The direct measurement of the attenuation length for an individual EAS through 200 g/cm² water has been made at Mt. Norikura (2770 m a.s.l.) from 1964 to 1968. The mean value of the observed attenuation length (120±20 g/cm²) in the interval of the size (10⁶>N≥10⁵) is less than the values which were estimated from the absorption length of the counting rate of EAS.
The attenuation length observed was sensitive to the age parameter and there was a difference between the age parameter estimated from the lateral structure (S_lateral) and that from the attenuation of EAS (S_longitudinal) as expressed by the following formula;
S_longitudinal=S_lateral+(0.5∼0.8).
The mutual dependence among various parameters (attenuation length, age parameter, size and core structure) led to the following results; (i) Large inelasticity of about 0.7 at E=10¹⁴ eV, (ii) The frequent large transverse momentum interactions and (iii) The change of the nuclear interaction mechanism at 10¹⁴ eV.

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Measurements of the photofission cross section, fragment angular distribution and fragment single kinetic energy distribution for ²³⁸U and ²³²Th over an energy range from 200 MeV to 1150 MeV are described. Semiconductor detectros were used for the measurements. It is found from a photon difference method that the photofission cross section shows a resonance at a photon energy of about 330 MeV and 350 MeV with a peak value of ∼120 mb and ∼40 mb for U and Th respectively. It is evident that this resonance can be attributed to the well known (3, 3) resonance in the pion photoproduction from a free nucleon. Furthermore, the result of the photofission cross section measurements was analyzed, by assuming that nuclear excitation resulting from the reabsorption of the created pions and the quasi-deuteron absorption within a nucleus induces the photofission in the heavy nucleus. From this analysis it is shown that these assumptions explain qualitatively the general properties of the photofission in the energy region studied. The fragment single kinetic energy distribution seems to be consistent with this conclusion. A preliminary result for the fragment angular distribution is shown.

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Bata-gamma angular correlations and beta spectra of the first forbidden beta transitions of ¹²²Sb have been studied. The result of the angular correlation measurement of the (734 keV β, 1256 keV γ) cascade indicates deviation from the ξ approximation for the 734 keV β transition. The analysis using exact electron radial wave functions which include finite nuclear size corrections shows that cancellation exists among the matrix elements. Thus, the ξ approximation is not fulfilled. The nuclear matrix parameters fitted to the angular correlation data are x=0.34±0.44, u=2.03±0.96, y′=25.0±13.8, w=1.63±4.94 and v′=−18.4±53.5. These parameters describe well the measured spectrum of the 734 keV β transition which shows deviation from the allowed shape. A comparison between the experimental results and the theoretical prediction based on the CVC theory is given.

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The conductivity tensor at finite frequencies for a narrow s-band is investigated on the basis of the Hubbard model. The frequency-dependent conductivity is expressed in terms of the Fourier transform of a retarded Green function. The Green function is calculated by the use of the equation of motion method. Like Hubbard’s first paper, decoupling approximations are made. The obtained frequency-dependent conductivity tensor expresses the optical absorption due to interband transition of electrons between two subbands split by the correlation effect. The spectrum of this optical absorption has some characteristic features different from the ordinary absorption due to interband transition. It is shown that Re σ(ω) has weak singularities like those for forbidden transitions. To demonstrate the result the expression of the conductivity is applied to the one-dimensional cosineband.

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One-dimensional Liesegang phenomena under the influence of electric field is studied quantitatively. Diffusion of ions under an uniform electric field is investigated by taking the effect of counterions into account. Diffused cations and anions in the electric field react similarly to the outer- and innerelectrolyte of the ordinary Liesegang phenomena. The time law is modified as x=k\sqrt2D₀t+wEt where w is the mobility of the cation and E the field. This is well confirmed quantitatively by Okaya’s experiments.
The effect of magnetic field is also studied by a similar method. It appears as a diminution of magnitude of diffusion coefficient D₀, which is so small as to be detected. This explains favorably Yanagihara’s experiments.

