Ground- and excited-state calculations of cluster radioactivity and alpha decay

Abstract

The present work presents calculations for different aspects of alpha and cluster decay within a preformed cluster model where the light cluster is considered to tunnel the Coulomb barrier formed by its interaction with the heavy daughter nucleus. In the models used to study such decay, the effective interaction between the daughter nucleus and alpha is an essential ingredient for the proper determination of the nuclear potential used for evaluating half-lives. A good interaction potential must include effects due to nonlocal interactions and deformations in the shapes of the nuclei if necessary. For nucleon-nucleus scattering processes, the nonlocality has been characterized in different ways such as by introducing energy or velocity-dependent local equivalent potentials, a coordinate-dependent mass, or by modifying the nuclear density distribution. In this work, a comparison of the alpha and cluster decay half-lives using different nonlocal approaches are performed for deformed and spherical nuclei. The sensitivity of the results can provide a complementary tool for improving the models of the nonlocal interaction which are usually constrained by reaction data.

Though the measured branching ratios of cluster radioactivity as compared to alpha decay are very small, the former rare decay may become important in hot environments such as those encountered in the nucleosynthesis of heavy elements. The r-process nucleosynthesis path is along highly unstable, exotic, and neutron-rich nuclei. Thus, the decay rates and fission, as well as the photo-dissociation and neutron capture cross sections, are important for the abundance evolution. The explosive conditions in supernovae and neutron star mergers leading to considerably high temperatures could result in nuclei existing in excited states. Though the possible influence of these nuclear thermal excitations is taken into account in the production reactions as well as in their reverse reactions, with libraries publicly available for the scientific community, the same is not true in the case of alpha and cluster decay. In order to include these effects, a model for the alpha and cluster decay of excited nuclei is developed in this work. Empirical formulae or universal decay laws obtained by performing fits to available data of excited nuclei are also provided. The latter can eventually be useful for nucleosynthesis calculations.

Finally, an important aspect of such studies is the knowledge of cluster preformation probability. Phenomenological calculations of the preformation factors in several known alpha and cluster decays are presented.