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W. -H. Steeb, A. Grauel
1984 Volume 53 Issue 6 Pages
1901-1903
Published: June 15, 1984
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The “singular point analysis” for partial differential equations due to Weiss, Tabor, and Carnevale is performed for soliton equations in (2+1) dimensions. The soliton equations are derived with the help of pseudo differential operators and include the Kadomtsev-Petviashvili (K-P) equation. We demonstrate that the equations under consideration have the Painlevé property.
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Ken-ichi Tozaki, Yûko Yamaguchi
1984 Volume 53 Issue 6 Pages
1904-1906
Published: June 15, 1984
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A selected spectrum (central frequency
f: 10 kHz, band width
Δf: 200 Hz) of the fluctuating voltage that is generated spontaneously between two electrodes which are filled with liquid glycerol, is investigated. It satisfies the Nyquist’s equation in normal liquid and metastable supercooling liquid. In the non-equilibrium state (crystallization process), the enormous fluctuations are observed; the distributions of the voltage are no more the Gaussian distribution and form a characteristic group.
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Toshiaki Sato, Toshio Osaka, Yasuharu Makita
1984 Volume 53 Issue 6 Pages
1907-1910
Published: June 15, 1984
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X-ray diffraction from (NH
4)
2ZnCl
4 and its dielectric property were studied. It was confirmed that the crystal in the intermediate phase between the ferroelectric transition point (−4.5°C) and the weak ferroelectric transition point (3°C) is commensurate.
It was found that the crystal has an incommensurate structure (δ≠0) characterized by the (
h k l±(1⁄4+δ)) satellite reflections between 91°C and 133°C. The dielectric constant along the
b axis shows a small peak at the incommensurate-commensurate phase transition point, 91°C.
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Shozo Ino, Hiroshi Daimon, Takashi Hanada
1984 Volume 53 Issue 6 Pages
1911-1914
Published: June 15, 1984
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On the basis of a detailed analysis of RHEED intensity distribution along reciprocal lattice rods taken from the Si(111)7×7 structure, a new structure model has been obtained. The structure consists of twelve raised atoms and a vacancy in the unit mesh. The raised atoms are arranged in regular triangular forms with side 2
a,
a being the size of the bulk unit mesh and they can be classified into four kinds of atoms A, B, C and D. Among their heights of the displacements Z
A, Z
B, Z
C and Z
D, an inequality Z
A>Z
B>Z
C>Z
D has been consequently obtained. The Ge(111)7×7-Sn surface has an identical structure with the Si(111)7×7. Similarly the Ge(111)2×8 structure consists of two of them, A and B, and the Ge(111)5×5-Sn and Si(111)5×5-Ge three of them, C, D and a vacancy.
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Shinji Kawaji, Junichi Wakabayashi, Junji Yoshino, Hiroyuki Sakaki
1984 Volume 53 Issue 6 Pages
1915-1918
Published: June 15, 1984
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Activation energies of the diagonal resistivity ρ
xx near the minima in the 1/3 and 2/3 fractional quantum Hall effect are determined in very high mobility GaAs/Al
xGa
1−xAs (
x\simeq0.3) heterostructures. Measurements of ρ
xx and ρ
xy are made at temperatures ranging from 1 K to 0.1 K in magnetic fields up to 15.5 T. The activation energies are 2.7 K and 0.89 K at the filling factor of a Landau level of 1/3 and 2/3, respectively. The former is in good agreement with theoretical predictions.
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Hidetoshi Fukuyama, Hiromichi Ebisawa, Sadamichi Maekawa
1984 Volume 53 Issue 6 Pages
1919-1922
Published: June 15, 1984
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Effects of localization on the critical temperature and the upper critical field have been examined for bulk superconductors in the weakly localized regime, i.e. ε
Fτ>>1; ε
F and τ being the Fermi energy and the life time, respectively. The life time is assumed to be short so that τ
−1>ω
D; ω
D being the Debye frequency, and modifications of density of states and renormalization of effective Coulomb interaction have been investigated by perturbation to the order of (ε
Fτ)
−2. The results indicate that there exists appreciable suppression of the critical temperature even in the weakly localized regime.