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Uniaxial stress dependence of the low-temperature thermal conductivity of lightly-doped p-type Ge and Si is calculated in detail by taking account of elastic and inelastic phonon scattering by holes bound to acceptor impurities. The stress modifies the temperature dependence as well as the magnitude of the thermal conductivity K(T). The most clearcut prediction is that K(T) of p-Si under the stress exhibits a dip as a function of temperature, which gives a direct evidence for the contribution of inelastic scattering to K(T). It is shown that a magnetic field also gives rise to a considerable change in K(T) of p-Si. In this connection, a brief discussion is given on the ultrasonic paramagnetic resonance of acceptor holes.

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The assumption of gaussian distribution of relaxation times adopted by Hill and Ichiki for the explanation of experimental data on frequency dependence of dielectric constants ε of TGS and DKDP is examined. It is known that the above assumption is inadequate since it fails to predict the critical slowing down around the phase transition temperature. It is shown analytically that the above assumption is not suitable for the explanation of ε in high frequency region. An alternative distribution function of relaxation times is shown.

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The perturbative version of the asymptotic expansion method proposed by N. N. Bogoliubov is applied to the derivation of kinetic equations for a system composed of gaseous plasma and radiation field, which is assumed to be non-relativistic and classical. The approximation that ions are uniformly smeared out is used. Bogoliubov’s boundary conditions are generalized so as to be applicable to the system including the radiation field.
As the result, up to the first order with respect to the interactions, the Vlasov equation with the Lorentz-force drift term is obtained as the kinetic equation for electrons. The collision terms appearing as the second-order terms are of the form similar to those for the Kramers-Chandrasekhar type equation, in which the “diffusion coefficients” and the “frictional drag forces” are functionals of the one-body distribution functions. This is a generalization of the Landau equation, and contains the collision terms due to the interaction with the radiation field. A kinetic equation for the field oscillators is also derived. The equilibrium Maxwell-Boltzmann distribution functions for electrons and field oscillators are shown to satisfy these kinetic equations.

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The v-expansion version of Bogoliubov’s asymptotic expansion method is applied to the derivation of kinetic equations for a system of electrons and electromagnetic fields. Electrons and Fields are treated from the classical and non-relativistic points of view. The boundary conditions and the functional forms for many-body distribution functions, which have been generalized in a previous paper, are used.
Up to the first order, the generalized Kramers-Chandrasekhar type equation is derived. In the spatially uniform case, this reduces to the Lenard-Balescu equation with drift-term.

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The magnetic absorption peak of flexural vibrations was experimentally studied for Invar-type alloys, Cu–Ni alloys and also in pure nickel and gadolinium. The absorption peak appearing at the Curie point was observed in Invar and the other metals and alloys, whereas another new peak was found only in Invar and Gd at a temperature below the Curie point. The latter peak appears upon the application of magnetic field, and its shape and location depend strongly on magnetic field. This anomalous peak corresponds to the maximum of linear magnetostriction in Invar, and to the minimum in Gd. It was also observed that the amplitude-independent internal friction decreases with increasing temperature in the magnetically saturated Fe–Ni alloys. This behavior is discussed in connection with the positive thermoelastic coefficient on assuming the application of the Voigt solid model to the alloys.

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Magnetomechanical damping in polycrystalline gadolinium was measured as a function of temperature, applied magnetic field and frequency of kilohertz range, and also the temperature dependence of ΔE effect was observed. Micro eddy current loss δ_i in demagnetized state was much smaller than that in metals of cubic structure, and was comparable with that in cobalt. At a constant temperature, after passing through a peak, δ_i increased again linearly with field in approximate saturating fields. These trends are explained qualitatively from the variation of relaxation frequency with field. Further the peak of macro eddy current loss was observed in the temperature range from 200 to 250°K, where the occurrance of the corresponding change in gradient of magnetostriction versus field curve is shown. In addition, the measured value of decrement was strongly influenced by the internal friction due to anelasticity.

