For potentials V(z) holomorphic in Rez>0 and bounded by
(Remark: Graphics omitted.)
we show that the double spectral “function” ρ(s, t) is ac ontinuous function of s and t s>0, t>0, and we obtain an upper bound for it. This upper bound shows clearly that the double integral of the Mandelstam representation in fact exists and defines an analytic function of s and t in two cut planes. We indicate how to generalize these results to the case when ρ(s, t) is no longer a function but a distribution.

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An attempt was tried to estimate the cross-sections of direct interactions and the compound nuclear process separately, using the experimental data of Al²⁷(p, p′)Al^27* scattering. Under three assumptions, 1) the similarity of the probability of direct collective excitations by alpha-particles and protons, 2) the 2J+1 rule for the yield of the compound nuclear process, and 3) a negligible effect of the interference between the both processes: the cross-sections of direct interactions, summed up the lower six proton groups, were estimated to be about 80 mb over the energy range of 8.5 to 14 MeV of incident protons. On the other hand, the compound part decreases exponentially from 140 mb to 30 mb in the same energy range.

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The ionization yield of the N¹⁴(n, p)C¹⁴ reaction produced by thermal neutrons in air was measured with a pulse ionization chamber. The uncorrected value of the reaction energy was obtained as 0.600±0.006 Mev. This value was corrected for columnar recombination and for the variation of W, the average energy to produce an ion pair, with particle energies. For the variation of W_α, the empirical formula obtained in the previous work was used. Assuming that W_p is equal to W_α for the same velocity and that the relative value of W_C with respect to Po alpha particles is 1.10, the corrected reaction energy was calculated as 0.621±0.006 Mev in good agreement with the established Q value. This result indicates that W_p for about 600 kev is actually equal to W_α for the same velocity in air. Some evidences, which suggest that the relative value of W_C is about 1.10 and W_α for the same velocity as C¹⁴ is probably equal to this value, were also discussed.

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The excited states of Si²⁸ were studied by the Al²⁷(p, p)Al²⁷ reaction in the energy region E_p=770–1390 keV. Definite anomalies of the excitation functions were observed at 140°46′ C.M. for the 991, 1117, 1182, 1198, 1362, 1380 and 1387 keV resonances and an ambiguous one for the 936 keV. For the 1117, 1182 and 1198 keV resonances the excitation functions were studied at 90° C.M. too.
The results were analyzed by the R-matrix formalism taking into account the energy spread which came from the beam energy spread and the target thickness. The spin-parities of the 1117, 1182 and 1198 keV resonances were determined to be 3⁻ or 4⁻, 2⁺ and 3⁻, respectively.

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Energy dependence of the elastic scattering of protons from Cu⁶³ and Cu⁶⁵ were investigated between 7.5 MeV and 14.6 MeV. At four angles of 30°, 60°, 95° and 165°, differential cross sections were measured at about every 200 keV and angular distributions were also observed at every 800 keV for both isotopes. The observed angular distributions showed the typical diffraction patterns. An optical model analysis was made for every angular distribution and the parameters of the optical potentials were obtained as functions of incident energies.

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Characteristics of the spark chamber (490 mm × 490 mm × 20 mm Height) whose electrodes are covered with glass are presented. Constant efficiency in the range of 1 to 1,500 particles/m² is obtained experimentally, and the possibility of extension to 10,000 particles/m² is shown. Zenith angle is measured from the projected length of the track from 20° to 90° through electrode. As the efficiencies of the chambers are uniform, and do not decrease during long operation, the extension to large area is very easy and the chamber is useful for cosmic ray study.

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Film thickness dependence of the Curie temperature of nickel films is investigated under various experimental conditions. The Curie temperature is found to be nearly constant for films of thickness above 50Å, when the films are deposited on sufficiently outgassed substrates and not exposed to the air after deposition. When the films are exposed to the air, a lowering of the Curie temperature occurs for thin films. The lattice constant of these air-exposed films is found to be increased and the largest increase of spacing is 0.7% of the bulk value. Correlation is found between the lattice constant and the Curie temperature.