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Masayuki Itoh, Toshinobu Tsuda, Hiroshi Yasuoka
1984 Volume 53 Issue 6 Pages
1923-1926
Published: June 15, 1984
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The microscopic magnetic properties of the paramagnetic state in the triangular Heisenberg antiferromagnet VX
2 (X=Cl, Br and I) have been investigated by using the NMR technique. From the
51V shift vs the magnetic susceptibility plot the hyperfine coupling constant due to the d-spin core polarization effect is determined to be −95±2, −79±2 and −69±2 kOe/μ
B for VCl
2, VBr
2 and VI
2, respectively. Also it has been revealed that the high temperature value of the
51V nuclear spin-lattice relaxation rate is explained from the Guassian model for the auto-correlation function of the spin fluctuations.
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Norio Akiyama, Katsuyasu Kawano, Yuzo Mori, Hiroshi Ohkura
1984 Volume 53 Issue 6 Pages
1927-1929
Published: June 15, 1984
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When the pumping light is modulated between right and left circular polarization, the magnetic circular polarization of
F center luminescence observed after passing through a linear polarizer has been called “the anomalous effect”. We measured this effect for the
F center in KI as a function of the magnetic field
H and the photon energy. These experimental data are explained by deriving a form which includes the parameter (ε
I) for the unbalancing of circular polarization in pumping light and the spin-lattice relaxation rate of the relaxed excited state (
T1*)
−1. The
H-dependence of (
T1*)
−1 is presented.
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Satoshi Hashimoto
1984 Volume 53 Issue 6 Pages
1930-1932
Published: June 15, 1984
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The very thin KI crystal has been grown from the melt inside a narrow gap of the cell composed of two quartz plates. Thickness of the crystal is determined to be about 0.2 μm from the interference fringes in the transparent region. Consequently, the transmitted light can be detected up to the absorption coefficient of 3×10
5 cm
−1. From the measurements of absorption and reflection spectra, it is shown that the 2
s exciton band consists of the oscillatory structures separated by about 16 meV, in contrast to the case of evaporated thin films.
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Miki Wadachi, Masa-aki Sakagami
1984 Volume 53 Issue 6 Pages
1933-1938
Published: June 15, 1984
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In the Nonlinear Schrödinger model, the correspondence between classical soliton and its quantum field theory is investigated. It is shown explicitly that moving soliton as well as soliton at rest arise as the matrix elements of a field operator in the limit
n→∞, where
n is the particle number making the bound state.
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Mitsuhiro Imai, Masaaki Ito
1984 Volume 53 Issue 6 Pages
1939-1942
Published: June 15, 1984
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The method of orbital separation is applied to the classical φ
4 model; φ
tt−φ
xx+
m2φ+λφ
3=0 to investigate the behavior of the solution. Our numerical results indicate that the solution of non-integrable φ
4 model with a positive λ is insensitive to the initial conditions even at high energy.
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Toshihiro Okada
1984 Volume 53 Issue 6 Pages
1943-1950
Published: June 15, 1984
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Simulation was performed both by a digital computer and by an analog circuit connected to a micro-computer, and stationary power spectra were measured. When only Gaussian white noise force was applied additively to an equation of inactive type, was observed the Lorentzian power spectrum, whose density decreased with increasing nonlinearity in low frequency region. An equation of active type also exhibits the Lorentzian power spectrum if random force was week. When random and periodic forces were applied simultaneously, the continuous part of the power spectrum was also Lorentzian, but the low frequency density was reduced considerably. The experimentally obtained results were consistent with those obtained theoretically by using the statistical linearization approximation developed by Budger, Lindenberg and Shuler.
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Masahiro Nakagawa, Tadashi Akahane
1984 Volume 53 Issue 6 Pages
1951-1960
Published: June 15, 1984
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A molecular statistical theory of smectic A liquid crystals is presented. Here the hard-core intermolecular repulsions are taken into account in addition to the attractions within the second-virial approximation. Our theory shows the significance of a symmetry-breaking component of one-body pseudo-potential, which represents the steric effects arising from the intermolecular repulsions, for the thermal stability of smectic A phase. The effects of the molecular packing along the layer normal are also discussed by varying the ratio of the layer spacing to the effective molecular length.
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Toshihiro Okada, Shigeharu Kabashima, Shigeru Iino
1984 Volume 53 Issue 6 Pages
1961-1970
Published: June 15, 1984
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An oscillator having a nonlinear resistance was simulated by an analog circuit, and its spectra were measured when periodic and random forces were applied. The oscillation without random forces was classified into several types. A new type of oscillation which showed an amplitude modification was detected, and its spectra consisted of many satellite lines in both sides of the central line, whose frequency was that of the applied periodic force. In another type of oscillation the hysteresis phenomena similar to that of Duffing oscillator were observed. The effects of external random forces were also examined.
