Semiclassical propagator approach for emission processes. I. Two body non-relativistic case

TL;DR

This paper compares semiclassical and coupled channels methods for modeling two-body emission, especially alpha decay from deformed nuclei, highlighting the accuracy of LWKB and the impact of deformation on decay widths.

Contribution

It introduces a rigorous 3D semiclassical formulation for deformed potentials and compares it with existing approximations, demonstrating improved accuracy.

Findings

LWKB closely matches the exact coupled-channels results.

Deformation significantly influences alpha decay widths.

The propagator approach effectively describes emission processes.

Abstract

We compare the coupled channels procedure to the semiclassical approach to describe two-body emission processes, in particular $\alpha$-decay, from deformed nuclei within the propagator method. We express the scattering amplitudes in terms of a propagator matrix, describing the effect of the deformed field, multiplied by the ratio between internal wave function components and irregular Coulomb waves. In the spherical case the propagator becomes diagonal and scattering amplitudes acquire the well-known form. We describe a more rigorous formulation of the 3D semiclassical approach, corresponding to deformed potentials, which leads to the exact results and we also compare them with the much simpler expressions given by the Angular Wentzel-Krames-Brillouin (AWKB) and Linearized WKB (LWKB) with its approximation, known as Fr\"oman WKB (FWKB) method. We will show that LWKB approach is closer than AWKB to the exact coupled-channels formalism. An analysis of alpha-emission from ground states of even-even nuclei evidences the important role played by deformation upon the channel decay widths.