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Quantum-statistical mechanics is applied to the spin echo method for liquid He³ in order, first, to derive quantum theoretically the expressions for the amplitudes, or the heights of peaks, of the echo signals and, secondly, to obtain the expression for the so-called “self-diffusion coefficient” measured by this method in terms of microscopic quantities of the system. Three cases are considered: the case of a 90°–180° pulse sequence, a 90°–180°–180° pulse sequence and the “B Method” by Carr and Purcell. It is found, among others, that the ratio of the amplitudes of two echoes in the second case is precisely expressed by the formula which has been obtained by several authors from classical or macroscopic standpoint, only with the spin diffusion coefficient D_s, of which the microscopic expression is given by Fukuda and Kubo, and also by Kadanoff and Martin, for the “self-diffusion coefficient”, under a usual experimental condition.

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The Néel temperature, T_N, of the spin density wave in a b. c. c. lattice, proposed by Tachiki and Nagamiya, is calculated. It is found that the transition of the second kind can be predicted only for k_FO (the Fermi radius at absolute zero)≥π⁄a (a: the lattice constant), where one has antiferromagnetic ordering immediately below T_N. For k_FO<π⁄a, a transition of the first kind at a certain temperature above T_N can be inferred, if one understands by T_N the temperature at which the amplitude of the spin density wave tends to zero.

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A study of the chlorine nuclear quadrupole resonance has been carried out at room temperature in single crystal of 2, 5 dichloro-nitro benzene. Two field gradients have been found in this crystal, one for each chlorine. The asymmetry parameter values have been determined for both the field gradients. The orientation of the principal axes have been found with respect to the crystallographic axes. Zeeman effect studies have shown that the two molecules in the unit cell are in physically equivalent positions. The molecular plane has been identified as the ‘ab’ plane of the crystal. The determination of the approximate coordinates of the atoms in the crystal is made. The C–Cl bond characters have been determined using the valence bond method. The π electron loss is calculated using Bersohn’s molecular orbital treatment.

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The magnetostriction of CoO single crystals were measured along three principal crystallographic directions in fields up to 11 KOe. The magnetostriction appears from ten degrees below the Néel temperature. The magnetostriction observed at liquid air temperature is strongly dependent on an applied field and can be described in the form of λ=[a+bcos2(φ−φ₀)]H², where H and φ are the intensity and direction of the field, respectively, and a, b, and φ₀ are constants independent of the field. The result is briefly discussed in connection with the magnetization process occurring in antiferromagnetic CoO single crystal and it is suggested that the displacement of antiferromagnetic domain walls plays the most important role in the magnetostriction induced by an applied field.

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Cyclotron resonance studies of the Ge-Si and Ge-Sn systems on the Ge side have been made with the aims of (1) exploring the electron scattering effect by the substituted isovalent impurity and (2) directly persuing the variation of the band parameters with the increasing percentage of the minority component of the alloy. The scattering cross section is found to be very small with the magnitude of less than one atomic cross sectional area, if any, for Sn and even smaller for Si. The variation of energy bands, or the effective mass properties, is in a qualitative agreement with the prediction of the pseudo-potential approach by Bassani et al. Comparison with the infrared absorption measurement by Braunstein shows a fairly good agreement in the low Si concentration range in the Ge-Si system.

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The free carrier-like absorptions observed at low temperatures have been interpreted, in the previous theory, as due to excitations of donor electrons into the lowest conduction band. This theory is modified by making use of the hydrogen-like wave function for the continuous spectrum of a donor electron. According to the present theory, the maximal value of the absorption coefficient appears at the photon energy of about 2.2 times the donor activation energy. And the qualitative behavior is similar to that by the previous theory. The theory is compared with experiments for n-type GaP and Si, and gives a better agreement with experiments for GaP with respect to the wavelength dependence.
The Faraday rotation due to donor electrons is calculated considering the presences of the excited donor states and the lowest conduction band. The result is found to be similar to that due to free carriers with respect to the magnitude and the wavelength dependence, for the photon energy larger than about three times the donor activation energy.

