust as expected from the generality of the central limit theorem.

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A non-quasi-neutral theory of the positive column of a glow discharge has been presented, on the basis of the analysis of the transition from free to ambipolar diffusion of electrons. In order to facilitate the understanding, the usual ambipolar diffusion theory owing to Schottky has been modified. According to the present theory, the electron temperature or the axial electric field has varied with not only p₀R (p₀: the pressure, R: the tube radius) but the electron density or the discharge current, which has never been obtained by the original quasi-neutral theory. Additionally, the condition under which the quasi-neutrality becomes valid has been given in terms of various parameters in weakly ionized gases.

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l=2 torsatrons are studied to improve the high energy trapped particle confinement with additional l=1 and/or l=3 helical coils. The winding laws are selected in two ways. One is to realize ‘σ-optimization’ by the additional helical coils, but this approach loses magnetic well region. The other selection is to produce or deepen the magnetic well by the additional helical coils. l=3 helical coils are usable to this end. In this case the improvement of the trapped particle confinement depends on magnetic axis position. Radial electric field producing sheared rotational motion is also considered to improve the trapped particle confinement in a standard l=2 torsatron. By excluding cancellation between E×B and ∇B drift motion occurred for the parabolic potential profile, all deeply trapped particles can be confined in the central region. Degradation of the trapped particle confinement by the Shafranov shift is mitigated by shifting the magnetic axis inside in the vacuum configuration.

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The stability of the spheromak against low n (n=1, 2, 3, 4, 5) and localized modes is investigated by use of ERATO-J code and by means of the Mercier criterion. Here n is the toroidal mode number. The shape of the plasma is assumed to simulate the experimental plasma in the flux conserver of CTCC-II at Osaka University. The beta limits for these modes are evaluated as a function of q_axis to elucidate which mode gives a lower limit. Here q_axis is the value of the safety factor on the magnetic axis. As a result, the beta limit of the spheromak is shown to be determined by the n=1, the n=2 and the localized modes. However, the Mercier criterion is shown to give an excellent measure for the stability against internal modes, if q_axis≤0.9.

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The velocity space diffusion equation which describes distortion of the velocity distribution function due to nonlinear Landau and cyclotron damping of electrostatic waves in a homogeneous magnetized plasma is derived from the Vlasov-Maxwell equations by perturbation theory. No restrictions are imposed on propagation angle to a uniform magnetic field, Larmor radius, frequencies, or wave numbers. The conservation laws for total energy and momentum densities of waves and particles are shown, and the time evolutions for energy and momentum densities of particles are given by means of nonlinear wave-particle coupling coefficient in kinetic wave equation. Further, the matrix elements in the limit of parallel or perpendicular propagation to a magnetic field and their various applications are given.

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The crystal structure of the mixed crystal K_0.77(NH₄)_0.23H₂PO₄ has been investigated at four temperatures between 90 K and 293 K by means of X-ray diffraction with particular interest to the temperature dependence of thermal parameters. It is revealed that thermal parameters U₁₁’s for K, P and O atoms deviate from the line to be in proportion to absolute temperature around at 110 K. The anomalies in U₁₁’s are understood as the result of random and static displacements of K, P and O atoms.

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We have measured elastic compliances for the elongation for several orientations by the composite-bar resonator method over a range of temperature from room temperature to −130°C including the upper phase transition (T_c=−79°C) and have obtained elastic compliances s₁₁, s₂₂, s₃₃, s₄₄+2s₂₃, s₅₅+2s₁₃, s₆₆+2s₁₂, s₁₅ and s₃₅. Elastic anomalies at the upper phase transition and characteristics of the phase transition are phenomenologically discussed based on the irreducible representations T7 at the point k₈=(b₁+b₃)⁄2 of the space group C_2h⁵.

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A series of spin-cluster approximation which is a mean field type approximation is derived systematically on the basis of a spin-cluster expansion formula of the free energy. Mean field critical temperature and mean field critical coefficients are calculated by the spin-cluster approximation for the two-, three- and more than four-dimensional ferromagnetic Ising systems. Analyzing them by the coherent anomaly method, the critical temperature and the critical exponents α, β, γ and δ are estimated. Accuracy of estimated values in this method are comparable to those given by other methods such as the high temperature series analysis. The present theory provides a new and useful tool to study the critical phenomena, especially of three-dimensional systems.

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The mean lifetimes of positrons in 4,4′-n-octyloxycyanobiphenyl and p-decyloxybenzylidene p′-amino 2-methyl butyl cinnamate were measured. The measurements of magnetic susceptibility and differential scanning calorimetry were also carried out to study the influence of molecular order and phase transition on the mean lifetime of positrons. The poistron lifetime spectra consist of two components. The mean lifetimes of the shortlived and the longlived components in these liquid crystals increase abruptly at the solid-smectic transition. It seems that the change in the shortlived component at the mesomorphic phase transitions depends on the magnitude of transition enthalpy. The longlived component shows a maximum in the smectic A phase. The maximum mean lifetime of the longlived component in the smectic A may be related to the size of defects in the well-defined fluid regions.