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The magnetic properties of Fe–Ru and Fe–Os alloys in hcp Fe-rich regions were studied in connection with magnetism of hcp Fe and antiferromagnetism was found at low temperatures by means of Mössbauer effect and thermoelectric power measurements. The Néel temperature and the internal magnetic field of hcp Fe obtained by extrapolation are 100°K and 16 kG, respectively. Magnetic moment of hcp Fe was estimated from the internal magnetic field to be about 0.1 μ_B consistent with the results of neutron diffraction measurements. The quadrupole splittings and the isomer shifts relative to bcc Fe of the alloys are extrapolated to 0.14 mm/sec and −0.21 mm/sec, respectively, at pure hcp Fe. In Fe–Ru alloys, gradients of the thermoelectric power versus temperature curves in high temperature region change sign as expected from the density of state of the alloys. On the other hand, the increase in the magnetic susceptibilities with approaching to pure hcp Fe is unexplainable simply by the composition dependence of the density of states.

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Antiferromagnetism in hcp Fe–Mn alloys (17.8, 25.9 and 28.6 at %Mn) was investigated by means of Mössbauer effect and neutron diffraction measurements. Néel temperatures and internal magnetic fields at 0°K were determined to be 230°K and 16 kG, respectively, over the composition range of the measured alloys. Consequently, hcp alloys have weaker internal magnetic fields and lower Néel temperatures than the fcc modifications. In the neutron diffractions on powder and sheets with preferred orientation of hcp Fe_0.714Mn_0.289, only (001) magnetic reflection was found. The averaged magnetic moment was evaluated to be 0.25 μ_B assuming the antiferromagnetic stacking of ferromagnetic (001) sheets. Isomer shifts relative to bcc Fe and quadrupole splittings of hcp alloys are extrapolated to the zero Mn concentration to be −0.20 mm/sec and 0.14 mm/sec, respectively. The results are discussed in connection with magnetism in hcp Fe.

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The magnetic spin structure of the antiferromagnetic Ni(NH₃)₂·Ni(CN)₄2C₆H₆ has been investigated by means of proton nuclear magnetic resonance measurements. From the angular dependence of resonance lines in an external field, an ordered magnetic structure (unit cell dimension, a^*=a, b^*=2a and c^*=2c) is inferred in which ferromagnetic chains parallel to a-axis, are arrayed antiferromagnetically to adjacent chains. The magnitude of internal fields at proton sites could be explained by single domain model. But the rotating diagram of the resonance patterns in the c-plane shows that the substance has antiferromagnetic domains.

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Three-layer type iron bearing minerals, Illite and Montmorillonite after different chemical treatments, were heated over a range of temperatures 100–950°C, with a view to study the migration of Fe³⁺ ions from the sites of their take-up and to examine the thermal stability of these clays. The increased temperature causes the progressive depletion of iron ions from the broken edges and consequent reinforcement of the iron population in the basal plane. In both the cases, the acid treatment weakens the structure whereas Fe(NO₃)₃ treatment reinforces it. On treatment with acid, Montmorillonite, with its capacity to expand along C-axis, is amenable to the creation of lattice defects in the Si-tetrahedra.

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Measurements of the magnetic properties and the electrical properties (the electrical resistivity, the Hall effect and the magnetoresistance effect) were performed on hot pressed polycrystalline samples of Hg_1−xAg_xCr₂Se₄ (0≤x≤0.0155) and of Hg_1−yIn_yCr₂Se₄ (0≤y≤0.02). It was found that the Curie temperature of Hg_1−xAg_xCr₂Se₄ increased as the amount of the Ag dopant increased, whereas the Curie temperature of Hg_1−yIn_yCr₂Se₄ decreased with increasing concentration of the In dopant. The In-doped HgCr₂Se₄ showed a high resistivity, a large Hall effect, and a large negative magnetoresistance effect; the Ag-doped HgCr₂Se₄ showed a low resistivity, a small Hall effect and a small critical scattering of positive magnetoresistance. The different effects of the dopants. Ag and In, on the properties of HgCr₂Se₄ which were studied is satisfactorily explained by the change in carrier concentration produced by the dopants.

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An expression for the Hall coefficient R is obtained using a variational calculation on the assumption that two kinds of scattering processes exist for the conduction electrons. The relation of the Hall coefficient to resistivities due to individual scattering processes is generally discussed. Temperature dependence of R in monovalent metals and their dilute alloys are interpreted from anisotropy of the relaxation times associated with different scattering mechanisms. The maximum of |R| vs temperature curve in monovalent metals is explained assuming that the umklapp process is more anisotropic than the normal process in the scattering of electrons by phonons.

