We present a systematic analysis of $\alpha$ transitions from the ground state of the parent nucleus to members of the favored band in the daughter nucleus. By using measured $\alpha$-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 $\alpha$-decay half-lives are in good agreement with the experimental data. The root-mean-square deviations of our expressions are $\sigma \equiv {\{{\sum }_{i=1}^n{\left[({\log }_{10}{T}_{\mathrm{cal}}^i-{\log }_{10}{T}_{\exp }^i)\right]}^2/n\}}^{1/2}=0.41$ for the even-even nuclei and $\sigma =0.35$ 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 $\alpha$-decay half-lives during the design of experiments and check the measured decay energies and half-lives after experiments.

• Received 2 August 2011

DOI:https://doi.org/10.1103/PhysRevC.84.044312