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The atomic scattering factors of magnesium and oxygen in magnesium oxide crystals were obtained by the intensity measurement of X-ray reflections from powder samples. The intensity measurements were carried out by the absolute and relative methods, with Cu Kα. In the former method, the Johann type LiF monochromator was used and the effect due to the circumstance that the monochromator crystal is not ideally imperfect was taken into account by adjusting the polarization factor in the intensity formula.
It was shown that the experimental values of the scattering factor for magnesium agreed with the theoretical ones within 1% at most, over the whole angular range observed. The experimental values of the scattering factor for oxygen were proved to agree with the ones calculated by Tokonami based on the wave function for O²⁻ in magnesium oxide crystals obtained by Yamashita using a variational principle, rather than the ones calculated by the Hartree-Fock self-consistent field method for free oxygen atoms or ions (Hoerni and Ibers, Berghuis et al., and Freeman), or fictitiously stabilized O²⁻ ions (Watson-Suzuki).

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The ferromagnetic resonance linewidth ΔH, the magnetic anisotropy constants K₁, K₂ and the g-factor are observed at 9.27 GC and in the temperature range from 80°K to 300°K for small spherical single crystal specimens of the composition Co_xNi_1−xFe₂O₄ where, x=0, 0.006, 0.03, 0.06, 0.12. The K₁, (−K₂) and ΔH increase linearly with the increase of the cobalt concentration at a fixed temperature. The ferromagnetic g-factor increases with cobalt content. The contribution of cobalt ion to the anisotropy is found to have nearly the same temperature dependence as that of cobalt ferrite, and the increase of K₁ caused by cobalt ions is well described by Tachiki’s theory after putting |αλ|=97 cm⁻¹ and r=0.7. The linewidth at room temperature increases by about 8 Oe for one percent of cobalt ions. The linewidth becomes anisotropic at low temperatures. It is concluded that the contribution of cobalt ions is most pronounced in Fe₃O₄, next in MnFe₂O₄, and smallest in NiFe₂O₄, in agreement with the degree of uniformity of the electric charge distribution on 16d sites.

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The ground state splitting of Fe³⁺ in a strong trigonal field is studied theoretically in order to account for the uniaxial anisotropy of hexagonal crystal BaFe₁₂O₁₉. The spin Hamiltonian DS_z² is derived as the second-order contribution of the spin-orbit interaction, the crystal field being treated as a part of the unperturbed Hamiltonian. It is shown that reasonable values of crystal field parameters lead to the observed value of D∼−2.0 cm⁻¹.

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It is shown that an anisotropy in relaxation times of current carriers plays an essential part in the Hall effect for Pd alloys. An expression for the Hall coefficient, containing parameters A which describe anisotropies in the relaxation times, is derived in the two-band model. A relation between A and scattering mechanisms for carriers is derived by a simple approximation. Using these expressions, it is shown that the temperature dependences of the Hall coefficients for dilute alloys can be explained qualitatively. The Hall coefficients of Pd-Ag system at room temperature are calculated as a function of Ag content c, using the anisotropy parameter determined for dilute alloys, and compared with experimental data. Agreements between the calculated and the observed results are quite satisfactory in region c≤0.5.

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The wave-number-dependent dielectric function is calculated for Si crystal along the three principal symmetry axes taking the detailed band structure into account. The effects of the core state, the higher bands and the Umklapp terms are found to be rather small. The value of 10.82±0.70 is obtained for the static dielectric constant in zero wave number limit, which is to be compared with the observed value of 11.7. Rather strong anisotropy and anomalous maximum are observed for relatively mall k.

