Pseudospin Dynamical Symetry in Nuclei

TL;DR

This paper reviews the relativistic origin of pseudospin symmetry in nuclei, its conditions, and implications, including partial symmetry and its connection to spin symmetry in anti-nucleon scattering.

Contribution

It provides a comprehensive review of the relativistic basis of pseudospin symmetry and explores conditions for its partial realization in nuclei.

Findings

Pseudospin symmetry is linked to the Dirac Hamiltonian with specific scalar and vector potentials.

Approximate pseudospin symmetry predicts approximate spin symmetry in anti-nucleon scattering.

Conditions for partial pseudospin symmetry depend on the smallness of the sum of scalar and vector potentials.

Abstract

Pseudospin symmetry has been useful in understanding atomic nuclei. We review the arguments that this symmetry is a relativistic symmetry. The condition for this symmetry is that the sum of the vector and scalar potentials in the Dirac Hamiltonian is a constant. We give the generators of pseudospin symmetry. We review some of the predictions that follow from this insight into the relativistic origins of pseudospin symmetry. Since in nuclei the sum of the scalar and vector potentials is not zero but is small, we discuss preliminary investigations into the conditions on the potentials to produce partial dynamic pseudospin symmetry. Finally we show that approximate pseudospin symmetry in nuclei predicts approximate spin symmetry in anti-nucleon scattering from nuclei.