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Martensite transformation in the NiTi alloy has been studied by selected area electron diffraction. The martensites have such close packed layer structures as 4H (2\bar2) and 12 R (3\bar1)₃. The 2H and 18R martensites are also sometimes observed. The 12R martensite appears dominantly at room temperature but the 4H martensite is formed below 0°C. They are closely connected with each other through stacking faults. The martensite transformation causes a considerable shear of layers, but, in order to release it, a new phase transformation occurs in the matrix neighbouring the martensites. By cold work, the 4H martensite and the new phase are also produced. The present results make crystallographically clear the nature of the martensite transformation in the NiTi alloy. On the basis of the results, mechanism of the memory effect in the alloy is interpreted. Origin of the memory effect in metals and alloys are also discussed.

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The photoconduction of metal 8-hydroxy-quinolinate (Me(C₉H₆NO)₂, where Me=Cu, Pd, Zn, Cd and Mg) was measured. The spectral response of the photoconduction was found in lower wavenumber region than the optical absorption bands. There is a linear relation between the wavenumber of the photoconductive peak and the electronegativity of metal ion. It seems that the photoconduction in the low wavenumber region arises from an intrinsic excitation of the constituent molecule.

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The thermal conductivity λ near the Curie points of SrTiO₃, KTaO₃ and BaTiO₃ is studied theoretically. The following results are obtained. (1) In SrTiO₃ λ decreases gradually in the high temperature region (about T^−0.5) and has a sharp decrease in the lower temperature side of the Curie point (32 K). (2) In KTaO₃ λ decreases as T⁻¹ in the high temperature side of T_max∼30 K, whereas it decreases sharply in low temperatures, T_max being the temperature of maximum λ. (3) For BaTiO₃ a dip near the Curie point (391 K) in the λ−T curve is derived. These features are in accord with recent experiments.

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The quantum efficiency and the thermal activation energy of photogeneration of charge carriers in α-sulfur have been investigated in the energy range from 3.6 to 6.2 eV. Quantum efficiency (η) was (1.7±0.3)×10⁻² both for electrons and holes in the energy range from 5.1 to 6.2 eV. Below 5.1 eV, η decreases with decreasing the photon energy. The thermal activation energy (ε) for electrons and holes is constant, (0.02±0.005) eV in the energy range from 4.0 to 6.2 eV, Below 4.0 eV, ε increases with decreasing the photon energy (hν) and fits a linear relation ε=4-hν. The absorption band of single crystal of α-sulfur is similar to the band of a sulfur molecule in cyclohexane. It may be concluded that the mechanism of the intrinsic photogeneration, though it is a single quantum process, is not a direct band-to-band transition, but it is an autoionization process, in which electrons are excited to molecular states and then are autoionized to the continum states.

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Electrical conductivity and magneto resistance effect of Ni, Cu, Zn and metal free phthalocyanine single crystals were investigated. The electrical conductivity and the activation energy in phthalocyanine were expressed by following equations
(Remark: Graphics omitted.),
and
E=I_G−2P.
The values of conductivity and the activation energy was calculated from these equations using calculated polarization energy and the mobility estimated from magneto resistance effect.

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Distribution of dislocations developed during tensile deformation was observed as a function of the strain by etch pit technique on germanium single crystals with an easy glide orientation. Laminar regions inside which forest dislocations dominated developed along the primary slip planes during deformation in stage I. They were revealed as the stripe pattern of etch pits on the specimen surface. The laminar regions were observed to develop by means of the nucleation of new ones and the tangential growth of preformed ones. No lateral growth of preformed laminar regions was found. The laminar regions were also revealed as the inhomogeneities in slip band distribution which have been known as bands of secondary slip.

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The electron spin resonance spectra of γ-irradiated TGSe single crystals were studied. The dominant stable damage center was identified as SeO₂⁻. The additional splitting and the change of intensity of the spectrum were observed below the Curie point. The infrared spectra showed that the absorption intensity of SeO₄²⁻ band changed by γ-irradiation.