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The magnetization along the trigonal axis of the single crystal of the anhydrous ferrous chloride has been studied at 4.2°K as a function of field strength up to 24kOe. The sharp transition from antiferromagnetic to ferromagnetic state was observed at the field strength of 11.6kOe. The atomic magnetic moment obtained from the saturation value of the magnetization was (4.4±0.2) μ_B, which was in good agreement with these obtained by the Mössbauer study and neutron diffraction.

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Seebeck effect measurements have been made between 60°K and 300°K on the various n-type cadmium sulfide single crystals. In all the temperature range measured, the anomalous Seebeck voltages caused by “phonon-drag” are found. An apparatus for making measurements of the Seebeck effect and the method for calculating the ordinary electronic part of Seebeck coefficient for the case of CdS are described. The temperature dependence of the phonon-drag part of Seebeck coefficient (Q_p) is ∼T^−2.5 for the sample of the least carrier number. It is observed that Q_p has the anisotropy with respect to the crystallographic orientation. These data are compared with those in the case of ZnO in which piezoelectric scattering occurs as a result of electron-phonon interaction and phonons are scattered by the polarizable neutral donor states. Phonon relaxation times in CdS are also estimated from Q_p.

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From the measurements of residual lines of crystalline quartz in infrared region of 5–28 micron, the following results were obtained:
(1) When a sample was rotated around its surface normal, alternation of reflectivity was observed between a pair of dichroismic residual lines.
(2) Nf, the product of ion pair concentration and oscillator strength of the residual line was succesfully calculated utilizing the maximum reflectivity of the residual line and it was found out that the oscillator strength of the dipole-moment laid in the R plane (10\bar11) had the largest value.
(3) Some slight mechanical pulse knocked onto the R plane caused incidentally the intensity change of the residual lines, and this phenomenon was interpreted as the following effect that the effective number of ion pair concentration which determined the residual line intensity had three types of distribution, and their mutual transition was easily induced.
(4) The disappearance and the reappearance of the residual lines were observed in the R plane and it was classified into three cases.

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To find a mechanism of stabilising the period of seven layers in the sinusoidal spin arrangement of Tm and Er, the contribution of the oscillating strain associated with the spin arrangement to the free energy is calculated. It is shown that this strain is effective below a certain temperature to stabilize the period of seven, as far as the period of the spin arrangement in the neighborhood of the Néel temperature is close to seven.

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The anisotropy and the temperature dependence of thermal expansion in NaNO₂ crystals were investigated over a temperature range from room temperature to near the melting point by a differential type dilatometer.
The anomaly of thermal expansion coefficients was recognized at 102°C, near the Curie point (163°C), and at 178°C, 189°C and 207°C respectively. The plots of the α⁻¹ vs T relation are on straight lines in the whole temperature range except for that from 102°C to 207°C in the [100] and [010] directions, though the similar linear relation exists only above 178°C in the [001] direction. These three straight lines extrapolated to the high temperature side terminate together at a point, whose temperature is higher than the melting point by a few degrees.
Obtained experimental results were discussed qualitatively in relation to the thermal motion of NO_2⁻ radicals.

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In crystals with a very small dislocation density such as in germanium, a long time is necessary to obtain an equilibrium concentration of Schottky-type defects. This is verified by successive-quenching experiments. Analysis of the equilibration process of acceptor centers in n-type germanium at high temperatures gives the activation energy of about 2.0 eV. The formation energy of the thermally induced acceptors is found to be roughly 2 eV from the saturation values of the introduction curves of acceptors. Preliminary results of annealing of thermal acceptors are also described. The results are discussed in terms of vacancies thermally induced into the crystal.

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The magnetoresistance effect in n-type germanium containing more than 2.10¹⁷ cm⁻³ antimony atoms has been measured at liquid helium temperature. These samples show a metallic impurity conduction and the resistivity decreases a few per cent when a magnetic field of 3 to 10 kφ is applied. The magnitude of the low field magnetoresistance coefficient is larger for samples containing higher concentration of donors, and becomes larger when the temperature is lowered. A phenomenological consideration is carried assuming that this negative magnetoresistance is due to the localized magnetic moments formed among the impurity electrons.

