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

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

Violation of pseudospin symmetry in nucleon-nucleus scattering: exact relations

An exact determination of the size of the pseudospin symmetry violating part of the nucleon-nucleus scattering amplitude from scattering observables is presented. The approximation recently used by Ginocchio turns out to underestimate the violation of pseudospin symmetry. Nevertheless the conclusion of a modestly broken pseudospin symmetry in proton-208Pb scattering at EL=800MeV remains valid.Comment: 8 pages, 2 figure

Test of Nuclear Wave Functions for Pseudospin Symmetry

Using the fact that pseudospin is an approximate symmetry of the Dirac Hamiltonian with realistic scalar and vector mean fields, we derive the wave functions of the pseudospin partners of eigenstates of a realistic Dirac Hamiltonian and compare these wave functions with the wave functions of the Dirac eigenstates.Comment: 11 pages, 4 figures, minor changes in text and figures to conform with PRL requirement

Isospin relations for four nucleons in a single j shell

We had previously used techniques involving isospin to count the number of states for three identical fermions in a single j shell with total angular momentum I=j. We generalize this to all I, but the main thrust of this work is to consider now a 4-fermion system. As before, one evaluates the eigenvalues of the Hamiltonian \sum_{i<j}[a + bt(i)t(j)] both from an isospin point of view and an angular momentum point of view. In the 4-particle case, we get a more limited result than in the 3-particle case, namely the number of T=0 states minus twice the number of T=2 states, all of a given angular momentum I.Comment: 6 pages, RevTex

An intrinsic state for an extended version of the interacting boson model

An intrinsic-state formalism for IBM-4 is presented. A basis of deformed bosons is introduced which allows the construction of a general trial wave function which has Wigner's spin-isospin SU(4) symmetry as a particular limit. Intrinsic-state calculations are compared with exact ones showing good agreement.Comment: 12 pages, TeX (ReVTeX). Content changed. Accepted in Phys. Rev.

Relativistic U(3) Symmetry and Pseudo-U(3) Symmetry of the Dirac Hamiltonian

The Dirac Hamiltonian with relativistic scalar and vector harmonic oscillator potentials has been solved analytically in two limits. One is the spin limit for which spin is an invariant symmetry of the the Dirac Hamiltonian and the other is the pseudo-spin limit for which pseudo-spin is an invariant symmetry of the the Dirac Hamiltonian. The spin limit occurs when the scalar potential is equal to the vector potential plus a constant, and the pseudospin limit occurs when the scalar potential is equal in magnitude but opposite in sign to the vector potential plus a constant. Like the non-relativistic harmonic oscillator, each of these limits has a higher symmetry. For example, for the spherically symmetric oscillator, these limits have a U(3) and pseudo-U(3) symmetry respectively. We shall discuss the eigenfunctions and eigenvalues of these two limits and derive the relativistic generators for the U(3) and pseudo-U(3) symmetry. We also argue, that, if an anti-nucleon can be bound in a nucleus, the spectrum will have approximate spin and U(3) symmetry.Comment: Submitted to the Proceedings of "Tenth International Spring Seminar-New Quests in Nuclear Structure", 6 page

Alternate Derivation of Ginocchio-Haxton relation [(2j+3)/6]

We address the problem, previously considered by Ginocchio and Haxton (G-H), of the number of states for three identical particles in a single j-shell with angular momentum J=j. G-H solved this problem in the context of the quantum Hall effect. We address it in a more direct way. We also consider the case J=j+1 to show that our method is more general, and we show how to take care of added complications for a system of five identical particles.Comment: 7 pages, RevTeX4; submitted to Phys. Rev.