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Makoto Kaburagi, Takashi Tonegawa, Junjiro Kanamori
1984 Volume 53 Issue 6 Pages
1971-1982
Published: June 15, 1984
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The phase diagram of the Ising model on the simple hexagonal lattice with competing interactions is studied within the mean-field approximation. The stability analysis of a paramagnetic phase shows that the present model exhibits a Lifshitz point separating the paramagnetic phase, an antiferromagnetic phase and a modulated phase. Numerical calculations are performed to investigate a gross feature of the phase diagram. It is shown that a large number of high-order commensurate phases are stable. The resulting phase diagram is strikingly different from the corresponding phase diagram of the axial next-nearest neighbor Ising (ANNNI) model.
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Mamoru Yoshida, Yoshio Toyoda, Toshiro Maeda
1984 Volume 53 Issue 6 Pages
1983-1994
Published: June 15, 1984
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An experiment to observe accompanied showers delayed relative to the bulk of extensive-air-shower particles near the core was carried out by using plural detectors set at separate places. Four delayed events hitting two or more detectors at the same time were observed. It is difficult to explain these events by accidental coincidence or conventional processes. However, these events can be explained, provided that a parent particle producing the delayed shower has a lifetime of the order of 1×10
−6 s and is heavier than a nucleon. The thickness of air shower disk was also measured at core distances less than 50 m.
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Yasuhisa Sakurai, Masaaki Doi, Tsutomu Imamura
1984 Volume 53 Issue 6 Pages
1995-2001
Published: June 15, 1984
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The effective Hamiltonian method is used to find the distribution function describing the positions as a function of time of a given pair of fluid particles subject to convection in steady, incompressible, statistically isotropic turbulent flow. By assuming a joint Gaussian distribution for the velocity field, a reasonable time dependence is obtained for the statistical average of the distance between the pair of fluid particles. The basis for Richardson’s four-thirds law is indicated and the proportionality constant
C* is shown to be related to the Kolmogorov constant
C by
C*=3
1⁄3C1⁄2⁄2
1⁄2.
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R. W. Lardner, S. K. Trehan
1984 Volume 53 Issue 6 Pages
2002-2011
Published: June 15, 1984
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Using the method of multiple scales, the propagation of quasi-harmonic capillary-gravity waves on a conducting fluid in the presence of a magnetic field is studied. The nonlinear Schrödinger equation governing amplitude modulation is derived and the stability condition is obtained. The effect of the magnetic field is to extend the stable region in the direction of small wave numbers.
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Yutaka Sasakura
1984 Volume 53 Issue 6 Pages
2012-2017
Published: June 15, 1984
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The instability of the density-stratified swirling flow in an azimuthal magnetic field is investigated for the axisymmetric disturbance. An assumption of positive Rayleigh-Synge-Michael’s discriminant is made. It is shown that the complex phase-velocity of any unstable axisymmetric mode must lie within the semi-ellipse which has the range of axial flow-velocity for major axis and (
Remark: Graphics omitted.) times the range for minor axis. Here
J represents an extended local Richardson number to the present flow and the suffix m means the minimum value in the flow field.
Jm must be less than 1/4 by the necessary condition for instability.
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Kazuya Uehara
1984 Volume 53 Issue 6 Pages
2018-2026
Published: June 15, 1984
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In current sustaining tokamak by use of Landau damping, resonant particles feel an effective DC field in the toroidal direction to drive the plasma current, and still the rf field reaches thousand times larger than the joule field due to the quasi-linear effect. The time evolution of the density and current profile have been simulated using one dimensional tokamak code including the current drive pinch term due to the inward
Erf×
Bθ drift. This effect could be the basis of the improvement of the confinement and the impurity control by the rf travelling wave.
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Tetsumori Yuyama, Toshinori Michishita, Sadao Nakamura, Mikio Takeyama ...
1984 Volume 53 Issue 6 Pages
2027-2031
Published: June 15, 1984
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An X-ray energy spectrum from plasma electrons at high temperature is numerically studied on the basis of a relativistic-quantum theory. The relativistic emission cross section is significantly larger than the non-relativistic one, which is indicated by modification of Gaunt factor. The relativistic Maxwellian energy distribution function is formed toward the higher side than the non-relativistic one. The relativistic X-ray intensity, as a result, is stronger and decreases more slowly with the X-ray energy than the non-relativistic one. The total emitted power due to a bremsstrahlung in the relativistic case is 1.5 times as large as that in the non-relativistic case at the temperature of 200 keV.