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The domain reversal in NaNO₂ by a dc electric field was found to occur in a very wide region outside the electrodes as well as the region under the electrodes, more remarkably in the a direction than in the c direction. In the observation of the 50 c/s D-E hysteresis loop, the residual polarization increased monotonously and the coercive field increased first and decreased next after passing through a peak, with decreasing ratio of the electrode area to the whole area of crystal surfaces. These peculiarities, which may together be called a “hamidashi” (bulging-out) effect, were not seen in BaTiO₃ and hence seem to be a character of ferroelectrcis such as NaNO₂ in which the polarization reversal would be realized by a rotational behavior of radicals.

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The cross sections of the charge exchange of the fast negative chlorine atomic ions inatomic chlorine are calculated by the impact parameter method. Values of the cross sections range between 404.772×10⁻¹⁶ cm² and 129.93×10⁻¹⁶ cm² for the energies 25 eV and 90 KeV of Cl⁻ ions, respectively. The above cross sections are a few times larger than those of the similar symmetric positive ion-atom charge exchange reactions. For Cl⁻ in chlorine, the cross sections are even higher than that of H⁻ in atomic hydrogen, calculated by Dalgarno and McDowell with the PSS method.

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The theory of helix-coil transition has been applied to Poly-L-lysine and Poly-L-glutamic acid. The transition is characterised by the fraction of hydrogen bonds broken and the average sequence lengths in the helical and random coil phases.

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The reflected power of microwave is experimentally examined, when the wave is incident on a plasma slab with a metal wall at its rear side. From the reflected power, it is found that the power is dissipated most effectively under a certain condition. This condition calculated with approximations is confirmed to be satisfactory in comparison with the experimental results.
An afterglow plasma produced by repeated pulses of high DC voltage in a part of an X-band rectangular waveguide is used as a plasma slab with electrons uniformly distributed. The collision frequency of electrons with ions which predominates over that with neutral atoms in the afterglow plasma during the time of interest is determined at the maximum absorption. The collision frequency found is slightly higher than that predicted by the theories of various authors and fairly agrees with the result previously measured by a different microwave method. The electron temperature can be estimated from the reflected power at the maximum absorption.

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By applying a weak magnetic field along the axis of positive column of discharge the resonance absorption was observed. The resonance due to surface wave of dipole mode showed splitting. However, the resonance due to dipole oscillation and the resonance due to longitudinal plasma wave did not change remarkably. An explanation for those phenomena was given.

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A theoretical investigation is made of the radiation from a point charge e gyrating in a plane almost perpendicular to a magnetic field. The perpendicular component of the velocity, v, of the charge is assumed to be non-relativistic but much larger than the thermal velocity v_T, lnv⁄v_T>>1. Under the conditions |ε₁|>>(sv_T⁄v)^4⁄3·s−2, ε₃>>(v_T⁄sv) and ω₀²<ω_r²=(sω_H)²<ω₀²+ω_H², the intensity of the s-th harmonic is enhanced and given by
\frac2e²ω_r²πsv\sqrt|ε₁ε₃|ln\fracvv_T.
Here ω₀ and ω_H are the plasma frequency and the electron cyclotron frequency, respectively, s is a positive integer larger than unity and ε₁=1−ω₀²⁄(ω_r²−ω_H²), ε₃=1−ω₀²⁄ω_r². A harmonic structure appears when ω_H or ω₀ is changed. It is pointed out that some features of the experiments on cyclotron harmonic waves can be explained by this theory.

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Gasdynamic equations for an electrically charged gas are simplified on the basis of quasi-static approximation. Electrogasstatics of the charged gas on a sinusoidal insulator wall is studied for various external electric fields and polytropic indices. Irrotational steady two-dimensional circulatory flow is also studied with special reference to the diameter of the vacuum core, which is shown to be increased in general by the electrostatic repulsion.

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