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

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

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

F-spin as a Partial Symmetry

We use the empirical evidence that F-spin multiplets exist in nuclei for only selected states as an indication that F-spin can be regarded as a partial symmetry. We show that there is a class of non-F-scalar IBM-2 Hamiltonians with partial F-spin symmetry, which reproduce the known systematics of collective bands in nuclei. These Hamiltonians predict that the scissors states have good F-spin and form F-spin multiplets, which is supported by the existing data.Comment: 14 pages, 1 figur