Formation region of emitted α and heavier particles inside radioactive nuclei

Abstract

We investigate the formation distance (R0) from the center of the radioactive parent nucleus at which the emitted cluster is most probably formed. The calculations are performed microscopically starting with the solution to the time-independent Schrödinger wave equation for the cluster-core system, using nuclear potentials based on the Skyrme-SLy4 nucleon-nucleon interactions and folding Coulomb potential, to determine the incident and transmitted wave functions of the system. Our results show that the emitted cluster is mostly formed in the pre-surface region of the nucleus, under the effect of Pauli blocking from the saturated core density. The deeper α-formation distance inside the nucleus allows less preformation probability and indicates a more stable nucleus for a longer half-life. Furthermore, the α-particle tends to be formed at a slightly deeper region inside the nuclei, with larger isospin asymmetry, and in the closed shell nuclei. Regarding the heavy clusters, we observed that the formation distance of the emitted clusters heavier than α-particle increased via increasing the isospin asymmetry of the formed cluster rather than by increasing its mass number. The partial half-life of a certain cluster-decay mode increased with increase of either the mass number or the isospin asymmetry of the emitted cluster.