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Yasutomo Ohguchi
1984 Volume 53 Issue 6 Pages
2032-2038
Published: June 15, 1984
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Global properties of nonequilibrium hydrogen positive columns are obtained in a range 1.0–0.1 cm of a tube radius and at moderately high pressure (1.0 and 0.1 atms) by computer simulation based on a two-temperature model. The hydrogen positive column itself has two stable states, an arc and a glow, and one unstable state. When a tube radius and/or a pressure decreases to a certain value, the arc region joins continuously to a glow region. If we use the experimental data of thermal conductivity of hydrogen gas, the results considerably deviate from the results by using the theoretical data. Mechanisms of existence of multiple states, of state transitions, and of parameter dependence of the global properties are explained.
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Shigenori Tanaka, Setsuo Ichimaru
1984 Volume 53 Issue 6 Pages
2039-2048
Published: June 15, 1984
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The inter-ionic density correlations and the associated screening potential are investigated for those dense, high-temperature plasmas with parameters appropriate to the inertially confined fusion experiments and the interior of main sequence stars. The hypernetted chain scheme is used for the analysis of the correlations, where the screening effect of the electrons is taken into account via the dielectric function with inclusion of partial degeneracy and the local-field correction. We derive explicit analytic expressions for the enhancement rate of thermonuclear reactions applicable uniformly over the entire parameter domain of plasmas with the ionic charge
Z=1 and 2.
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Kazuyuki Itoh
1984 Volume 53 Issue 6 Pages
2049-2053
Published: June 15, 1984
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An atomic order parameter is defined by the difference of the probabilities with which the atom occupies two local equilibrium positions in the split-atom potential. An expression of this order parameter is given as a function of the temperature and the potential difference between two local equilibrium positions. It is shown that the thermal averages of the atomic position and the square of the atomic thermal amplitude, which can be determined from the crystal structure analysis, are expressed as a function of this atomic order parameter. The characteristic temperature variation of these values observed in the ferroelectric CsD
2PO
4 is successfully explained by the predicted temperature dependence of the atomic order parameter.
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Masaru Sugiyama
1984 Volume 53 Issue 6 Pages
2054-2060
Published: June 15, 1984
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General properties of instability phenomena in crystals caused by external forces are studied by the continuum approximation of the self-consistent Einstein model. A new criterion for an occurrence of the instability is proposed on the basis of the response of lattice vibration to a change of the stress. A method to classify the instability phenomena is briefly shown by utilizing a simple example.
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A. Bieber, F. Gautier
1984 Volume 53 Issue 6 Pages
2061-2074
Published: June 15, 1984
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The role of multiatom interactions in determining both the stability of ordered structures in the ground state and the short range order, occurring in transition metal alloys, has been investigated by means of the generalized perturbation method discussed previously. This method enables to compute the multiatom interactions from the electronic structure; as a result of the angular dependence of the transfer integrals it is shown that, contrarily to what is generally believed, the most important interactions, coming from “d” bands, are not those corresponding to the most compact clusters (triangles, tetrahedrons…) but to straight self-retraced paths. However the pair approximation is generally valid for the study of stability as long as no self-retraced paths, connecting neighbouring minority atoms, occur in the ordered structures and provided the concentration dependence of the pair interactions is taken into account. An expression of the configurational energy in terms of irreducible two and three body interactions is given.
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Haruyasu Yamashita, Itaru Tatsuzaki
1984 Volume 53 Issue 6 Pages
2075-2083
Published: June 15, 1984
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Second order elastic constants of ammonium bromide were measured near λ-point in disordered phase under hydrostatic and uniaxial pressures by means of an ultrasonic method. Third order elastic constants were calculated from pressure derivatives of the second order elastic constants. Cubic and third order invariants in free energy expressed in terms of irreducible strains were derived near λ-point. It was found that the third order invariant played a dominant role in the vicinity of λ-point in comparison with the cubic invariant.
