The multichannel cluster model (MCCM) is generalized to investigate the effect of nuclear collective vibrations on the $\alpha$-decay fine structure. Vibrational excitations up to two-phonon states are taken into account and coupled-channels calculations are performed for vibrational Rn, Ra, Th, and U isotopes. Without introducing any additional adjustable parameter, the calculated $\alpha$-decay branching ratios to various vibrational states show good agreement with the experimental data. In particular, it is shown that the $\alpha$-decay fine structure is strongly correlated with vibrational excitations, offering an alternative tool to explore the phonon states in daughter nuclei. Despite the $N=126$ shell closure, the calculated $\alpha$-decay half-lives are also found to be in good agreement with the experimental data. A unified description of the $\alpha$-decay fine structure has been achieved by the MCCM for both rotational and vibrational nuclei.

• Received 19 December 2019
• Revised 27 February 2020
• Accepted 20 March 2020

DOI:https://doi.org/10.1103/PhysRevC.101.044308