Conservation and breaking of pseudospin symmetry

TL;DR

This paper explores how pseudospin symmetry (PSS) is conserved or broken in single-nucleon resonant states using Green's function method, revealing the conditions and effects of PSS restoration and breaking.

Contribution

It introduces a novel Green's function approach to analyze PSS in resonant states, providing detailed insights into the evolution of PSS with potential depth.

Findings

PSS is exactly conserved when scalar and vector potentials are equal and opposite.

PSS breaking occurs gradually with increasing potential depth.

Density distributions and resonant parameters reflect PSS restoration and breaking.

Abstract

Pseudospin symmetry (PSS) is a relativistic dynamical symmetry connected with the lower component of the Dirac spinor. Here, we investigate the conservation and breaking of PSS in the single-nucleon resonant states, as an example, using Green's function method that provides a novel way to precisely describe not only the resonant energies and widths but also the spacial density distributions for both narrow and wide resonances. The PSS restoration and breaking are perfectly displayed in the evolution of resonant parameters and density distributions with the potential depth: In the PSS limit, i.e., when the attractive scalar and repulsive vector potentials have the same magnitude but opposite sign, PSS is exactly conserved with strictly the same energy and width between the PS partners as well as identical density distributions of the lower components. As the potential depth increases, the PSS is broken gradually with energy and width splittings and a phase shift in the density distributions.