Spin symmetry in Dirac negative energy spectrum in density-dependent relativistic Hartree-Fock theory

TL;DR

This study investigates the spin symmetry in the negative energy spectrum of Dirac particles within the density-dependent relativistic Hartree-Fock theory, revealing its origins and robustness in nuclear systems like oxygen-16.

Contribution

It is the first to analyze the spin symmetry in the negative energy spectrum using DDRHF, highlighting the role of Hartree-Fock cancellations in spin symmetry properties.

Findings

Spin symmetry is a good approximation in the negative energy spectrum of $^{16}$O.

Cancellation between Hartree and Fock terms enhances spin symmetry.

Spin-orbit splitting is influenced by Hartree-Fock cancellations even with meson-antinucleon coupling deviations.

Abstract

The spin symmetry in the Dirac negative energy spectrum and its origin are investigated for the first time within the density-dependent relativistic Hartree-Fock (DDRHF) theory. Taking the nucleus $^{16}$O as an example, the spin symmetry in the negative energy spectrum is found to be a good approximation and the dominant components of the Dirac wave functions for the spin doublets are nearly identical. In comparison with the relativistic Hartree approximation where the origin of spin symmetry lies in the equality of the scalar and vector potentials, in DDRHF the cancellation between the Hartree and Fock terms is responsible for the better spin symmetry properties and determines the subtle spin-orbit splitting. These conclusions hold even in the case when significant deviations from the G-parity values of the meson-antinucleon couplings occur.