Semiclassical trace formula for truncated spherical well potentials: Toward the analyses of shell structures in nuclear fission processes

TL;DR

This paper derives a semiclassical trace formula for truncated spherical potentials, incorporating end-point corrections via marginal orbits, and demonstrates significant effects of these orbits in nuclear fission models.

Contribution

It introduces a new formula for end-point corrections in semiclassical trace formulas, enhancing the analysis of shell structures in nuclear fission.

Findings

Marginal orbits have unexpectedly large effects.

The formula improves understanding of shell effects in truncated potentials.

Applications show relevance to nuclear fission modeling.

Abstract

Trace formulas for the contributions of degenerate periodic-orbit families to the semiclassical level density in truncated spherical hard-wall potentials are derived. In addition to the portion of the continuous periodic-orbit family contribution which persists after truncation, end-point corrections to the truncated family should be taken into account. I propose a formula to evaluate these end-point corrections as separate contributions of what I call marginal orbits. Applications to the two-dimensional billiard and three-dimensional cavity systems with the three-quadratic-surfaces shape parametrization, initiated to describe the nuclear fission processes, reveal unexpectedly large effects of the marginal orbits.