Transfer reactions on ⁵²Cr, ⁵³Cr, ⁵⁰Ti and ⁵⁴Fe nuclei induced by ¹⁴N and ¹²C projectiles were studied at energies of 60, 70 and 90 MeV, about two to three times higher than the Coulomb barrier. It is seen from this experiment that energy spectra of emitted particles consist of two parts: the one corresponding to selectivepeaks at low excitation energies and the other a broad bump at higher excitationregion. In sigle nucleon transfer, several peaks were observed in the energy spectrum and the yield of the bump was small, whereas the cross sections of selectivepeaks were very small and the broad bumps were prominently observed in multi-nucleon transfer. In the case of selective peaks on single proton stripping the differential cross sections could be analyzed by DWBA method including recoilcorrection.

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Phase transitions in the hydrogen halide crystal which is composed of an array of linear molecules with nearest neighbor coupling are theoretically investigated by making use of the Frenkel model. The Hamiltonian is a sum of dipolar and quadrupolar interactions. The method of symmetry-breaking potential is applied with the use of an inverse temperature expansion. The results obtained are compared with those of the theory by Krieger and James, who investigated the orientational transitions with no attention to a particular substance by making use of the Pauling model. Depending upon the ratio of the coupling constants, we have a single second order transition, a single first order transition, two successive first order transitions, or a first order transition followed by a second order transition as the temperature lowers. A triple point is found, at which two different types of ordered phases and a disordered phase coexist.

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Spectra of light scattered from MBBA in the nematic phase near the convective instability point are measured using a quasi-elastic light scattering technique. It is observed that, in the polarized scattering one of coupling modes among the viscous made, the relaxation mode of a space charge and the combinational mode of “splay” and “bending” shows a critical slowing down at the instability threshold, while in the depolarized scattering the observed mode is independent of an electric field. The angular dependence of these modes also is measured. These results are found to be in agreement with recent theoretical predictions.

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The adiabatic magnetization is studied on Cu(NO₃)₂·5H₂O under a pulsed magnetic field with various starting temperatures T_i from 4.2 K to 0.4 K. The peak of ∂M⁄∂t around level crossing field H_c gives the indication of the cooling of the spin system. If T_i≥2.0 K, the spin system behaves like a paramagnet showing the nearly symmetric peak around H_c. If T_i≤1.5 K, asymmetic double peaks are observed, which correspond to the appearance of the short range order of the spin system found by van Tol et at. At low temperature limit, T_i<0.7 K, the signals are observed corresponding to the long range ordering. The explanation is given for the observed asymmetric double peaks on the base of the molecular field theory taking account of the higher energy levels.

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Some of the physical properties of the compound MnAs_1−xP_x(x=0.075) are investigated by the various measurements, and they can be divided into four different temperature ranges. The compound is: i) for T>T₂, a high spin state paramagnet with the NiAs type (B8₁), ii) for T₁<T<T₂, a high spin state paramagnet with the MnP type (B31), iii) for T_N<T<T₁, an intermediate spin state paramagnet with the MnP type and iv) for T<T_N, a low spin state antiferromagnet with the MnP type. Especially in the region iii), an interesting phenomenon of a high spin-low spin transition is observed, and characterized by a large change in the lattice constants and the electrical resistivity.

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Spin-lattice relaxation time of the f² ion in the cubic XY₈ cluster, such as U⁴⁺ in ThO₂, is calculated by the nearest-neighbor point charge model.
For the direct process, the ratio of two processes, one with a single- and another with a double-magnetic-quantum transition is a constant, 1 : 7.4. The Raman process relaxation time becomes so short that EPR spectrum is too broad to be observable somewhere between the liquid hydrogen and the liquid nitrogen temperatures. The Orbach relaxation process is absent because the crystal field splitting exceeds the maximum Debye phonon energy in ThO₂. The desirability of low temperature relaxation experiments is stressed.

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Ultrasonic paramagnetic resonance absorption coefficients by f² ions in a cubic field are calculated with special reference to U⁴⁺ in ThO₂. The UPR absorption coefficients at liquid helium temperature are large and comparable in magnitude to those of lanthanide tons with an even number of electrons, however they drop very rapidly with the elevation of temperature. The tetragonal and the trigonal coupling constants, A_o and B_o, in the orbit-lattice interaction Hamiltonian can be determined independently by measuring the absorption coefficients with longitudinal and transverse waves, respectively. The characteristic angular dependences of absorption coefficients are also discussed.

