Spheroidal Cavity Model Research Articles

Shell structure and orbit bifurcations in finite fermion systems

We first give an overview of the shell-correction method which was developed by V.M. Strutinsky as a practicable and efficient approximation to the general self-consistent theory of finite fermion systems suggested by A.B. Migdal and collaborators. Then we present in more detail a semiclassical theory of shell effects, also developed by Strutinsky following original ideas of M.C. Gutzwiller. We emphasize, in particular, the influence of orbit bifurcations on shell structure. We first give a short overview of semiclassical trace formulae, which connect the shell oscillations of a quantum system with a sum over periodic orbits of the corresponding classical system, in what is usually called the “periodic orbit theory”. We then present a case study in which the gross features of a typical double-humped nuclear fission barrier, including the effects of mass asymmetry, can be obtained in terms of the shortest periodic orbits of a cavity model with realistic deformations relevant for nuclear fission. Next we investigate shell structures in a spheroidal cavity model which is integrable and allows for far-going analytical computation. We show, in particular, how period-doubling bifurcations are closely connected to the existence of the so-called “superdeformed” energy minimum which corresponds to the fission isomer of actinide nuclei. Finally, we present a general class of radial power-law potentials which approximate well the shape of a Woods-Saxon potential in the bound region, give analytical trace formulae for it and discuss various limits (including the harmonic oscillator and the spherical box potentials).

THREE-DIMENSIONAL FLAW RECONSTRUCTION FROM WAVEFORMS MEASURED ON THE SIDE OF A CYLINDER

A modified three-dimensional inverse scattering method is applied to reconstruct the shape of a three-dimensional flaw in a cylindrical specimen. In this modified method, a measurement plane is restricted to the plane perpendicular to the axis of the cylindrical specimen. Thus the crosssectional image of the flaw can be obtained. By moving the measurement plane along the axis of the cylindrical specimen, the cross-sectional image is obtained for each measurement plane. The three-dimensional flaw image is reconstructed by piling up the obtained cross-sectional images. Cylindrical specimens with a cylindrical cavity model and with a hemi- spheroidal cavity model are prepared. The performance of the modified method to reconstruct the three-dimensional flaw is verified by using the experimentally measured waveforms.

２．逆問題 円柱側面からの計測波形による三次元欠陥像の再構成

A modified three-dimensional inverse scattering method is applied to reconstruct the shape of a three-dimensional flaw in a cylindrical specimen. In this modified method, a measurement plane is restricted to the plane perpendicular to the axis of the cylindrical specimen. Thus the crosssectional image of the flaw can be obtained. By moving the measurement plane along the axis of the cylindrical specimen, the cross-sectional image is obtained for each measurement plane. The three-dimensional flaw image is reconstructed by piling up the obtained cross-sectional images. Cylindrical specimens with a cylindrical cavity model and with a hemi- spheroidal cavity model are prepared. The performance of the modified method to reconstruct the three-dimensional flaw is verified by using the experimentally measured waveforms.

Spectroscopic Studies of Hexadecylquinolinium Tricyanoquinodimethanide

Hexadecylquinolinium tricyanoquinodimethanide (1), a unimolecular rectifier of electrical current with a large ground-state dipole moment (43 ± 8 D), reveals large hypsochromic shifts of the absorption spectrum. Two fluorescent emissions were observed: one in the visible region (quantum yield φ ≈ 0.01, not solvatochromic) and one in the near-infrared spectrum (weakly solvatochromic). Using a prolate spheroidal cavity model and the absorption maxima measured in eight solvents, the excited-state dipole moment of 1 is estimated as 8.7 D. The NMR spectral lines broaden above 330 K and lose the multiplet structure. The core-level N 1s XPS spectrum reveals the three expected N valence states. The valence-level XPS spectrum can be correlated with theory. Simultaneous cyclic voltammetry and electron spin resonance of the radical anion of 1 shows that the spin density in the LUMO of 1 is concentrated on the tricyanoquinodimethanide portion of the anion. The molecule is clearly zwitterionic in the ground state, bo...

Semiclassical Origin of Superdeformed Shell Structure in the Spheroidal Cavity Model

Classical periodic orbits responsible for emergence of the superdeformed shell structures for single-particle motions in spheroidal cavities are identified and their relative contributions to the shell structures are evaluated. Both prolate and oblate superdeformations (axis ratio about 2:1) as well as prolate hyperdeformation (axis ratio about 3:1) are investigated. Fourier transforms of quantum spectra clearly show that three-dimensional periodic orbits born out of bifurcations of planar orbits in the equatorial plane become predominant at large prolate deformations, while butterfly-shaped planar orbits bifurcated from linear orbits along the minor axis are important at large oblate deformations.

The Interaction Energy of an Ion Pair with Overlapping Hydration Shells. II. A Spheroidal Cavity Model

The energy of interaction of two monovalent ions of opposite charge with overlapping hydration shells and in an aqueous medium is discussed in terms of a spheroidal cavity model. Some of the calculations carried out in an earlier paper by Levine and Rosenthal (1966) are shown to be inadequate and an improved model is tested for consistency with the "truncated spheres model" proposed in Part 1. The calculations suggest that this new model can be adapted to an examination of the water molecules in the first hydration shells of an ion pair. Only calculations for the K + and F- ions are included.

The Interaction Energy of an Ion Pair with Overlapping Hydration Shells. I. A Truncated Spheres Model

The energy of interaction of two univalent ions of opposite charge with overlapping hydration shells and in an aqueous medium is discussed in terms of a truncated spherical cavity model. The general trend of the effective dielectric constant considered as a function of the separation between the ion centres is found to be in agreement with some earlier results on a spheroidal cavity model. The present investigation has the advantage that the boundary of the ion pair , varies continuously with separation and hence that no matching of a two� sphere model onto a spherical cavity model is required. It is found that the effective dielectric constant has a maxinum value at very small ion overlap.