# A systematic study of the factors affecting central depletion in nuclei

## TL;DR

This study systematically investigates how various relativistic mean-field models predict central proton density depletion in nuclei with specific neutron numbers, revealing model dependence and limited impact on neutron-skin thickness trends.

## Contribution

It provides a comprehensive analysis of central depletion factors across different RMF models, highlighting the role of nuclear shape and model specifics in depletion phenomena.

## Key findings

- Central depletion disappears in deformed nuclei regardless of 2s_{1/2} occupancy.
- Model-dependent variations in spin-orbit potential influence depletion.
- Central depletion has minimal effect on neutron-skin thickness trends.

## Abstract

A systematic study of the central depletion of proton density has been performed in the isotonic chains of nuclei with neutron numbers $N = 20$ and $28$ using different variants of the relativistic mean-field (RMF) models. These models include either the non-linear contributions from the mesons with the coupling constants being density independent or the non-linearity of the mesonic fields realized through the density dependent coupling strengths. The central depletion in deformed nuclei tends to disappear irrespective of the occupancy of $2s_{1/2}$ state in contrast to the spherical nuclei in which the unoccupancy of $2s_{1/2}$ state leads to the central depletion. Due to the differences in the strength of spin-orbit potentials in these models, the central depletions are found to be model dependent. The influence of the central depletion on the neutron-skin thickness is also investigated. It appears that the effects of the central depletion do not percolate far enough to display its finger prints on the trends of the neutron-skin thickness.