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The atomic positions of protons in water molecules and in methyl radicals have been determined by the angular variation of the proton magnetic resonance spectra at 38 MHz and at 4.2 K. The shift can be fitted by the dipolar interaction between the protons and electron spins which have the spin density of (80±5)% on the copper and (20\mp5)% on the four coordinated oxygens. About 0.03% of the spin density is deduced to be on the protons in the methyl radicals from the isotropic shift. In a temperature range down to 1.3 K, the shift with H_o along the c-axis shows the crystal behaves as a pure paramagnet with a negligible Weiss constant. The possibility of one-dimensional exchange interaction is discussed.

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Parallel pumping and ferromagnetic resonance experiments in (C₄H₉NH₃)₂CuCl₄ at 8.9 GHz and liquid helium temperatures show that in the magnetic field tilted away from the a- and b-axes the spin-wave spectrum splits into two branches and the width of the spin-wave band becomes narrow. These results are understood as follows: the spin-wave frequency of one ab-plane is different from those of the ab-planes immediately above and below because the interlayer exchange interaction is very weak and the adjacent layers are magnetically inequivalent and therefore the exchange and dipolar interactions of the transverse components of the spin precessions between adjacent layers vanish. Quantitative agreement between experiment and spin-wave theory is obtained. Accordingly it can be concluded that the spin-wave spectrum is indeed two-dimensional.

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Measurements of the Mössbauer effect of ⁵⁷Fe in powder and single-crystal absorbers of FeCl₂·4H₂O have been made in a temperature region 0.16–0.18 K, far below its Néel temperature (1.1 K). The unit cell of this salt comprises two inequivalent Fe sites whose environments are related by 180° rotation about the b axis. The Mössbauer effect parameters and the orientations of the EFG principal axes and of the internal magnetic field, relative to the crystalline axes, are determined by computer analysis of the observed spectra. A possibility is pointed out that the EFG major axis and the internal field vector at each site tip out of the a′b plane.

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The internal field H_int at ⁵⁷Fe nuclei in Fe_1−xCr_x alloys has been measured at 4.2 K and 1.7 K in the concentration range 0≤x≤0.96 by means of the Mössbauer effect. In the concentration range 0≤x≤0.93, H_int varies almost linearly with increasing x from the value 340 kOe at x=0 to 120 kOe at x=0.93. As for alloys Fe_0.15Cr_0.85 and Fe_0.13Cr_0.87, the temperature dependence of the internal field has been examined from 300 to 4.2 K. In each of both alloys, the field vs temperature curve shows two plateaus around 40 K and 4 K, having respectively values of 35 and 120 kOe. This suggests that the magnetic moments of Fe in the alloys thermally fluctuate above 30 K, and the observed field of 35 kOe is mainly ascribed to the magnetic moments of Cr ordered in an antiferromagnetic state, while the magnetic moments of Fe become ordered below 30 K, producing the larger internal field of about 120 kOe at 4.2 K.

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Molecular field approximation is applied to a triangular Ising lattice with antiferromagnetic nearest neighbor interaction J and ferromagnetic second neighbor interaction J′ to study the magnetic behavior at finite temperatures. In the range of 0>J′⁄J>−0.8, with increasing temperature the system is found to have a second-order transition from a ferrimagnetic state to an antiferromagnetic state in which one of three sublattices is completely disordered. Another second-order transition occurs in the ferrimagnetic state. Magnetic structure factor, free energy, magnetic specific heat, differential magnetic susceptibility as well as sub-lattice magnetization are calculated numerically with parameter J′⁄J. Critical magnetic field of first-order transition from antiferromagnetic state to ferrimagnetic state is also evaluated. Discussion is given in connection with magnetic ordering in CsCoCl₃ and CsCoBr₃.

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Effects of external magnetic field and orbital degeneracy on the spin fluctuations in weakly ferromagnetic metals are studied based on the recent self-consistently renormalized spin fluctuation theory to obtain expressions for the spin fluctuation contributions to the nuclear magnetic relaxation rate 1/T₁ and the specific heat. By using these expressions and taking account of the orbital relaxation contribution, our experimental data of the temperature and magnetic field dependences of 1/T₁ for ⁹¹Zr in ZrZn₂ are well interpreted and are analysed semi-quantitatively yielding useful informations on the electronic structure of ZrZn₂. The spin fluctuation contribution to the specific heat at low temperatures in ZrZn₂ is also estimated.

