Alpha-particle formation and clustering in nuclei

TL;DR

This paper investigates the roles of the nucleonic localization function and density in alpha-particle formation and clustering in nuclei, clarifying their interpretations and providing criteria for predicting alpha-clusters.

Contribution

It offers a detailed analysis of how the nucleonic localization function and density relate to alpha-cluster formation, using both analytic and microscopic calculations.

Findings

The localization function measures anti-centrifugal effects, not alpha compactness.

Density indicates the compactness of alpha-particle clusters.

Criteria for predicting alpha-clusters in nuclear states are established.

Abstract

The nucleonic localization function has been used for a decade to study the formation of 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 alpha-particle formation in cluster states or in 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 anti-centrifugal effect, and is not sensitive to the level of compactness of the 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 alpha-particle cluster. The respective roles of the nucleonic localization function and the density are also analyzed in the case of alpha-particle emission. More generally, criteria to assess the prediction of alpha-cluster in nuclear states are provided.