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In this paper we report results concerning the second order Raman spectrum in pure RbCl crystals and the impurity induced first order Raman spectra in these crystals. The impurities used were thallium and copper. The observed experimental results are compared with earlier theoretical and infrared work.
Three first order Raman lines at 86,100 and 125 cm⁻¹ arising due to the break of symmetry in the host lattice because of the presence of an impurity are reported.

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The contributions of inelastic and elastic phonon scattering by neutral donors to the low-temperature thermal resistance of Ge are calculated in detail. It is shown that the inelastic and elastic scattering mechanisms make almost the same contribution to the thermal resistance in Sb-doped Ge. The sum of the both contributions gives a good agreement with experiments.

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The edge emission in CdS was studied, paying special attention to the acceptors involved. At least seven different exciton lines, which are believed to be related with the acceptors responsible for the edge emission, were found in the wavelength region between 4892.6Å and 4876.8Å in various crystals, indicating a wide range of ionization energies of the acceptors. The sample showing two acceptor exciton lines exhibits corresponding edge emissions relevant to these two acceptors. This was confirmed by the observation and analysis of the time-resolved spectra of these edge emissions. The variety of acceptor-bound exciton lines requires prudence for the identification of the chemical nature of the acceptors. Evidence is presented as to similar variety of the edge emission in ZnSe.

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The electron microscopic image formed by electrons scattered through large angle gives well resolved fringes at stacking faults. The spacing of these fringes near the entrance surface depends on the Bragg condition of the incident electron, while that near the exit surface depends on the Bragg condition of electrons which form the image. The contrast of the fringe formed by large angle scattering is opposite to that by small angle scattering. The contrast reversal is interpreted qualitatively by the dynamical theory of electron diffraction. The contrast loss observed in ordinary images for thick crystals is also discussed.

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The two X-ray wave fields in elastically distorted silicon single crystals have separately been studied by using a highly parallel incident beam obtained in the double-crystal arrangement of parallel setting. Three crystals bent with a uniform curvature, compressed with knife edges and oxidized partly on the surface were studied. For each case of distortion, the existence of the two wave fields has directly been confirmed. It was observed that positions at which narrow beams of the two wave fields leave the crystal and the intensities of the transmitted and diffracted waves for each beam vary characteristically with the incident angle depending on the elastic distortion in the crystal.

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The Harris method with 50-term and 56-term Schwartz-type-like correlated trial functions is applied to the s-wave elastic electron and positron scattering, respectively, by the hydrogen like ions He⁺, Li⁺⁺, Be³⁺ and B⁴⁺. These systems are difficult to treat by the Kohn or the Hulthén method. However, the matrix elements necessary in the Harris method can be obtained without numerical integration of the coulomb wave functions. In the case of the e+He⁺ scattering, the results are compared with those of other previous calculations.

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The collision induced dissociation of HD⁺ ion by electron impact has been considered by applying Born approximation to the transition from the ground to the first excited repulsive state. The angular distribution of the proton or deuteron produced as dissociation fragments has been considered in detail. Due to the heteronuclear nature of HD⁺ ion some interesting deviations from the results obtained for proton from the dissociation of homonuclear H₂⁺ ion have been observed.

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The cross sections for one-electron stripping from the ground (σ₀₁) and metastable (σ₀*₁) state helium atoms in helium, nitrogen, neon and argon have been measured by beam attenuation technique in the energy range from 13 to 50 keV.
The cross sections σ₀*₁ are larger than the cross sections σ₀₁ by a factor ranging from 10 in higher energy region to 20 in lower energy region in helium, nitrogen and argon. The corresponding factor in neon is about three. The present values of σ₀*₁ are generally consistent with the results of Miers and Anderson for all gases investigated and with those of Gilbody et al. or their extrapolation except for neon. These are also in agreement with the results predicted theoretically by Bates et al. for neon and argon, but differ by a factor of about three from those of Bastien et al. for neon.

