Proton and neutron skins and symmetry energy of mirror nuclei

TL;DR

This paper explores the relationship between neutron skins and symmetry energy in mirror nuclei using theoretical models, providing new insights into nuclear structure and the density dependence of symmetry energy.

Contribution

It introduces a comprehensive analysis of neutron and proton skins in mirror nuclei, linking them to symmetry energy characteristics with novel theoretical predictions and correlations.

Findings

Neutron skin thickness correlates with symmetry energy parameters.

Proton skins are predicted for several mirror pairs.

Results show consistent behavior across different nuclear models.

Abstract

The neutron skin of nuclei is an important fundamental property, but its accurate measurement faces many challenges. Inspired by charge symmetry of nuclear forces, the neutron skin of a neutron-rich nucleus is related to the difference between the charge radii of the corresponding mirror nuclei. We investigate this relation within the framework of the Hartree-Fock-Bogoliubov method with Skyrme interactions. Predictions for proton skins are also made for several mirror pairs in the middle mass range. For the first time the correlation between the thickness of the neutron skin and the characteristics related with the density dependence of the nuclear symmetry energy is investigated simultaneously for nuclei and their corresponding mirror partners. As an example, the Ni isotopic chain with mass number $A=48-60$ is considered. These quantities are calculated within the coherent density fluctuation model using Brueckner and Skyrme energy-density functionals for isospin asymmetric nuclear matter with two Skyrme-type effective interactions, SkM* and SLy4. Results are also presented for the symmetry energy as a function of $A$ for a family of mirror pairs from selected chains of nuclei with $Z=20$, $N=14$, and $N=50$. The evolution curves show a similar behavior crossing at the $N=Z$ nucleus in each chain and a smooth growing deviation when $N\neq Z$ starts. Comparison of our results for the radii and skins with those from the calculations based on high-precision chiral forces is made.