Nascent fragment shell effects on the nuclear fission processes in semiclassical periodic orbit theory

TL;DR

This paper introduces a novel semiclassical periodic orbit theory method to evaluate shell effects in nuclear fission prefragments, revealing their influence on asymmetric fission fragment distributions.

Contribution

It presents the first method to isolate and evaluate shell effects of nascent nuclear fragments using classical periodic orbits within the semiclassical framework.

Findings

Prefragment shell effects dominate early after neck formation.

Magic numbers in prefragments influence asymmetric fission.

Shell effects are linked to the establishment of asymmetric saddle shapes.

Abstract

Making use of the semiclassical periodic orbit theory (POT), we propose, for the first time, a method to exclusively evaluate the shell effects associated with each of the nascent fragments (prefragments) generated by the neck formation in nuclear fission processes. In spite of the strong indication of such shell effects in asymmetric fragment mass distributions, they could not have been accessed by any previous theoretical approach since most of the single-particle wave functions are delocalized. In the POT, we have found that the prefragment shell effects can be naturally and unambiguously identified as the ontributions of the classical periodic orbits localized in each of the prefragments. For a numerical test, simple cavity potential models are employed with the shape described by the three-quadratic-surface shape parametrization. Deformed shell energies are studied with the trace formula for degenerate orbits in a runcated spherical cavity which was recently derived [K. Arita, Phys. Rev. C 98, 064310 (2018)]. In this simple model, it is shown that the prefragment shell effect dominates the total shell energy shortly after the neck formation, and the magicity of the heavier prefragment plays a significant role in establishing the fission saddle with asymmetric shape which leads to an asymmetric scission.