Background: While many phenomenological models for nuclear fission have been developed, a microscopic understanding of fission has remained one of the most challenging problems in nuclear physics.

Purpose: We investigate an applicability of the generator coordinate method (GCM) as a microscopic theory for cluster radioactivities of heavy nuclei, which can be regarded as a fission with large mass asymmetry, that is, a phenomenon in between fission and $\alpha$ decays.

Methods: Based on the Gamow theory, we evaluate the preformation probability of a cluster with GCM while the penetrability of the Coulomb barrier is estimated with a potential model. To this end, we employ Skyrme interactions and solve the one-dimensional Hill-Wheeler equation with the mass octupole field. We also take into account the dynamical effects of the pairing correlation using Bardeen-Cooper-Schrieffer (BCS) wave functions constructed with an increased strength of the pairing interaction.

Results: We apply this scheme to the cluster decay of ${}^{222}\mathrm{Ra}$, i.e., ${}^{222}\mathrm{Ra}\to {}^{14}\mathrm{C}+{}^{208}\mathrm{Pb}$, to show that the experimental decay rate can be reproduced within about two order of magnitude. We also briefly discuss the cluster radioactivities of the ${}^{228}\mathrm{Th}$ and ${}^{232}\mathrm{U}$ nuclei. For these actinide nuclei, we find that the present calculations reproduce the decay rates with the same order of magnitude and within two or three order of magnitude, respectively.

Conclusions: The method presented in this paper provides a promising way to describe microscopically cluster decays of heavy nuclei.

• Received 24 December 2021
• Revised 24 February 2022
• Accepted 11 March 2022

DOI:https://doi.org/10.1103/PhysRevC.105.034326