Patterns of spin and pseudo-spin symmetries in nuclear relativistic mean-field approaches

TL;DR

This paper investigates spin and pseudo-spin symmetries in nuclear structures using a covariant relativistic mean-field approach, employing perturbative expansion to understand their behavior and differences.

Contribution

It introduces a second-order perturbative expansion within a covariant framework to analyze spin and pseudo-spin symmetry breaking in nuclear models.

Findings

Spin and pseudo-spin doublets exhibit specific A dependence.

Lower components of Dirac bi-spinors are involved in spin symmetry.

Both components are involved in pseudo-spin symmetry.

Abstract

The behavior of spin doublets is known to play a major role in nuclear structure and shell effects. Pseudo-spin doublets are also known to impact the single-particle spectrum. The covariant framework, having these two effects encoded in its approach, is an excellent tool to understand the main mechanism driving theses spin and pseudo-spin symmetries and their breaking. A perturbative expansion of the degeneracy raising related to spin and pseudo-spin effects is proposed, up to second order. It allows to understand the main behavior of spin and pseudo-spin energy doublets, such as their A dependence, as well as their common footing and differences. In the case of the spin symmetry, only the lower component of the Dirac bi-spinor is involved, whereas in the case of the pseudo-spin one, both the upper and lower components are involved. Their interplay with the covariant potentials is also analyzed.