Critical view of WKB decay widths

TL;DR

This paper critically examines various WKB approximation methods for calculating decay widths, highlighting the importance of consistent fitting procedures and the sensitivity of results to nuclear interaction parameters.

Contribution

It provides a detailed comparison of different WKB decay width formulas, emphasizing the need for consistent fitting within the WKB framework in fission models.

Findings

Simple WKB gives order-of-magnitude estimates

Decay widths are sensitive to nucleon-nucleon interaction density dependence

Half-lives depend on Bohr-Sommerfeld quantization implementation

Abstract

A detailed comparison of the expressions for the decay widths obtained within the semiclassical WKB approximation using different approaches to the tunneling problem is performed. The differences between the available improved formulae for tunneling near the top and the bottom of the barrier are investigated. Though the simple WKB method gives the right order of magnitude of the decay widths, a small number of parameters are often fitted. The need to perform the fitting procedure remaining consistently within the WKB framework is emphasized in the context of the fission model based calculations. Calculations for the decay widths of some recently found super heavy nuclei using microscopic alpha-nucleus potentials are presented to demonstrate the importance of a consistent WKB calculation. The half-lives are found to be sensitive to the density dependence of the nucleon-nucleon interaction and the implementation of the Bohr-Sommerfeld quantization condition inherent in the WKB approach.