The formation region of emitted $\alpha$ and heavier particles inside radioactive nuclei

TL;DR

This study microscopically analyzes where within radioactive nuclei alpha and heavier particles are most likely formed, revealing their formation regions and how these relate to nuclear stability and composition.

Contribution

It introduces a microscopic method to determine the formation distance of emitted clusters inside nuclei, considering nuclear potential and wave functions, and links formation regions to nuclear stability and composition.

Findings

Clusters are mostly formed in the pre-surface region of nuclei.

Deeper formation distances correlate with longer half-lives.

Formation distance increases with isospin asymmetry for heavier clusters.

Abstract

We investigate the formation distance ($R_0$) from the center of the radioactive parent nucleus at which the emitted cluster is most probably formed. The calculations are microscopically performed starting from solving the time-independent Schr\"{o}dinger wave equation for the $\alpha$-core system, using nuclear potential based on the Skyrme-SLy4 nucleon-nucleon interaction and folding Coulomb potential, to determine the incident and transmitted wave functions of the system. Our results advocate 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 $\alpha$-formation distance inside the nucleus gives rise to less preformation probability, and indicates more stable nucleus of longer half-life. Also, the $\alpha$-particle tends to be formed at a bit deeper region inside the nuclei having larger isospin asymmetry and in the closed shell nuclei. Regarding the emitted nuclei heavier than $\alpha$-particle, we find that the formation distance of the emitted clusters heavier than $\alpha$-particle increases with increasing the isospin asymmetry of the formed cluster, rather than with increasing its mass number. The partial half-life of a certain cluster-decay mode increases upon increasing either the mass number or the isospin asymmetry of the emitted cluster.