Universal decay rule for reduced widths

TL;DR

This paper introduces a universal decay rule linking reduced widths to the fragmentation potential, unifying various decay processes and explaining empirical rules through a common theoretical framework.

Contribution

It derives a linear relation between the logarithm of reduced width squared and the fragmentation potential, providing a unified understanding of decay systematics and empirical rules.

Findings

Linear relation between log of reduced width squared and fragmentation potential.

Universal decay rule applicable to multiple emission processes.

Explanation of empirical rules like Viola-Seaborg and Blendowke scaling.

Abstract

Emission processes including $\alpha$-decay, heavy cluster decays, proton and di-proton emission are analyzed in terms of the well known factorisation between the penetrability and reduced width. By using a shifted harmonic oscilator plus Coulomb cluster-daughter interaction it is possible to derive a linear relation between the logarithm of the reduced width squared and the fragmentation potential, defined as the difference between the Coulomb barrier and Q-value. This relation is fulfilled with a good accuracy for transitions between ground states, as well as for most $\alpha$-decays to low lying $2^+$ excited states. The well known Viola-Seaborg rule, connecting half lives with the Coulomb parameter and the product between fragment charge numbers, as well as the Blendowke scalling rule connecting the spectroscopic factor with the mass number of the emitted cluster, can be easily understood in terms of the fragmentation potential. It is shown that the recently evidenced two regions in the dependence of reduced proton half-lives versus the Coulomb parameter are directly connected with the corresponding regions of the fragmentation potential.