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The electrical resistivity and the magnetization were measured from 4.2 K to room temperature in the CsCl-type compounds, Ni_1+xAl_1−x, (Ni_1−yCo_y)_1.04Al_0.96, and (Ni_1−zFe_z)_1.04Al_0.96. The electrical and magnetic anomalies in the pseudo-binary compounds seem to be the Kondo effect due to the substitutional cobalt and iron atoms in the Pauli-paramagnetic NiAl matrix. From this point of view, the Kondo temperatures estimated from the temperature dependence of the excess resistivity and susceptibility are ∼100 K for the former atoms and ∼1 K for the latter ones, respectively. These values are nearly equal to those in the dilute magnetic alloys of copper and gold hosts.

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Nuclear spin lattice relaxation time T₁ of Mn⁵⁵ in βMn metal and alloy with 1% Ge has been measured in a temperature range from 1.2 to 300 K. In pure metal the total relaxation rate is separated into the parts due to electron spin-nuclear spin interaction, 35.3\sqrtT sec⁻¹ and d orbit-nuclear spin interaction, 1.7T sec⁻¹. The alloy with 1.0% Ge shows antiferromagnetism with T_N=6 K. The temperature dependence of T₁ in the alloy is compared with the theoretically expected one. Except near T_N the observed dependence is in good agreement with the theory. The concentration dependence of T_N has been obtained from the peak in 1/T₁ vs T plot.

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Neutron diffraction study was carried out on single crystals of the perovskite oxide SrFeO_3−x(x=0.1). SrFeO_3−x(x=0.1) has a proper screw spin structure with the propagation vector parallel to [111] direction and its Néel temperature is 118 K. The electron configuration of Fe⁴⁺(3d⁴) ion is close to the low-spin state (t_2g⁴) and the oxygen ion has the unpaired electron with the magnetic moment of 0.3μ_B antiparallel to the vector sum of the magnetic moments of two iron ions lying on the neighbouring planes perpendicular to the screw axis. The absolute value of the propagation vector is almost constant, 0.130×√3·2π/a Å⁻¹, at temperatures below 50 K, while it decreases gradually at higher temperatures reaching 0.118×√3·2π/a Å⁻¹ at T_N.

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The density of electronic states have been calculated for liquid mercury based on the perturbation theory by using the non-local energy dependent Evans model potential. The result at 20°C shows a modest dip below the Fermi level. Though a shallow dip is evidently observed at 200°C, there is a tendency for the dip to disappear at higher temperature. This calculation shows that it is important to include the non-locality of the modal potential in liquid mercury.
A good agreement between experiment and calculation was found in the electrical resistivity and thermoelectric power over a wide temperature range.

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The de Haas-van Alphen (dHvA) effect in LaB₆ single crystal has been studied in detail using the field modulation technique. Observed dHvA frequencies in the (010) and (1\bar10) planes range from the order of 10⁶ to 10⁸ gauss. The angular dependence of the dHvA frequencies and the disappearance of the oscillation in some angular regions indicate that the Fermi surface of LaB₆ consists of a multiply connected surface, large pieces of which are centered at the point X (or M) in the simple cubic Brillouin zone. The electron density calculated from the Fermi surface is 1.39×10²² cm⁻³ which corresponds to just one electron per unit cell.

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The Knight shift (K_H) and the spin-lattice relaxation time T₁, of protons have been measured in vanadium-hydrogen alloys (VH_x) with hydrogen concentration x=0.042∼0.736, at temperatures between 100° and 200°C. The resolution of ±1 ppm in the shift was attained by using a high-resolution spectrometer, and the effect of demagnetizing field was isolated by using a single sheet of foil as a specimen. This allowed the simultaneous determination of K_H and the bulk magnetic susceptibility. K_H measured relative to bare protons was found to be negative and change little with hydrogen concentration. No temperature dependence of the shift was observed, even across the phase transition. These results are interpreted in terms of a contact interaction with the uniform spin-polarization in the interstitial region and some additional contributions from H-induced states. An evidence for the electron-electron interaction in VH_x is derived from comparison of K_H and T₁.