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The Heisenberg antiferromagnet with both the nearest neighbor and the next nearest neighbor interactions is studied in two and three dimensions. The spin wave excitation spectrum is obtained based on the general four sublattice mean field ground state in the region where the next nearest neighbor interactions prevail. It is shown that the continuous degeneracy of the mean field ground state is lifted by the zero-point spin wave fluctuations and the “strip” state with collinear spin ordering is stabilized.

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The investigations of dilatometry and X-ray diffraction for the polycrystalline of (Ag_xCu_1−x)Br in the composition range 0.3≤x≤1.0 have been carried out. An abrupt increase of lattice constant a₀ was observed at about 230°C and the composition dependence of a₀’s showed considerable deviations from the Vegard’s law. The observed anomalous expansion of the lattice was caused due to the occupation of Cu⁺ ions at the interstitial sites which possess relatively small cavity. It is considered that the lattice expansion enables even Ag⁺ ions having larger ionic radius to migrate to the interstitial sites. The disordered distribution of cations is the reason of high ionic conductivity in the mixed crystals of silver and cuprous bromides.

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We study the dynamical properties of the degenerate impurity Anderson model, obtain rigorous expressions of the single particle density of states, the dynamical spin susceptibility and the dynamical charge susceptibility of the localized electron in the limit of the large orbital degeneracy and discuss the results compared with the phenomena observed in the heavy electron systems and the CuO₂-high-T_c superconducting materials, suggesting a possibility that the localized charge fluctuation may play a crucial role to obtain the high-T_c superconductivity.

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We have measured the magnetoresistance and the de Haas-van Alphen (dHvA) effect in LaIn₃. The magnetoresistance increases in the all field directions, indicating that this material is a compensated metal without open orbits. About ten dHvA branches have been detected in the frequency range of 9.5×10⁵ Oe to 7×10⁷ Oe, which are almost explained by the APW band calculation done by Hasegawa.

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Taking quasi-two dimensional nature of the carrier distribution, the critical superconduting current in the accumulation layer formed on Si-superconducting transistor is calculated in the dirty limit as a function of surface carrier concentration. The caluculated result reproduces the tendency of the gate voltage dependence of the critical current observed by Nishino et al.

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The nuclear spin lattice relaxation rate, T₁⁻¹, for ⁶³Cu in zero field from 8 K down to 0.3 K, has been measured in Nb–Cu multilayered thin films where both the Nb- and Cu-layer thicknesses are much smaller compared to the coherence lengths. A BCS-like temperature dependence of T₁⁻¹ replaced gradually by a Korringa-law-like one at low temperatures has been found. A dependence of the relaxation on the Cu-layer thickness at low temperatures has also been found. It has been proposed and confirmed by a series of experiments that superconductivity in the Cu-layer induced by the proximity effect has an anisotropic energy gap, reflecting the geometrical feature of a thin film.

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The nearest-neighbor XY spin glasses with ±J distribution of interactions are studied in both two and three dimensions by use of the domain-wall renormalization group method at zero temperature, with a focus on the chiral ordering. In two dimensions, both the chiral and XY-spin orientational components are found to order at zero temperature with mutually different correlation-length exponents ν\simeq1.2 and ν_k\gtrsim2.6, respectively. In three dimensions, by contrast, we find that the system exhibits a finite-temperature chiral spin-glass ordering accompanied with a broken reflection symmetry with orientational symmetry preserved, whereas the conventional orientational spin-glass ordering occurs only at zero temperature.

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Two-dimensional spin-1/2 antiferromagnetic Heisenberg model on a triangular lattice is investigated by a mean field theory. The spin is expressed by Schwinger bosons, and order parameters corresponding to the resonating valence bond (RVB) state is retained. Due to the frustration built in the model, the ground state of this model has not been clarified. In the present method the lowest energy solution has a long range order at T=0, which corresponds to the classical 120° structure. Other self-consistent solutions, including that which has no long range order, are also found. Properties of these solutions are examined.

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EPR measurements of Mn²⁺ ions at the orthorhombic substitutional site in MgF₂ have been made at 4.2 K with 34 GHz-band and at 300 K with 9 GHz-band microwaves. The spin-Hamiltonian parameters have been determined unambiguously relative to the ligand octahedron by observing the associated ligand fluorine-ENDOR transitions. The principal z axis with the maximum component of the 2nd-rank fine structure tensor D has been found to be along the [110] direction in the (1\bar10) plane which contains Mn²⁺ and four equatorial ligand-F⁻ ions. Apically-compressed configurations of ligand octahedra in MgF₂: Mn²⁺ and ZnF₂:Mn²⁺ have been confirmed by the analyses of ligand-hyperfine parameters.

