Shoichiro Koide

On the Lifetime of the Lower Triplet States of Benzene

Transition probabilities and selection rules are calculated for the lower triplet‐singlet transitions of benzene. The relativistic spin‐orbit coupling term combines the triplet state with an intermediate singlet state, and then dipole transition to the ground state occurs. The selection rules are deduced group‐theoretically, and the transition probabilities are calculated using the LCAO one‐electron approximation. The effect of vibration is discussed. The theoretical results obtained agree with Shulls and McClures experimental results.

Transverse Vibrations of Viscoelastic Cylinders

The effect of shear stress on transverse vibrations of incompressible viscoelastic materials of the Voigt type is studied theoretically for vertical cylinders fixed on a horizontal vibrating plane.The displacement, inclination and shearing angle are calculated as functions of the position for various frequencies and cylinder diameters. It is shown that even if the mechanical loss tangent is much smaller than unity, the existence of viscosity plays a fundamental role. It is shown that when the cylinder is thick and short enough, vibrations can be thought of as almost purely shearing, and that when the cylinder becomes thin enough, vibrations can be considered almost as purely flexural. A brief discussion is made for the validity of the vibrating reed method,and the formulae for the method are corrected with respect to the shift of resonance frequency caused by viscosity.

One-Center Molecular Orbital Wave Function for Methane

The validity of the spherical approximation for the potential due to nuclei used in the calculation of molecules with good symmetry by means of one-center MO method is examined for methane molecule. Molecular orbital wave functions are set up as harmonic expansion about the central carbon nucleus, and energy expectation values are calculated with respect to the exact Hamiltonian. Results obtained by using various approximations are compared. It is shown that while the effect of the angular dependent part of the nuclear potential on the energy value is not so large as is expected, the electron charge distribution has fairly large directional dependence caused by the non-central part of the potential.

Vibrationally induced electronic transitions in crystals of magnetic compounds

A simple model is proposed for the spin-dependent infrared absorption band observed in antiferromagnetic NiO crystals. The transition is attributed to the coupled action of the radiation field with the lattice vibrations. The variation of the exchange parameter due to the electric field and the displacement of the ions is taken as the perturbation giving rise to the electric dipole transition between different spin states accompanying the change in the vibrational states. The molecular field approximation is adopted to describe the spin states. The general features of the spectral pattern and its temperature dependence thus obtained are in good agreement with the experiments byNewman andChrenko.RésuméUn modèle simple est proposé pour l’absorption infra-rouge dépendant du spin trouvée dans les cristaux anti-ferromagnétiques de NiO. La transition est attribuée à l’action conjuguée de la radiation et des vibrations du réseau. La variation de l’interaction d’échange causée par le champ électrique et le déplacement des ions est considéré comme la perturbation responsable de la transition dipôlaire électrique entre les états différents de spin total et les états de vibration. Afin de décrire le système des spins, on adopte le modèle du champ moléculaire. L’allure générale du spectre prévu théoriquement et sa dépendance avec la température sont en accord avec les résultats expérimentaux deNewman etChrenko.ZusammenfassungDas spin-abhängige Infrarot-Absorptionsband in antiferromagnetischen NiO-Einkristallen wird auf Grund eines einfachen Modells untersucht. Die Übergänge werden durch den kombinierten Einfluß von Strahlungsfeld und Gitterschwingungen verursacht. Die Modulation der Austauschwechselwirkung durch das elektrische Feld und die Bewegung der Ionen sind die Störungen, welche die elektrischen Dipolübergänge zwischen den verschiedenen Spin- und Phononzuständen ergeben. Die Spinzustände werden mit Hilfe eines Molekularfeldes beschrieben. Das Spektrum und dessen Temperaturabhängigkeit, die sich aus unserem Modell ergeben, stimmen mit den Meßresultaten vonNewman undChrenko gut überein.

Positron Mobility in Diamond

The mobility of a thermal positron in diamond is studied theoretically and experimentally. An approximate wave function of a positron is obtained by the Wigner-Seitz method for an effective hard sphere potential with radius determined by the WKB method. The dilatation due to the acoustic wave gives rise to a change in the energy determined as a function of the Wigner-Seitz cell radius, which yields the positron-phonon interaction of the deformation potential type. The estimated mobility has ambiguities but may have the order of magnitude 50∼500 cm/volt · sec. The experimental value of the mobility obtained by means of the angular correlation in positron annihilation is less than 20 cm 2 /volt · sec at room temperature, much smaller than the mobility 1200 cm 2 /volt · sec of a hole in the valence band.

On the Vibrational Properties of High-Elastic Gels

A new method is presented for determining dynamic mechanical properties of high-elastic gels by measuring the amplitude and phase of forced longitudinal vibrations excited in get blocks themselves. It is shown that the Youngs modulus and viscosity can be determined by analysing these quantities. Theoretical analyses are also made for the vibrations excited in the vertical cylindrical samples with no viscosity by horizontal oscillations of the bottom ends. The calculated results are illustrated by strains (displacement, inclination and shearing angle) for various values of cylinder diameters and frequencies used. It is shown that an approximate value of rigidity can be obtained from the frequency dependence of the strains. On an basis of this method the dependence of dynamic mechanical constants of agar-agar gels on cylinder diameters, concentrations and frequencies is studied, and reasonable values are obtained.

A Calculation of Multi-Magnon Side-Band

A calculation is made for the multi-magnon side-band recently observed by Hirano et al. on FeBO 3 . The change in the coupling constants between Fe 3+ spins due to the exciton creation is treated as the final state interaction. The perturbation expansion is adopted with respect to the change expressed in terms of magnon operators. The general features of the observed spectrum can be well accounted for by assuming appropriate values for some parameters introduced in the calculation.

A Model for the Transfer of Magnetic Excitons between Antiparallel Spin Sites

A model is proposed for the transfer of magnetic excitations between antiparallel spin sites. Formulation is made for the 4 A 2 g → 2 E g transition of Cr 3+ ( d e 3 ) ions in antiferromagnetic crystals. Since the spin component is not conserved in the transfer, the mechanism is attributed to the second order effect of the spin-orbit interaction similar to the anisotropic super-exchange interaction derived by Moriya. It is shown that the model gives the correct order of magnitude for the transfer matrix elements. Unfortunately, angular dependence of the transfer matrix elements characteristic to the present model does not agree with the experimental results obtained so far.