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Ko Sugihara, Takuro Tsuzuku
1984 Volume 53 Issue 6 Pages
2084-2091
Published: June 15, 1984
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Jay-Gerin and Maynard proposed a theory to interpret the anomaly of thermoelectric power (TEP) of graphite taking place near 35 K. They ascribed the anomaly to the phonon drag effect due to the so-called “Kohn phonons” satisfying
q⊥=2
kF⊥, where
kF⊥ denotes the maximum Fermi momentum perpendicular to the
c-axis. Their theory is based on an assumption applicable only to the cylindrical Fermi surface. If we take into account the ellipsoidal Fermi surface, their theory loses its validity. Supposing that the cylindrical model is valid, their theory has several inconsistencies in itself and cannot explain the observed negative dip. From the experimental point of view, this theory conflicts with the fact that the lower the structural perfection the deeper the negative dip. Appropriate interpretation of the phonon drag TEP can be obtained by introducing the normal phonon-phonon scattering in the phonon relaxation process.
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Hatsuo Tange, Yasuhiro Yamada, Mitita Goto
1984 Volume 53 Issue 6 Pages
2092-2098
Published: June 15, 1984
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The temperature dependence of forced volume magnetostriction dω⁄d
H for Ni
1−xTi
x (
x≤0.1) and Ni
1−xV
x (
x≤0.08) alloys has been measured using the 3-terminal capacitance method. The values of dω⁄d
H for Ni∼8 at%Ti–Ni and ∼6 at%V–Ni alloys change their sign from positive to negative with raising the temperature. Pressure coefficients, d ln μ⁄d
p and d ln
Tc⁄d
p, have been deduced from the temperature dependence of dω⁄d
H using the thermodynamical and the Kornetzki-Kouvel relations. The relation between two pressure coefficients above are analysed according to Inoue and Shimizu’s discussion. The values of the coefficient
C⁄χ
hfTc obtained decrease gradually from 2 to 1 with decreasing
Tc toward 0 K for both alloy systems.
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Hidenori Kubo, Norikiyo Uryû, Hironori Nishihara, Hiroshi Yasuok ...
1984 Volume 53 Issue 6 Pages
2099-2110
Published: June 15, 1984
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Proton NMR measurements were carried out to clarify the spin structure in the intermediate phase of CsMn
1−xCo
xCl
3·2H
2O. Hyperfine fields at proton sites are compared with the calculated values of dipole fields. In Mn-rich antiferromagnetic phase, the moments including Co impurities point to the
b-axis, while in Co-“rich” antiferromagnetic phase, most of the moments point to the
c-axis. In the intermediate phase, three kinds of NMR lines were observed which are due to the moments parallel to the
b-axis,
c-axis and distributed in the
bc-plane. The fraction of the moments parallel to the
c-axis increases with increasing Co concentration. It is shown that in the intermediate phase the
b- and
c-axis domains coexist, and at the boundary of both domains the moments tilt continuously from the
b- to
c-axis. The tilting of the averaged moment is achieved by the change in the fraction of each domain. This model is supported by the fact that the relative intensities of the peaks change with an external field.
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Masao Shimizu, Hirotada Kobayashi
1984 Volume 53 Issue 6 Pages
2111-2119
Published: June 15, 1984
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Mössbauer spectra of Fe–Ni Invar alloys are calculated by means of the mixture model of the ferromagnetic and paramagnetic phases proposed before in the itinerant electron model. Gaussian distribution of the effective fields to Fe
57 nucleus is assumed. It is shown that the calculated spectra agree well with the observed ones. The origin of the distribution of the effective fields is discussed in terms of the environment of Fe
57 atom, spin fluctuations and the relaxation process of itinerant electron spins. It is shown that this model can explain the observed Mössbauer spectra in Fe–Ni Invar alloys.
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Kazuyoshi Yoshimura, Satoshi Hirosawa, Yoji Nakamura
1984 Volume 53 Issue 6 Pages
2120-2129
Published: June 15, 1984
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The magnetic environment effect of cobalt in Dy
1−xY
xCo
2 has been studied by means of bulk magnetization and
59Co spin-echo NMR measurements at 4.2 K. Clearly resolved satellite structures of the NMR spectra have been observed. The hyperfine field distributions of
59Co are decomposed into contributions of Co atoms in various nearest neighbor configurations of rare earth atoms. In this analysis the dipole field due to nearest neighbor rate earth moments plays an important role. The result indicates that the magnetic moment of Co in the RCo
2 cubic Laves phase pseudobinary compounds is quite sensitive to the nearest neighbor rare earth environment.
