Exact conservation and breaking of pseudospin symmetry in single particle resonant states

TL;DR

This paper investigates pseudospin symmetry in single particle resonant states within nuclei, demonstrating conditions for its exact conservation and breaking using relativistic quantum models and specific potential examples.

Contribution

It provides a rigorous justification for pseudospin symmetry in resonant states and analyzes its conservation and breaking in different potential models.

Findings

PSS is conserved when scalar and vector potentials are equal in magnitude and opposite in sign.

Exact conservation and breaking of PSS are demonstrated in spherical square-well and Woods-Saxon potentials.

Resonant states exhibit pseudospin symmetry under specific relativistic potential conditions.

Abstract

In this contribution we present some results on the study of pseudospin symmetry (PSS) in single particle resonant states. The PSS is a relativistic dynamical symmetry connected with the small component of the nucleon Dirac wave function. Many efforts have been made to study this symmetry in bound states. We recently gave a rigorous justification of the PSS in single particle resonant states by examining the zeros of Jost functions corresponding to the small components of the radial Dirac wave functions and phase shifts of continuum states [1, Phys. Rev. Lett. 109 (2012) 072501]. We have shown that the PSS in single particle resonant states in nuclei is conserved when the attractive scalar and repulsive vector potentials have the same magnitude but opposite sign. Examples of exact conservation and breaking of this symmetry in single particle resonances are given for spherical square-well and Woods-Saxon potentials.