A Relativistic Symmetry in Nuclei: Its origins and consequences

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 nucleon-nucleus scattering for a Dirac Hamiltonian with realistic nuclear scalar and vector potentials.Comment: Invited Talk for "Nuclei and Nucleons", Darmstadt, Germany, Oct. 11-13,2000; International Symposium on the occasion of Achim Richter's 60th Birthda

Pseudo-spin symmetry in density-dependent relativistic Hartree-Fock theory

The pseudo-spin symmetry (PSS) is investigated in the density-dependent relativistic Hartree-Fock theory by taking {the} doubly magic nucleus $^{132}$Sn as a representative. It is found that the Fock terms bring significant contributions to the pseudo-spin orbital potentials (PSOP) and make it comparable to the pseudo-centrifugal barrier (PCB). However, these Fock terms in the PSOP are counteracted by other exchange terms due to the non-locality of the exchange potentials. The pseudo-spin orbital splitting indicates that the PSS is preserved well for the partner states \lrb{\nu 3s_{1/2}, \nu2d_{3/2}} of $^{132}$Sn in the relativistic Hartree-Fock theory.Comment: 6 figue

Dynamical symmetries of two-dimensional systems in relativistic quantum mechanics

The two-dimensional Dirac Hamiltonian with equal scalar and vector potentials has been proved commuting with the deformed orbital angular momentum $L$. When the potential takes the Coulomb form, the system has an SO(3) symmetry, and similarly the harmonic oscillator potential possesses an SU(2) symmetry. The generators of the symmetric groups are derived for these two systems separately. The corresponding energy spectra are yielded naturally from the Casimir operators. Their non-relativistic limits are also discussed.Comment: 3 pages, Accepted by Annals of Physics (New York

Relativistic Pseudospin Symmetry in Nuclei

We review recent developments that show that pseudospin symmetry is an approximate relativistic symmetry of the Dirac Hamiltonian with realistic nuclear mean field potentials.Comment: 8 pages, 5 figures, Proc. NATO Advanced Research Workshop, The Nuclear Many-Body Problem 2001, Brijuni, Pula, Croatia, June 2-5, 200

Critical Points in Nuclei and Interacting Boson Model Intrinsic States

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 $\gamma$-unstable nuclei. We show that intrinsic states with an effective $\beta$-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.Comment: 10 pages, 3 figures, Proc. Int. Conf. on "Symmetry in Physics", March 23-30, 2003, Erice, Ital

On the Relativistic Foundations of Pseudospin Symmetry in Nuclei

We show that the generators of pseudospin symmetry are the non - relativistic limit of the generators of an SU(2) symmetry which leaves invariant the Dirac Hamiltonian with scalar and vector potentials equal in magnitude but opposite in sign, $V_V = - V_S$. Furthermore, within this framework, we demonstrate that this symmetry may be approximately conserved for realistic scalar and vector potentials.Comment: 11 pages, Revtex, Phys. Lett. B, in pres

Relativistic Pseudospin Symmetry and the Structure of Nuclear States

We show that a natural explanation for characteristic features (angular momentum and radial quantum numbers) of pseudospin doublets and intruder levels in nuclei can be obtained by combining the relativistic attributes of pseudospin symmetry with known properties of Dirac bound states.Comment: 6 pages, 6 figures, Proc. NATO Advanced Research Workshop, "The Nuclear Many-Body Problem 2001, Brijuni, Pula, Croatia, June 2-5, 200

Confinement of spinless particles by Coulomb potentials in two-dimensional space-time

The problem of confinement of spinless particles in 1+1 dimensions is approached with a linear potential by considering a mixing of Lorentz vector and scalar couplings. Analytical bound-states solutions are obtained when the scalar coupling is of sufficient intensity compared to the vector coupling.Comment: 14 pages, 2 figure