Pseudospin symmetry in single particle resonances in spherical square wells

TL;DR

This paper investigates the conditions under which pseudospin symmetry is conserved or broken in single particle resonances within spherical square wells, revealing threshold effects and anomalies related to potential depth variations.

Contribution

It provides a systematic analysis of pseudospin symmetry in resonant states using Jost functions, clarifying the mechanisms behind symmetry breaking and the emergence of intruder states.

Findings

Threshold effect in energy splitting observed.

Anomaly in width splitting identified.

PSS breaking linked to potential depth variations.

Abstract

The pseudospin symmetry (PSS) has been studied extensively for bound states. Recently we justified rigorously that the PSS in single particle resonant states is exactly conserved when the attractive scalar and repulsive vector potentials of the Dirac Hamiltonian have the same magnitude but opposite sign [PRL 109, 072501 (2012)]. To understand more deeply the PSS, we focus on several issues related to the exact conservation and breaking mechanism of the PSS in single particle resonances. In particular, we are interested in how the energy and width splittings of PS partners depend on the depth of the scalar and vector potentials. We investigate the asymptotic behaviors of radial Dirac wave functions. Spherical square well potentials are employed in which the PSS breaking part in the Jost function can be well isolated. By examining the zeros of Jost functions corresponding to small components of the radial Dirac wave functions, general properties of the PSS are analyzed. By examining the Jost function, the occurrence of intruder orbitals is explained and it is possible to trace continuously the PSS partners from the PSS limit to the case with a finite potential depth. The dependence of the PSS in resonances as well as in bound states on the potential depth is investigated systematically. We find a threshold effect in the energy splitting and an anomaly in the width splitting of pseudospin partners when the depth of the single particle potential varies from zero to a finite value. The conservation and the breaking of the PSS in resonant states and bound states share some similar properties. The appearance of intruder states can be explained by examining the zeros of Jost functions. Origins of the threshold effect in the energy splitting and the anomaly in the width splitting of PS partners, together with many other problems, are still open and should be further investigated.