Tunneling half-lives in macroscopic-microscopic picture

TL;DR

This paper introduces a new method combining Transmission Matrix and WKB techniques to estimate nuclear tunneling half-lives, addressing limitations of traditional models with position-dependent mass effects.

Contribution

It proposes a novel tunneling probability estimation approach that accounts for variable effective mass, improving the reliability of nuclear decay lifetime predictions.

Findings

The new method yields significantly different tunneling probabilities from traditional WKB.

Relative lifetime trends are consistent across isotopes despite model simplifications.

An empirical scaling law with a stable parameter effectively predicts actual half-lives.

Abstract

Tunneling half lives are obtained in a minimalistic deformation picture of nuclear decays. As widely documented in other deformation models, one finds that the effective mass of the nucleus changes with the deformation parameter. However, contrary to the approach used in literature, a position-dependant mass potentially makes using WKB tunneling probabilities unreliable for estimating nuclear lifetimes. We instead use a new approach, a combination of the Transmission Matrix and WKB methods, to estimate tunneling probabilities. Because of the simplistic nature of the model, the calculated lifetimes are not accurate, however, the relative trends in the lifetimes of isotopes of individual nuclei are found to be consistent. Using this, we develop an empirical scaling to obtain the actual half-lives, and find the primary scaling parameter to have remarkably consistent values for all nuclei considered. The new tunneling method proposed here, which produces very different probabilities as compared to the usual WKB approach, is another key result of this work, and can be utilized for arbitrary potentials and mass variations.