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Temperature dependence of the g value, linewidth and peak height of the conduction electron spin resonance in silver has been studied with the static magnetic field parallel to the sample surface at the frequency of 22.7 GHz and in temperature 2.0–38 K. The temperature variation of the g value has been consistent with the previous study under the perpendicular magnetic field. The linewidth in the parallel field has been slightly broader than the perpendicular linewidth, indicating a temperature-independent surface effect due to extra relaxation at the sample edge.

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We reconsider the possibility of the existence of the acoustic plasmon using a simple model. The previously employed models for the prediction of the acoustic plasmon assume that two overlapping conduction bands with light and heavy masses independently give an electron-gas like form of the dielectric response function. The new model takes account of the complete mixing of the two conduction bands and assumes an approximate form of the dielectric response function which has a contribution from both interband and intraband transitions, involving a few adjustable parameters describing the relative intensities and positions of the two transitions. It is found that in the strict sense of the terminology the acoustic plasmon does not exist in the limit of small wavenumbers, but the optical plasmon of the conduction electrons can be reduced to one tenth of its original value estimated from the density of the conduction electrons under the influence of the interband transition.

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Optical absorption spectra of RbI, RbBr and KBr crystals containing MnO₄⁻ or MnO₄²⁻ ions and effects of the uv-light irradiation on these crystals have been investigated. Several absorption bands and some vibronic structures are observed in the visible and uv regions. Assignments of electronic transitions are given to these absorption bands. Depending upon the formation process of MnO₄²⁻ ions, absorption spectra due to these ions show some differences, which are interpreted by location of anion vacancies near MnO₄²⁻ ions. Formation of V_K centers by the uv-light irradiation at low temperature is confirmed in the quenched RbI:MnO₄²⁻ and in the RbI:MnO₄⁻, RbBr:MnO₄⁻ and KBr:MnO₄⁻. The V_K-center formation is explained by an intra-molecular charge-transfer transition in the crystals containing MnO₄⁻ ions, and probably by an excitation in the exciton-band tail in the crystals containing MnO₄²⁻ ions.

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X-ray Raman profiles were calculated for solid lithium on the KKR method. The narrow energy range of 30 eV above the threshold was investigated intensively. The lifetime broadening due to the excited electrons was also considered. In contrast with the K X-ray absorption spectrum, we have successfully performed a quantitative comparison between the theoretical X-ray Raman profiles and the experimental profiles in the absolute scale and also the information on the momentum dependence has been obtained. With respect to the energy positions of the significant fine structures, we have achieved a good agreement with the experiment, especially in the energy range extending to about 5 eV above the threshold.

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The core-level and the 4f-valence electron photoemission spectra of CeSb are analyzed considering the screening by both the 5d and the 4f-electron. The calculation is done based on the cluster model. The screening by the 5d-electron leads to the energy dependent reduction of the mixing value between the 4f and the band-electrons. As a direct evidence of the dynamical screening by the 5d-electron, a satellite is expected at about 10 eV higher binding energy than the main peak with about a half of intensity for the main peak. This satellite corresponds to the p-d anti-bonding state and explains the peak seen in the experiment which has been attributed to the plasmon side band. Similar satellite is expected also in the core-level XPS of the Sb site.

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Fluorescence spectra have been measured in Ca(PO₃)₂:Eu³⁺ at 77 K under dye laser excitation at various energies within the absorption lines due to the transitions ⁷F₀, ⁷F₁−⁵D₀, ⁵D₁. It has been found that the ⁵D₀−⁷F₀ transition probability and the mean energy of the three ⁵D₀−⁷F₁ lines are linearly correlated with the energy of the ⁵D₀−⁷F₀ line, and also that this energy is quadratically correlated with the transition energy between ⁵D₀ and the lowest level of ⁷F₁. These results are interpreted in terms that the spreads of these energies and the transition probability are due to the site-to-site variation in the second-order crystal-field parameter. Further, the forbidden ⁵D₀−⁷F₀ transition is concluded to be allowed by the borrowing of the intensity from the ⁵D₀−⁷F₂ (M_J=0) line through the J-mixing. Using polarization characteristics of fluorescence, whether the lines are due to the electric or magnetic dipole transition is determined and the Stark levels of the ⁷F₁ and ⁵D₁ manifolds are assigned. It is also shown that the point symmetry of the Eu³⁺ site is C_2V or C₂.

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The laser-induced fluorescence spectra of Eu³⁺ in Ca(PO₃)₂ glass are analyzed in detail. It is shown that the site-to-site variation of the energies of several levels of Eu³⁺ is expressed using the second-order crystal-field parameters B₂₀ and |B_2±2|. From the analysis of the spectral shape of the laser-induced fluorescence lines, the distributions of the above two parameters are determined. The fluorescence linewidth has been found to be very different for the lines to excite. This is explained by the difference in the dependence of the energies of the levels concerned on the crystal-field strength. The inhomogeneously broadened lineshape of the ⁵D₀−⁷F₀ fluorescence excited by the broad-band ultraviolet light is shown to be reproduced by assuming Gaussian distributions of the crystal-field parameters.

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