A shell model mass formula for exotic light nuclei

TL;DR

This paper develops an analytic shell model mass formula tailored for light nuclei, incorporating their unique charge distributions and shell features, and explores implications for nuclear structure near the neutron drip line.

Contribution

It introduces a novel phenomenological shell model mass formula that accounts for the specific properties of light nuclei and their behavior near the neutron drip line.

Findings

The formula fits light nuclei masses well with parameters consistent with optical models.

A correlation between the skin effect and optical potential symmetry is established.

Potential well depth and shell gaps decrease near the neutron drip line, affecting nuclear structure.

Abstract

An analytic phenomenological shell model mass formula for light nuclei is constructed., The formula takes into account the non locality of the self consistent single particle potential and the special features of light nuclei, namely: a) charge and mass distributions are closer to a Gaussian shape than to the shape characteristic in medium and heavy nuclei; b) the central charge and mass densities are larger than, and decrease towards, the "asymptotic" values that are the reference parameters for nuclear matter; and c) after a shell closure, the next level has a larger orbital angular momentum and a noticeably larger mean square radius. Only then a good numerical fit is obtained with parameters consistent with optical model analysis and empirical spin-orbit couplings. A correlation between the "skin effect" and the symmetry dependence of the optical potential is established. Towards the neutron drip line the potential well depth, the spin-orbit splitting of the single particle levels and the gap between major shells decrease, as has been observed. The ensuing shift and contraction of the single particle level scheme may lead to: a) to strong configuration mixing and new magic numbers, and b) the onset of the halo effect, to avoid the expulsion of single particle levels to the continuum.