αdecay to members of favored bands in both even-even and odd-Anuclei

Abstract

We present a systematic analysis of $\ensuremath{\alpha}$ transitions from the ground state of the parent nucleus to members of the favored band in the daughter nucleus. By using measured $\ensuremath{\alpha}$-decay energies and partial half-lives, the well-known Geiger-Nuttall law is examined for these transitions in both even-even and odd-$A$ nuclei. Accurate expressions are proposed for the evaluation of partial half-lives of these transitions based on microscopic quantum tunneling theory. The calculated partial $\ensuremath{\alpha}$-decay half-lives are in good agreement with the experimental data. The root-mean-square deviations of our expressions are $\ensuremath{\sigma}\ensuremath{\equiv}{{{\ensuremath{\sum}}_{i=1}^{n}{[({\mathrm{log}}_{10}{T}_{\mathrm{cal}}^{i}\ensuremath{-}{\mathrm{log}}_{10}{T}_{\mathrm{exp}}^{i})]}^{2}/n}}^{1/2}=0.41$ for the even-even nuclei and $\ensuremath{\sigma}=0.35$ for the odd-$A$ nuclei. A set of parameters for the Viola-Seaborg (V-S) formula is also given by fitting the available experimental data. The proposed expressions and the V-S formula with our parameters will help experimentalists quickly evaluate the expected $\ensuremath{\alpha}$-decay half-lives during the design of experiments and check the measured decay energies and half-lives after experiments.