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

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

New insight on pseudospin doublets in nuclei

The relevance of the pseudospin symmetry in nuclei is considered. New insight is obtained from looking at the continuous transition from a model satisfying the spin symmetry to another one satisfying the pseudospin symmetry. This study suggests that there are models allowing no missing single-particle states in this transition, contrary to what is usually advocated. It rather points out to an association of pseudospin partners different from the one usually assumed, together with a strong violation of the corresponding symmetry. A comparison with results obtained from some relativistic approaches is made.Comment: 27 pages, 18 figure

Algebraic-eikonal approach to medium energy proton scattering from odd-mass nuclei

We extend the algebraic-eikonal approach to medium energy proton scattering from odd-mass nuclei by combining the eikonal approximation for the scattering with a description of odd-mass nuclei in terms of the interacting boson-fermion model. We derive closed expressions for the transition matrix elements for one of the dynamical symmetries and discuss the interplay between collective and single-particle degrees of freedom in an application to elastic and inelastic proton scattering from $^{195}$Pt.Comment: latex, 14 pages, 4 figures uuencoded, to be published in Physical Review

Dynamical Symmetries of Dirac Hamiltonian

Several dynamical symmetries of the Dirac Hamiltonian are reviewed in a systematic manner and the conditions under which such symmetries hold. These include relativistic spin and orbital angular momentum symmetries, SO(4)\times SU_{\sigma}(2) symmetry for the Dirac Hydrogen atom, SU(3)\times SU_{\sigma}(2) symmetry for the relativistic simple harmonic oscillator. The energy spectrum in each case is calculated from group-theoretic considerations.Comment: 15 pages, V3 typos removed and some new material include

Relativistic Mean Field Approach and the Pseudo-Spin Symmetry

Based on the Relativistic Mean Field (RMF) approach the existence of the broken pseudo-spin symmetry is investigated. Both spherical RMF and constrained deformed RMF calculations are carried out employing realistic Lagrangian parameters for spherical and for deformed sample nuclei. The quasi - degenerate pseudo-spin doublets are confirmed to exist near the fermi surface for both spherical and deformed nuclei.Comment: 9 pages RevTex, 4 p.s figures, to appear in Phys. Rev. C as R.

A First-Landau-Level Laughlin/Jain Wave Function for the Fractional Quantum Hall Effect

We show that the introduction of a more general closed-shell operator allows one to extend Laughlin's wave function to account for the richer hierarchies (1/3, 2/5, 3/7 ...; 1/5, 2/9, 3/13, ..., etc.) found experimentally. The construction identifies the special hierarchy states with condensates of correlated electron clusters. This clustering implies a single-particle (ls)j algebra within the first Landau level (LL) identical to that of multiply filled LLs in the integer quantum Hall effect. The end result is a simple generalized wave function that reproduces the results of both Laughlin and Jain, without reference to higher LLs or projection.Comment: Revtex. In this replacement we show how to generate the Jain wave function explicitly, by acting with the generalized ls closed-shell operator discussed in the original version. We also walk the reader through a classical 1d caricature of this problem so that he/she can better understand why 2s+1, where s is the spin, should be associated with the number of electrons associated with the underlying clusters or composites. 11 page

Implications of Pseudospin Symmetry on Relativistic Magnetic Properties and Gamow - Teller Transitions in Nuclei

Recently it has been shown that pseudospin symmetry has its origins in a relativistic symmetry of the Dirac Hamiltonian. Using this symmetry we relate single - nucleon relativistic magnetic moments of states in a pseudospin doublet to the relativistic magnetic dipole transitions between the states in the doublet, and we relate single - nucleon relativistic Gamow - Teller transitions within states in the doublet. We apply these relationships to the Gamow - Teller transitions from $^{39}Ca$ to its mirror nucleus $^{39}K$.Comment: 17 pages, 2 figures, to be published in PRC. Slightly revised text with one reference adde

Generator Coordinate Truncations

We investigate the accuracy of several schemes to calculate ground-state correlation energies using the generator coordinate technique. Our test-bed for the study is the $sd$ interacting boson model, equivalent to a 6-level Lipkin-type model. We find that the simplified projection of a triaxial generator coordinate state using the $S_3$ subgroup of the rotation group is not very accurate in the parameter space of the Hamiltonian of interest. On the other hand, a full rotational projection of an axial generator coordinate state gives remarkable accuracy. We also discuss the validity of the simplified treatment using the extended Gaussian overlap approximation (top-GOA), and show that it works reasonably well when the number of boson is four or larger.Comment: 19 pages, 6 eps figure

Relativistic Harmonic Oscillator with Spin Symmetry

The eigenfunctions and eigenenergies for a Dirac Hamiltonian with equal scalar and vector harmonic oscillator potentials are derived. Equal scalar and vector potentials may be applicable to the spectrum of an antinucleion imbedded in a nucleus. Triaxial, axially deformed, and spherical oscillator potentials are considered. The spectrum has a spin symmetry for all cases and, for the spherical harmonic oscillator potential, a higher symmetry analogous to the SU(3) symmetry of the non-relativistic harmonic oscillator is discussed