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The temperature and impurity concentration dependences of the far-infrared photoconductivity in GaAs crystals have been studied. The small ionization energy of the 2p excited state experimentally estimated is well explained by use of the “cascade capture theory”. The effect of the increase of the impurity concentration on the photoconductive response is ascribed to the decrease of the ability of the electron-transfer of the high excited states. The impurity conduction through the “excited state band” is also discussed.

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A resistivity decrease due to ESR has been observed in the metallic concentration region of P-doped Si at temperatures 1.5–4.2 K. This result is discussed in terms of the spin-dependent transport, the ESR-associated cavity loss effect and the resistivity decrease effect associated with the localized region. The results of the resistivity changes due to ESR and also due to microwave irradiation at off resonance suggest that the localized region plays an important role for these phenomena even in metallic samples of P-doped Si.

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Photoconduction and fluorescence were studied in solid state chlorophyll-a (Chl-a) films which were composed of microcrystals of Chl-a-water adduct. The transient photocurrent, rising without time delay for an exciting flash, decayed with a second order reaction. Two types of response were distinguished in the action spectrum of photocurrent on continuous illumination: One of them corresponded to the absorption of Chl-a molecular crystal, and the other, appearing at longer wavelength (820 nm, 1.51 eV), was ascribed to the direct transition to a conduction band below the first excited singlet state. The thermal band gap of 1.48±0.02 eV was obtained from the activation energy for dark conductivity. The fluorescence of crystalline Chl-a was observed at 794 nm.

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Electronic structures of water and ice are investigated by means of XPS, UPS and VUV absorption spectroscopy. All the bands found in the XPS spectra of ice show a fairly good agreement with the electronic band structure theoretically calculated for cubic ice using molecular tight binding approximation. From the UPS spectra the vacuum level of ice is found at 10.5 eV above the top of the valence band, and a conduction band level of high density of states at 3.5 eV above the vacuum level. In VUV spectra D₂O ice film shows a well separated absorption band at 8.75 eV, whose shape is almost independent of temperature, and it is suggested that ice is essentially a kind of molecular crystal. The absorption coefficients in the tail regions of the fundamental absorption bands of water and ice show nearly exponential dependence on the photon energy, and they seem to be well expressed as the tail of a Gaussian band.

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Using the galvanic cell Cu|CuBr·C₆H₁₂N₄CH₃Br|Cu_2−δVI|Pt, the deviation δ from the stoichiometric composition is varied up to 0.2 for Cu_2−δSe, Cu_2−δS and their alloys. Electronic conductivity, thermoelectric power and Hall coefficient are measured as functions of e.m.f. of the cell, E, and of temperature, T, (20°C∼200°C). The phase diagrams are constructed from these results, especially from E vs T plots, and the electrical properties are interpreted by the use of a simple model. Further, the ionic conductivity is measured with the use of the cell in low temperature phase as well as in high temperature one. The value of E seems not to represent the Fermi kinetic energy even in the high temperature phase having the average structure. This is because of the largeness of δ, and can be interpreted as being due to the screening effect of carriers (holes) on copper ion vacancies.

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Ionic conductivity of LiH crystal has been measured. The energy for Schottky vacancy pair formation (2.3±0.3 eV) and energies of a positive ion vacancy for migration and for the association with a divalent cation impurity (0.54 eV and 0.50 eV, respectively) were obtained from the ionic conductivity curve. The energy for the rotation of a vacancy around divalent cation was 0.38±0.02 eV from the measurements of ionic thermocurrent (ITC). Photoconductivity peaks at 5.05 eV and 6.7 eV are ascribed to the exciton and to the photoemission state, respectively. It is suggested that the defect properties of LiH are similar to those of LiCl and LiF and that the electronic properties are close to those of LiI.

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In addition to the well known intrinsic luminescence at 4.22 eV, two new luminescences at 3.67 and 2.78 eV are found under the excitation in the fundamental absorption bands at low temperatures in undoped NaI crystals. The 2.78 eV luminescence appears under the excitations in the band-to-band transition region and the first exciton absorption band, but the 3.67 eV luminescence appears only under the excitation in the exciton band. Three distinctive exponential decay time components are observed for these new luminescences whose decay times vary with temperature. The intrinsic character of these two luminescences are discussed. In Tl⁺-doped NaI, it is concluded that the energy transfer from free excitons to Tl⁺ ions takes place at low temperatures.

