Periodic-orbit approach to the nuclear shell structures with power-law potential models: Bridge orbits and prolate-oblate asymmetry

TL;DR

This paper uses a power-law potential model to analyze nuclear shell structures, revealing how bridge orbit bifurcations influence deformed shell phenomena and prolate-oblate asymmetry.

Contribution

It introduces a simple semiclassical model with a power-law potential to systematically study nuclear shell structures and the role of bridge orbit bifurcations.

Findings

Shell structures emerge at specific deformation and diffuseness parameters.

Bridge orbit bifurcations are crucial for normal and superdeformed shell structures.

Prolate-oblate asymmetry is explained through bridge orbit contributions.

Abstract

Deformed shell structures in nuclear mean-field potentials are systematically investigated as functions of deformation and surface diffuseness. As the mean-field model to investigate nuclear shell structures in a wide range of mass numbers, we propose the radial power-law potential model, V \propto r^\alpha, which enables a simple semiclassical analysis by the use of its scaling property. We find that remarkable shell structures emerge at certain combinations of deformation and diffuseness parameters, and they are closely related to the periodic-orbit bifurcations. In particular, significant roles of the "bridge orbit bifurcations" for normal and superdeformed shell structures are pointed out. It is shown that the prolate-oblate asymmetry in deformed shell structures is clearly understood from the contribution of the bridge orbit to the semiclassical level density. The roles of bridge orbit bifurcations in the emergence of superdeformed shell structures are also discussed.