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arXiv · 2609.36625

Semiclassical description of quadrupole-hexadecapole correlation in nuclear shape evolution

Kenichiro Arita
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Abstract

Background: Theoretical investigations of nuclear shapes with realistic effective interactions or mean field potentials have suggested a remarkable systematics in the hexadecapole shape evolution with varying particle number: Within each single-particle shell, from one spherical magic number to the next, a diamond type (beta_4>0) appears in the first half, and then turn into oblong type (beta_4<0) in the second half. Purpose: Nuclear deformation is essentially governed by the single-particle shell structure. In semiclassical periodic orbit theory (POT), level density is expressed as the sum over contributions from classical periodic orbits, and the origins of the gross shell structures can be understood by the contribution of one or a few shortest orbits. Using the POT, I examine how the hexadecapole degree of freedom affect the contribution of the orbits to the deformed shell structure through their bifurcations to explain the mechanism of above shape evolution. Methods: Ground state deformations are systematically investigated by the shell correction method, taking account of axially symmetric quadrupole and hexadecapole shape degrees of freedom. For simplicity, I employ two simplest mean field potentials to obtain the shell corrections: the oscillator and the cavity (infinite well) potentials. After confirming the the systematics in shape evolution under these simplest mean-field models, semiclassical analyses are made, focusing on the role of PO bifurcation. Results and conclusions: Systematics in the hexadecapole shape evolution in each single-particle shell is clearly explained by the bifurcations of two different types of periodic orbits in the cavity model, which suggest strong correlation between quadrupole and hexadecapole parameters. This also ensures the mechanism of nuclear prolate-shape predominance within this simple potential model.

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Kenichiro Arita. 2026-09-29. Semiclassical description of quadrupole-hexadecapole correlation in nuclear shape evolution. https://arxiv.org/abs/2609.36625

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