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The symmetry aspect of the dipole interaction in Rochelle salt has been studied for arbitrary wave vector. The Fourier-transformed Lorentz factor matrix is given in a convenient form which reflects well the symmetry of the prototypic space group of P2₁2₁2. The dipole configuration at the X point, corresponding to the basis functions of the two dimensional X representation and applicable to the case of ammonium Rochelle salt, is concretely derived, and the feature of energy splitting at the X point is clarified.

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The dielectric constant of KH₂PO₄ along the ferroelectric axis is measured at 1 kHz between 90 K and 130 K by a thermal noise method by which one can obtain the dielectric constant without applying the external field. The results well agree with the values obtained by the usual bridge method, using the external field of 1 to 20 V/cm, when extrapolation has been made toward zero external field. In the ferroelectric phase, the initial dielectric constants of the multi-domain crystal thus determined are of the order of 10² times as large in magnitude as those of the single domain crystal. It is concluded that the most part of the initial dielectric constants of multi-domain KH₂PO₄ crystal are due to the domain wall motion. A simple model is proposed to give a relation between the domain wall motion and the initial dielectric constant.

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The electrical resistivities of 3d-transition (V and Ti) and 4d-transition solutes (from Y to Ag except for Tc) in liquid tellurium have been measured from the melting temperature to about 850°C. The measured additional resistivities are positive for the “less than half” transition solutes and are negative for the “more than half”. They don’t agree with Friedel theory. The additional resistivities have been explained with the number of the conduction electrons which increases with the addition of the “more than half” transition solutes and decreases with the addition of the “less than half” on the basis of the formation of sp-d mixing near the pseudo-gap. The additional resistivities of transition solutes in liquid tellurium change as a sine function of the number of d-electrons per solute ion.

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Detailed theoretical analysis of non-Ohmic transport of electrons on the liquid ⁴He surface is given. The correct form of the electron-ripplon scattering as well as the electron-⁴He gas scattering is taken into account. A characteristic electric field at which electron mobility deviates from the Ohmic value is estimated as a function of temperature and the holding field on the basis of the electron effective temperature approximation.

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Statistical mechanical expression of the surface tension for molecular fluid including the liquid crystalline phase is formulated. It is applied to the nematic-vapour and nematic-isotropic interface, and the surface tension is calculated using several approximations. A semi-quantitative agreement of the theoretical value with the experimental one is obtained.

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Anisotropy in intensity of fluorescence lines of YAlO₃ : Cr³⁺ single crystal is measured at 77 K. A relation of some of effective Hamiltonian parameters to the optical anisotropy of Cr³⁺ ions doped in a low symmetry crystal such as YAlO₃ is presented. From the intensity ratio of R₁ to R₂ line, we find that two of five effective Hamiltonian parameters, b and λ_z, are −13.6 cm⁻¹ and 13.2 cm⁻¹, respectively.

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A group-theoretical method is developed for the many-beam dynamical theory of the symmetric Laue case. When the incident wave is directed so that the Laue point lies on a symmetric position in the reciprocal lattice, the dispersion matrix in the fundamental equation can be reduced to a block diagonal form. The transformation matrix is composed of column vectors belonging to irreducible representations of the group of the incident wave vector. Without performing reduction, the reduced form of the dispersion matrix is determined from characters of representations. Practical application is made to the case of symmorphic crystals, where general reduced forms and all solvable examples are given in terms of some geometrical factors of reciprocal lattice arrangements.

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X-ray diffraction experiments of a single crystal of magnetite at 84 K were carried out to investigate the crystal symmetry below the transition temperature. A new lattice deformation which makes the crystal symmetry lower than rhombohedral was clarified. The extra reflections which appear in the low temperature phase were observed for the first time with X-ray diffraction. The extinction of (Remark: Graphics omitted.) reflections, which was found by Iizumi and Shirane by means of neutron diffraction, was also confirmed. All the experimental results can be explained reasonably by assuming that the low temperature phase of magnetite has monoclinic symmetry, and the space group is either C_s⁴−Cc or C_2h⁶−C2⁄c.