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Experiments of the Zeeman effect in the nuclear quadrupole resonance of N¹⁴ in solid hydrazine have been made at liquid nitrogen temperature. The principal axes of the field gradient tensors at the positions of N¹⁴ were determined. In the coordinate system in which the z-axis is parallel to the crystallographic b-axis and the x-axis is parallel to the N–N bond direction, their polar angles are (θ_z=37°, φ_z=206°), (θ_x=59°, φ_x=−11°) and (θ_y=72°, φ_y=90°). The principal z-axis is not coincident with the lone-pair direction and the angle between them was 33°. The bond angles ∠H–N–H=90°, ∠N–N–H=106° are calculated by neglecting the ionicity of the N–H bond as well as the N–N bond.

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The composition and temperature dependence of thermal diffusion factor α_T of the system argon-methane have been studied by the swing separator and two-bulb methods. This system has the special feature that the heavier component has a smaller collision diameter than the other one. The α_T vs. composition curves show a dip for both the temperatures at which measurements have been made. This apparently anomalous behaviour which has also been observed for the hydrogen-helium system cannot be explained either by the elastic or the available inelastic theories for thermal diffusion.

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Effects of an alternating electric field on collisionless drift waves driven by density gradient are investigated theoretically. The alternating electric field is applied along the magnetic field, the frequency of which is close to that of the drift wave. It is assumed that the electron temperature is much greater than that of ions. The applied field is treated as a perturbation like ion-acoustic wave. The contribution of the “nonlinear Landau damping” due to the coupling between the drift and ion-acoustic waves to the damping coefficient, as well as the effect of the frequency shift, is calculated. It is found that the unstable drift waves can be stabilized for the suitable applied intensities. The damping mechanism is caused mainly by the increasing of the frequency of the drift wave. The results are compared with experimental observations.

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An rf electric field near the ion cyclotron frequency is applied perpendicularly to the magnetic field of cusp regions in order to plug up cusp ends and to heat ions. A helium plasma is steadily fed from one of point cusps into the containment region whose density is varied from 1×10⁸ to 1×10¹¹cm⁻³. For the line cusp loss good plugging is satisfied up to 1×10¹¹ cm⁻³, but for the point cusp loss it is not obtained for the density above 1×10¹⁰ cm⁻³. Under the resonance condition the ion energies consist of two components both of which display Maxwellian-like distribution of T_i of about 40eV and 150∼200eV respectively when E_rf=100V/cm.

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Standing waves of longitudinal electron oscillation are excited spontaneously in an electron beam-plasma system. Amplitude pattern of each standing mode whose frequency ω_n is nearly equal to nω₁, where n is a mode number and ω₁ is the first mode frequency, has been measured. Antinodes of oscillating potential are observed at boundaries. When the signal whose frequency ω_m is applied to the gun spontaneous oscillation with ω_n is suppressed but the resonant oscillation with ω_m=ω_n±1 is excited. The results are quantitatively examined by solving simultaneously two van der Pol equations including a mode-mode coupling term. The excited oscillation is also a standing wave and the amplitude pattern of it is similar to that of the spontaneous one.

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Initial and boundary value problems of wave equations with nonlinear perturbation will be discussed.
The non-existence of solutions for the above problems primarily depends upon the structure of nonlinear perturbation.
Some sufficient conditions for the non-existence of global solutions of the above problems will be derived.

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Linear stability theory is applied to the problem of the onset of convective instability in a horizontal layer of fluid heated from below, when the fluid is bounded above by a free surface and below by a solid layer of finite heat conductivity and finite thickness. As the agencies causing instability, both surface tension and buoyancy are taken into account. A Fourier series method is used to obtain the eigenvalue equation, from which various critical values for the onset of a stationary convection are computed numerically for a broad range of thermal boundary conditions. By solving the time-dependent eigenvalue equation numerically, it is shown that, as assumed previously, the neutral state is indeed a stationary rather than an oscillatory one.

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Steady rotation of a very thin plane vortex filament with uniform angular velocity −Ω in the direction opposite to the circulatory rotation around it is discussed on the basis of the localized induction equation. It is shown that the possible form of the filament is that of the plane elastic filament of flexural rigidity B under the action of thrust F applied at its ends provided that
G⁄Ω=B⁄F,
where G is the coefficient of local induction proportional to the circulation of the filament.

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