Microscopic description of cluster decays based on the generator coordinate method

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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 α 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 ²²²Ra, i.e., ²²²Ra→¹⁴C+²⁰⁸Pb, 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 ²²⁸Th and ²³²U 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.

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  • Physical Review C

    Physical Review C 105 (3), 2022-03

    American Physical Society (APS)

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