Narrow Results

Pseudospin symmetry is an approximate relativistic symmetry of the nucleus as demonstrated by experimental data. This symmetry follows from the fact that the vector and scalar potentials of nucleons moving in a relativistic mean field are approximately equal in magnitude and opposite in sign. QCD sum rules in nuclear matter support this conclusion. Such an observation suggests a fundamental reason for pseudospin symmetry. We review the status of pseudospin symmetry conservation in the nucleon–nucleon interaction.

We review some of the empirical and theoretical evidence supporting pseudospin symmetry in nuclei as a relativistic symmetry. We show that the eigenfunctions of realistic relativistic nuclear mean fields approximately conserve pseudospin symmetry. We discuss the implications of pseudospin symmetry for magnetic dipole transitions and Gamow-Teller transitions between states in pseudospin doublets. We explore a more fundamental rationale for pseudospin symmetry in terms of quantum chromodynamics (QCD), the basic theory of the strong interactions. We show that pseudospin symmetry in nuclei implies spin symmetry for an anti-nucleon in a nuclear environment.

Pseudospin symmetry is a relativistic symmetry of the Dirac Hamiltonian. We show that the eigenfunctions of realistic relativistic nuclear mean fields approximately conserve pseudospin symmetry.

We consider properties of critical points in the interacting boson model, corresponding to flat-bottomed potentials as encountered in a second-order phase transition between spherical and deformed γ-unstable nuclei. We show that intrinsic states with an effective β-deformation reproduce the dynamics of the underlying non-rigid shapes. The effective deformation can be determined from the the global minimum of the energy surface after projection onto the appropriate symmetry. States of fixed N and good O(5) symmetry projected from these intrinsic states provide good analytic estimates to the exact eigenstates, energies and quadrupole transition rates at the critical point.

The evidence that pseudospin symmetry is a relativistic symmetry is reviewed. Search for pseudospin symmetry beyond the mean field approximation is motivated.

We review the status of quasi-degenerate doublets in nuclei, called pseudospin doublets, which were discovered about thirty years ago and the origins of which have remained a mystery, until recently. We show that pseudospin doublets originate from an SU(2) symmetry of the Dirac Hamiltonian which occurs when the sum of the scalar and vector potentials is a constant. Furthermore, we survey the evidence that pseudospin symmetry is approximately conserved in nuclear spectra and eigenfunctions and in magnetic dipole transitions for a Dirac Hamiltonian with realistic nuclear scalar and vector potentials.

Shell model states of N bosons or fermions with integer or (odd-integer)/2 angular momentum are written in terms of the elementary spinors on the sphere. This representation introduces a new quantum number which is the part of the single particle angular momentum not paired to zero. The new quantum number gives a complete labelling of the two and three-particle shell model states.

Pseudospin doublets were discovered about thirty years ago but their origins had been a mystery. We show that pseudospin doublets originate from an SU(2) symmetry of the Dirac Hamiltonian which occurs when the scalar and vector potentials are opposite in sign but equal in magnitude. Furthermore, we survey the evidence that pseudospin symmetry is approximately conserved for realistic nuclear scalar and vector potentials. We demonstrate that pseudospin symmetry is partially conserved in medium energy nucleon-nucleus scattering as well. We briefly discuss the relationship of pseudospin symmetry with chiral symmetry.

The following sections are included:

• Introduction

• Pairing Correlations in Nuclei

• Double Charge Exchange Operator

• Transition Matrix Elements

• Results And Discussion

• REFERENCES

We show that pseudospin symmetry is a symmetry of the Dirac Hamiltonian for which the sum of the scalar and vector potentials are a constant. In this paper we discuss some of the implications of this relativistic symmetry and the experimental data that support these predictions. We show that pseudo-U(3) symmetry is a symmetry of the Dirac Hamiltonian for which the sum of harmonic oscillator vector and scalar potentials are equal to a constant, and we give the generators of pseudo-U(3) symmetry. We also show that pseudospin for nuclei implies spin symmetry for anti-nucleons moving in a nuclear environment.

A generalization of the quasispin group for monopole pairing to a group which includes both monopole and quadrupole pairing is discussed. Shell model hamiltonians with monopole and quadrupole pairing are shown to have a rich variety of eigenspectra.