Charge radii of Sn isotopes in the relativistic mean field approximation

TL;DR

This study investigates the kink in Sn isotopes' charge radii around N=82 using the relativistic mean-field model, highlighting the role of Dirac spinor components and spin-orbit partner states.

Contribution

It reveals the importance of small components of Dirac spinors and spin-orbit partners in explaining the charge radius kink in Sn isotopes within the RMF framework.

Findings

Small components of Dirac spinors influence the charge radius.

Differences in spin-orbit partner states affect neutron contribution.

Small components alone do not fully explain the observed kink.

Abstract

The kink observed in the nuclear charge radius of Sn isotopes around neutron number $N = 82$ is investigated within the relativistic mean-field (RMF) framework using the NL3$^*$ parameter set. It is shown that the small components of the Dirac spinors for the neutron single-particle states near the Fermi level play a crucial role in forming the kink through their contribution to the proton central potential. In particular, the significant differences between the radial parts of the small components of spin-orbit partner states make neutrons with $j = l - 1/2$ more efficient in increasing the nuclear charge radius than those with $j = l + 1/2$. However, the effect induced by the small components alone does not fully account for the magnitude of the kink observed in Sn isotopes.