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The cross sections for the processes: A^(Z_A−1)+(1s)+H(1s)→A^Z_A++e+H, were calculated in the classical binary-encounter approximation (BEA), where the H⁺ and e in H are assumed to separately collide with the ion, and in the plane-wave Born approximation (PWBA), where the contributions due to the stripping reactions by H⁺ and e in the scattering amplitude are superposed. The cross sections are evaluated for the processes which produce H(1s)(σ_A) and those which produce excited and ionized H(σ_B) in the final state. For ions with Z_A≥6, the BEA total cross sections, scaled with respect to Z_A, agree with those (σ_A+σ_B) calculated in the PWBA to within a factor of 1.1 at relative velocities less than 1.5 a.u. and to within a factor of 1.5 up to 10 a.u. In the PWBA approximation, the average excitation energy for atomic hydrogen is introduced in order to evaluate σ_B, while the cross section becomes independent of this energy at sufficiently high incident energies. In the BEA, such an average excitation energy is unnecessary.

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The long-range interaction potentials between He^* (2¹P, 3¹P) and electrons, protons as well as neutral spherically-symmetric atoms are calculated using oscillator strength, the expectation value of r² for He^* and the polarizabilities of the inert gas atoms. The potentials are attractive in the neutral atomic case. They are found to have a strong anisotropy in the case of a point charge, being attractive or repulsive according to the magnetic quantum number of the He^* state.
This information should prove useful in research involving the collision processes of optically-allowed excited He.

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Formation of metastable state molecular ions in electron impact ionization of some atmospheric gases is studied by the neutralization method. In this method, the metastable neutrals produced by neutralization of metastable ions through collision with neutralizer gases are detected with a secondary electron multiplier. The secondary electron currents relative to the primary ion currents are plotted against the energy of ionizing electrons, and called R-curve. Four breaks are found on the R-curves for N₂⁺ at \lesssim16.5, 20.9, 22.2 and 23.1 eV. The first one corresponds to N₂⁺(A ²Π_u)_v=0.1 and/or (X ²Σ_g⁺)_v=1∼5. The latter three correspond to the quartet states following ⁴Σ_g⁺. Three breaks are found for CO⁺ at 16.5, 20.1 and 21.8 eV. Two breaks are found for O₂⁺ at 16.5 and 25.5 eV, the former corresponding to O₂⁺(a ⁴Π_u). One break is found for NO⁺ at 16.5 eV corresponding to NO⁺(a ³Σ⁺).

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Self-consistent stationary solutions for the envelope of Langmuir waves, the ion density perturbation and the ion distribution function are obtained for a one-dimensional unmagnetized plasma. Allowance for trapped ions yields an arbitrariness for the shape of the solutions. Two special solutions are obtained: one is an envelope solitary wave in which the width is decreased due to the trapped ions compared with the case obtained by the fluid theory, and the other is an envelope shock in which the density jump is determined only by the shock width and is independent of the Langmuir wave amplitude; the propagation velocity is decreased due to the effect of trapped ions.

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A nonlinear theory of the collisionless drift wave is developed in a planner geometry with an arbitrary one-dimensional density profile. An equation describing the potential variation in the direction of density gradient is derived. The dispersion relation and the corresponding waveform are obtained from solutions of an eigenvalue problem. A special density profile is analyzed in detail. It is shown that the drift wave is localized in the x-direction and also has a solitary wave structure in the y-z plane, which is described by a modified Korteweg-de Vries equation.

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Kink instabilities in a screw pinch with a circular cross-section are studied in a toroidal geometry for β_p∼ε^−1⁄2 and q(a)∼1, where ε is an inverse aspect ratio and q(a) is a safety factor at a plasma surface r=a. The constant-pitch force-free field surrounding a main plasma improves MHD stability, compared with a high β tokamak. However, it is necessary to satisfy the Kruskal-Shafranov limit, in order to ensure stable discharges in the toroidal geometry.

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A possible modification to the well known Clemmow-Mullaly-Allis diagram is analyzed by taking into account the ponderomotive force due to a large-amplitude electromagnetic field in magnetoplasmas. We restrict our attention here to the propagations parallel (the right- and left-hand circularly polarized waves) and/or perpendicular (the ordinary and extraordinary modes) to the static magnetic field. Simple expressions are obtained for the cut-off conditions of the waves except for the extraordinary mode. In the latter case, the cut-off condition is calculated numerically by solving an integral equation. The cut-off lines are shown to move towards the higher densities with increasing wave amplitude.

