α -particle formation and clustering in nuclei

Abstract

The nucleonic localization function has been used for a decade to study the formation of $\ensuremath{\alpha}$ particles in nuclei, by providing a measure of having nucleons of a given spin in a single place. However, differences in interpretation remain, compared to the nucleonic density of the nucleus. In order to better understand the respective role of the nucleonic localization function and the densities in the $\ensuremath{\alpha}$-particle formation in cluster states or in the $\ensuremath{\alpha}$-decay mechanism, both an analytic approximation and microscopic calculations, using energy density functionals, are undertaken. The nucleonic localization function is shown to measure the anticentrifugal effect, and is not sensitive to the level of compactness of the $\ensuremath{\alpha}$ particle itself. It probes the purity of the spatial overlap of four nucleons in the four possible (spin, isospin) states. The density provides, in addition, information on the compactness of an $\ensuremath{\alpha}$-particle cluster. The respective roles of the nucleonic localization function and the density are also analyzed in the case of $\ensuremath{\alpha}$ particle emission. More generally, criteria to assess the prediction of $\ensuremath{\alpha}$ cluster in nuclear states are provided.