# Pseudo-spin symmetry restoration and the in-medium balance between nuclear attractive and repulsive interactions

## TL;DR

This paper investigates how pseudo-spin symmetry is restored in nuclear systems using the relativistic Hartree-Fock approach, emphasizing the role of in-medium interactions and the $
ho$-tensor coupling in balancing nuclear forces.

## Contribution

It reveals the impact of $
ho$-tensor coupling and density-dependent isoscalar interactions on PSS restoration, providing guidance for nuclear modeling.

## Key findings

- $
ho$-tensor coupling significantly influences PSS restoration.
- Density-dependent behaviors of $g_\sigma$ and $g_\omega$ are crucial.
- Model discrepancy on PSS is verified through Fock term effects.

## Abstract

The mechanism that restores the pseudo-spin symmetry (PSS) are investigated under the relativistic Hartree-Fock (RHF) approach, by focusing on the in-medium balance between nuclear attractive and repulsive interactions. It is illustrated that the modelings of both the equilibrium of nuclear dynamics and the in-medium effects can be essentially changed by the $\rho$-tensor coupling that play the role almost fully via the Fock terms, from which the model discrepancy on the PSS restoration is verified. Specifically, the largely different density-dependent behaviors of the isoscalar coupling strengths $g_\sigma$ and $g_\omega$, deduced from the parametrization of the RHF Lagrangian PKA1, play an essential role in restoring the PSS of the high-$l'$ pseudo-spin doublets around the Fermi levels. Qualitatively, a guidance is provided for the modelings of both the equilibrium of nuclear dynamics and the in-medium effects via the PSS restoration.