Shell-structure and octupole instability in fermion systems

Abstract

Simulating the one-particle spectra of the infinite-well potential by a model, we study the symmetry and the shell-structure of octupole deformations as well as the possible occurrence of octupole (and quadrupole) instabilities. Among various types of octupole deformations investigated the Y32-type deformation is found to have a strong shell-structure as well as a very interesting symmetry which leads to the occurrence of highly-degenerate single-particle levels. One particle spectra of the octupole-coupled two-level model (with ~ and f + 3) are analytically studied in the limit of large angular-momentum, f.

Modified Nilsson model for large sodium clusters

“…As recently shown by Hamamoto et al [40], nonaxial shapes of both quadrupole and octupole multipolarity can be expected to play a role, in particular in the mid-shell regions between the major spherical systems. The inclusion especially of nonaxial deformations is expected to further wash out the oscillations in dE due to their breaking of the angular momentum (A) degeneracy.…”

Non-axial octupole deformations of N=Z nuclei in A∼60–80 mass region

“…In this system the mean-field for the valence electrons resembles with the nuclear meanfield except for its effectively zero ls potential [12]. Non-axial octupole deformatios seem to be one of the dominant deformations in this system as demonstrated by means of schematic models [13,14] and more recent mean-field calculations [15,16]. In particular, the tetrahedron shape or the Y 32 deformation is predicted to be stable because of the shell gaps generated at N electron = 40, 70, 112, 156 [13,15,16].…”

“…Non-axial octupole deformatios seem to be one of the dominant deformations in this system as demonstrated by means of schematic models [13,14] and more recent mean-field calculations [15,16]. In particular, the tetrahedron shape or the Y 32 deformation is predicted to be stable because of the shell gaps generated at N electron = 40, 70, 112, 156 [13,15,16]. In this paper, we will show that the tetrahedron shape is expected in the nucleus 80 Zr with N = Z = 40, being in parallel with the metal cluster system in spite of the difference in the ls potential and the pairing correlation present in nuclei.…”

Symmetry-unrestricted Skyrme–Hartree–Fock–Bogoliubov calculations for exotic shapes in nuclei from 64Ge to 84Mo

“…As shown by Hamamoto, Mottelson, Xie and Zhang [79], the tetrahedral symmetry associated with the Y 32 deformation brings about a bunching of the single-particle levels and create a remarkable shell structure: The N = Z = 40 is one of the magic numbers for such tetrahedral shapes. Such a shell effect is common to various finite Fermion systems, and in fact the tetrahedral deformation has been predicted, for instance, for sodium clusters consisting of 40 atoms by the density functional Kohn-Sham calculation [80,81], in which there is no spin-orbit coupling.…”