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Hiroshi Daimon, Akitoshi Ishizaka, Keisuke L. I. Kobayashi, Yoshitada ...
1984 Volume 53 Issue 6 Pages
2130-2136
Published: June 15, 1984
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Valence band photoemission spectra of six kinds of Ni
xSi (
x=3, 2.5, 2, 1.5, 1, and 0.5) were measured with synchrotron radiation at photon energies around the Ni 3p core excitation threshold. The resonance in the Ni 3d band shows two minimum structures in the photon energy dependence of the peak height with a separation of 1.7 eV, which corresponds to the spin orbit splitting in the final state of Ni 3p core emission. Strong resonance at valence band satellite and main 3d band is found in Ni-rich compounds and the behavior of the resonance changes from Ni-like to Cu-like with decreasing
x. These changes are interpreted by a rigid band model, in which the partially empty d band becomes to be fully occupied with decreasing
x.
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Shintaro Kawata, Tatsuji Hayaishi, Sadao Aoki, Yoshimi Sakayanagi
1984 Volume 53 Issue 6 Pages
2137-2144
Published: June 15, 1984
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A high intensity pulse light source from a high density plasma in a sliding spark with an electron beam is useful in the vacuum ultraviolet (vuv) and soft X-ray regions. Its spectra in the 100–500 Å region are shown and line profiles are compared with numerical results calculated from the local thermodynamic equilibrium (L.T.E.) plasma model.
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Katsumi Tanimura, Takashi Eshita, Noriaki Itoh
1984 Volume 53 Issue 6 Pages
2145-2150
Published: June 15, 1984
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Luminescence emitted by photo-excitation of self-trapped excitons in KI has been studied. It is found that the luminescence due to free excitons is generated when the self-trapped excitons at the lowest triplet state from which the π-luminescence is emitted is excited with 2.5 eV photons. Furthermore studies of the dependence of the increment of the σ-luminescence and the decrement of the π-luminescence induced by photoexcitation revealed that the collisions between free excitons and the self-trapped excitons annihilate the former.
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Hiroyoshi Ishii, Tsuneaki Miyahara, Takaaki Hanyu, Shigeo Yamaguchi
1984 Volume 53 Issue 6 Pages
2151-2156
Published: June 15, 1984
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The photoelectron spectra of the valence bands have been measured on the pure Rh metal and Cu-based Rh alloys over the excitation energy range from 30 eV to 130 eV. The band occurring at 1.25 eV below the Fermi edge with the width of 0.5 eV is interpreted as being due to the virtual bound state. From the result of the virtual bound state the number of the electrons of the Rh virtual bound state and the phase shift for the d-partial component is estimated to be 8.79 electrons and 2.76 radians respectively. A satellite, which can be observed in valence band photoemission spectra for some transition metals, can not be detected for pure Rh metal.
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Toshihiro Kobayashi, Riso Kato
1984 Volume 53 Issue 6 Pages
2157-2161
Published: June 15, 1984
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Low temperature optical spectra of highly purified NaNO
2 crystals have been investigated in near
uv region. The width of the zero-phonon absorption line at ν
00 due to the electronic transition
1A
1→
1B
1 in NO
2− is remarkably reduced in the purified crystal and three satellite absorption lines are observed separately from the high energy tail of the strong zero-phonon absorption line. The energy separations of these lines from ν
00 are 4±1, 6±1 and 7.5±1 cm
−1 and are identified as the isotope shifts of the zero-phonon transition in NO
17O
−, NO
18O
− and
15NO
2−, respectively.
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Yoshinori Isogai, Toshiyuki Itoh
1984 Volume 53 Issue 6 Pages
2162-2171
Published: June 15, 1984
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The tertiary structures of 43 proteins selected so as to cover the five structural classes of protein molecule are analyzed with a geometrical theory called fractal theory with the intention of devising a new tool for quantitative description of the tertiary structure of protein. A brief introduction to the fractal theory is given in the text. It is demonstrated that the principles dictating the folding of the local backbone structure and the global backbone structure are well characterized in terms of the representation of the fractal theory. Comparison of the fractal character of protein molecules with that of the ideal Gaussian chain revealed several characters of these principles. It is also shown that the proteins in the structural class of β type are distinguished quantitatively from other classes with this representation. A curious discovery that several proteins take the fractal dimension greater than two is reported and discussed.
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