Pseudospin Dynamical Symmetry in Nuclei

Joseph N Ginocchio

doi:10.1088/1742-6596/580/1/012036

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.

Highlights

Fifty years ago Aldo and I first met at Rutgers University
We have remained in touch primarily through the 10 seminars in nuclear physics that he has organized in different venues in and near the Bay of Naples for the last 28 years
It comes as a surprise that pseudospin symmetry in nuclei is a relativistic symmetry

Summary

Introduction

Fifty years ago Aldo and I first met at Rutgers University. We both were starting our first post-doctoral appointments. About five years after our post-doctoral appointments at Rutgers, a quasi-degeneracy in the single nucleon states of spherical nuclei with quantum numbers (n lj, n′l′j′) was discovered [1, 2], where n′ = n − 1, l′ = l + 2, j′ = j + 1 and n, l, j are the radial, orbital angular momentum, and total angular momentum quantum numbers, respectively. These quasi-degeneracies persist in recent measurements in nuclei far from stability [3]. Hamiltonian [5, 6]

Symmetries of the Dirac Hamiltonian

Conclusions