# Spin-orbit splittings of neutron states in $N = 20$ isotones from covariant density functionals and their extensions

## TL;DR

This paper compares relativistic and nonrelativistic density functional models in predicting spin-orbit splittings of neutron states in N=20 isotones, highlighting the importance of relativistic effects in nuclear shell structure.

## Contribution

It provides a systematic comparison of spin-orbit splittings in N=20 isotones using various density functionals and experimental data, emphasizing the role of relativistic models.

## Key findings

- Relativistic models naturally produce larger spin-orbit splittings.
- Nonrelativistic models tend to underestimate splittings.
- Experimental data favor relativistic density functional predictions.

## Abstract

Spin-orbit splitting is an essential ingredient for our understanding of the shell structure in nuclei. One of the most important advantages of relativistic mean-field (RMF) models in nuclear physics is the fact that the large spin-orbit (SO) potential emerges automatically from the inclusion of Lorentz-scalar and -vector potentials in the Dirac equation. It is therefore of great importance to compare the results of such models with experimental data. We investigate the size of $2p$ and $1f$ splittings for the isotone chain $^{40}$Ca, $^{38}$Ar, $^{36}$S, and $^{34}$Si in the framework of various relativistic and nonrelativistic density functionals. They are compared with the results of nonrelativistic models and with recent experimental data.