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When the ion beam-plasma system is stimulated by a pump field with frequency f₀ near the ion Langmuir frequency f_pi, the ion sound wave (f_s) is enhanced and, at the same time, a new wave (f_b) corresponding to the slow wave of the beam appears, and among their frequencies, the resonant condition, f_b=f_pi+f_s, is satisfied. The resonant condition for the wave numbers, k_b=k_pi+k_s, is ascertained by a test wave method. The test wave grows temporally at the frequencies coinciding with the frequencies of f_b and f_pi and, at the same time, the wave with the frequency of f_b−f_pi=f_s grows also temporally. Their growing is affected by an ion beam energy, an initial intensity of the pump field and its frequency. These phenomena will be discussed with a nonlinear theory of the explosive instability for the coherent three-wave interaction.

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Stationary one-dimensional propagation of Langmuir waves trapped in a local density cavity in a plasma is investigated for the case in which the frequency spectrum of the Langmuir waves is broad as compared with the ion acoustic frequency, but in which their wavenumbers are comparable to the inverse scale length of the density cavity. Analytical solutions for the density cavity, which traps many Langmuir wave modes and which is self-consistent with the ponderomotive potential coming from these eigenmodes, are obtained. The Langmuir wave envelopes exhibit oscillations at the beat frequencies of the different eigenmodes. These solutions are valid when the intensity of the trapped Langmuir waves normalized by the electron thermal energy is much greater than the electron-to-ion mass ratio.

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A two-dimensional viscous flow induced by sinusoidal wavy motion of an infinite wall is considered for Reynolds numbers which are of the order of magnitude both less and greater than unity. It is found that the induced mean steady flow is proportional to the ratio 4π²a²⁄L²(a⁄L<<1), where a and L are the amplitude and the wavelength of the wavy wall, respectively. It is also found that the steady flow velocity approaches to a constant value in the form of damped oscillation with respect to the distance from the wall.

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A theoretical study is made of the slow motion of a small sphere in an incompressible viscous fluid in a wedge-shaped domain bounded by two plane walls. Forces and torques experienced by the sphere which is translating in any direction without rotation on and across the bisector of the wedge are calculated up to the first-order effect of the boundary on the basis of the Stokes equations.

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Contribution of the second order terms in the reductive perturbation theory has been investigated for the nonlinear shallow water waves. The fundamental equations are reduced to a coupled set of the Korteweg-de Vries equation for the first order horizontal velocity and a linear inhomogeneous equation for the second order arbitrary function. Structure of the coupled set of equations turns out to be the same as in the case of nonlinear ion acoustic wave. A steady state solution of the coupled set of equations has been examined in comparison with Laiton’s analysis of the second order contribution of the Friedrich’s expansion for the nonlinear shallow water waves.

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The steady flow which is induced by the slow rotation of a solid sphere immersed in an infinite incompressible viscous fluid is studied, on the basis of the Navier-Stokes equations. The solution is obtained in the form of power series with respect to the Reynolds number R. By delegating the routine operations to a digital computer, the expansion is proceeded to the order of R¹⁴, in which convergence is found up to about R=12. The vorticity distribution, the pressure and the skin-friction on the sphere surface are displayed, and some flow properties are discussed.

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The axisymmetric steady flow of an infinite or cylindrically bounded, inviscid, compressible fluid is investigated assuming that the magnetic Reynolds number and the interaction parameter are small. For the unbounded flow the radial velocity alone is evaluated with reference to the potential theory. For the channel flow, the solutions are obtained using the finite Hankel transform and they consist of two parts, namely, the convolution integral term and the magnetic field integral term. In the subsonic case, the first term is negligible because of its exponential damping so that the flow field is explicitly determined by the magnetic field applied. In the supersonic case, the first term is rather dominant and periodic so that the flow field remains oscillatory to infinity downstream. This oscillatory behavior results from the existence of discontinuity (Mach cones or lines) continuing by reflection off the wall of the cylinder.

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Equations for an irreversible nonlinear network, which is equivalent to Volterra’s competition equations, are solved by the inverse scattering method. The duality satisfied by the equations play an essential role not only in formulating the inverse method but also in finding solutions. N-soliton solutions obtained are in agreement with Hirota and Satsuma’s. The relation to N-soliton solutions of the Toda lattice is given explicitly.

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Direct observation of the critical slowing down has been made for the first time in the magnetic system by AC susceptibility measurement in Mn(CH₃COO)₂·4H₂O.
We have found a dip in the real part of the susceptibility along the easy axis just at T_N, 3.18 K, in the frequency range from 180 MHz to 350 MHz.

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