Universal decay rule for reduced widths

Abstract

Emission processes including $\ensuremath{\alpha}$ decay, heavy cluster decay, and proton and di-proton emission are analyzed in terms of the well-known factorization between the penetrability and the reduced width. By using a shifted harmonic oscillator 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 the Q value. This relation is fulfilled with a good accuracy for transitions between ground states, as well as for most $\ensuremath{\alpha}$ 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 Blendowske scaling 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.