[show abstract][hide abstract] ABSTRACT: We show that a Dirac Hamiltonian with equal scalar and vector harmonic oscillator potentials has not only a spin symmetry but a U(3) symmetry and that a Dirac Hamiltonian with scalar and vector harmonic oscillator potentials equal in magnitude but opposite in sign has not only a pseudospin symmetry but a pseudo-U(3) symmetry. We derive the generators of the symmetry for each case.
[show abstract][hide abstract] ABSTRACT: Recent interest in symmetries at a critical point of phase transitions in nuclei prompts a revisit to the fermion monopole and quadrupole pairing model. This model has an exactly solvable symmetry limit that is transitional between spherical nuclei and γ-unstable deformed nuclei. The eigenenergies, eigenfunctions, pairing strength, and quadrupole transtion rates in this limit are derived. Comparison with empirical quadrupole transition rates suggest that the Xe isotopes may have this symmetry.
Physical Review C 06/2005; 71(6). · 3.72 Impact Factor
[show abstract][hide abstract] ABSTRACT: 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.
Physical Review C 03/2005; 69. · 3.72 Impact Factor
[show abstract][hide abstract] ABSTRACT: Relativistic symmetries of the Dirac Hamiltonian had been discovered many years ago but only recently have these symmetries been recognized empirically in nuclear and hadronic spectroscopy. The empirical data supporting spin symmetry in hadron spectroscopy and pseudospin symmetry in nuclear spectroscopy are reviewed. Realistic relativistic mean field calculations of nuclei and QCD sum rules are reviewed and shown to support approximate pseudospin symmetry. These revelations suggest a more fundamental rationale for pseudospin symmetry motivating an investigation for pseudospin conservation in the nucleon nucleon interaction. Open questions regarding hadron spin symmetry and nuclear pseudospin symmetry are discussed.
[show abstract][hide abstract] ABSTRACT: More than thirty years ago it was observed that certain quantum energy levels in atomic nuclei were almost degenerate in energy [1View all references]. The states that are almost degenerate (quasi-degenerate) have different radial quantum numbers and different orbital angular momenta, features that made the reason for their degeneracy difficult to penetrate.
[show abstract][hide abstract] ABSTRACT: The Dirac Hamiltonian has an invariant SU(2) symmetry in two limits. For vector and scalar potentials that are equal in magnitude but opposite in sign, the Dirac Hamiltonian is invariant under pseudo-spin symmetry. Approximate pseudo-spin symmetry in nuclei was observed in nuclear spectra more than thirty years ago but its relativistic origin has only recently been discovered. The conditions on the Dirac eigenfunctions imposed by pseudo-spin symmetry are derived and tested for realistic relativistic mean field eigenfunctions. Predictions for magnetic moments and Gamow-Teller transitions and nucleon-nucleus scattering are reviewed. Pseudo-spin symmetry is connected with quark degrees of freedom via a QCD sum rule.
For vector and scalar potentials that are equal, the Dirac Hamiltonian is invariant under spin symmetry. The possibility of approximate spin symmetry occurring for an anti-nucleon in a nuclear enviroment is discussed. The exact eigenfunctions and eigenenergies for the relativistic harmonic oscillator in this limit are derived.
[show abstract][hide abstract] ABSTRACT: Pseudospin symmetry is a relativistic symmetry of the Dirac Hamiltonian with scalar and vector mean fields equal and opposite in sign. This symmetry imposes constraints on the Dirac eigenfunctions. We examine extensively the Dirac eigenfunctions of realistic relativistic mean field calculations of deformed nuclei to determine if these eigenfunctions satisfy these pseudospin symmetry constraints. Comment: 14 pages, 9 EPS figure, submitted to Phys. Rev. C; v3: 3-D figures changed to 2-D ones
Physical Review C 03/2004; 69(3):034303. · 3.72 Impact Factor
[show abstract][hide abstract] ABSTRACT: 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.
[show abstract][hide abstract] ABSTRACT: At a critical point of a second-order phase transition the intrinsic energy surface is flat and there is no stable minimum value of the deformation. However, for a finite system, we show that there is an effective deformation which can describe the dynamics at the critical point. This effective deformation is determined by minimizing the energy surface after projection onto the appropriate symmetries. We derive analytic expressions for energies and quadrupole rates which provide good estimates for these observables at the critical point.
[show abstract][hide abstract] ABSTRACT: Using relations between wave functions obtained in the framework of the relativistic mean field theory, we investigate the effects of pseudospin and spin symmetry breaking on the single nucleon wave functions in spherical nuclei. In our analysis, we apply both relativistic and non-relativistic self-consistent models as well as the harmonic oscillator model. Comment: 6 pages, 3 postscript figures, submitted to Phys. Rev. C
[show abstract][hide abstract] ABSTRACT: The orthogonal transformation from the spin representation to the pseudospin representation for the nucleon-nucleon scattering matrix is derived. The phase shifts and mixing angles are calculated in the pseudospin representation using the measured phase shifts and mixing angles in the spin representation. The scattering matrix in both representations is investigated and the extent of spin and pseudospin symmetry violation is determined. Finally, a speculation is made that the pseudospin symmetry generators relevant for relativistic mean field models and optical models may need to be generalized for the two-nucleon interaction.
[show abstract][hide abstract] ABSTRACT: Pseudospin symmetry imposes conditions on the Dirac eigenfunctions independent of the potentials, from triaxial to spherical potentials. The general conditions on the relativistic mean field eigenfunctions in the pseudospin symmetry limit are derived. For the upper components, these conditions include differential realtions. These differential realtions are tested for realistic eigenfunctions in the spherical symmetry limit.
Physical Review C 01/2002; 66(6). · 3.72 Impact Factor
[show abstract][hide abstract] ABSTRACT: 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.
[show abstract][hide abstract] ABSTRACT: We review recent developments that show that pseudospin symmetry is an approximate relativistic symmetry of the Dirac Hamiltonian with realistic nuclear mean field potentials.
[show abstract][hide abstract] ABSTRACT: 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.
[show abstract][hide abstract] ABSTRACT: A generalized M1 sum rule for orbital magnetic dipole strength from excited symmetric states to mixed-symmetry states is considered within the proton-neutron interacting boson model of even-even nuclei. Analytic expressions for the dominant terms in the B(M1) transition rates from the first and second $2^+$ states are derived in the U(5) and SO(6) dynamic symmetry limits of the model, and the applicability of a sum rule approach is examined at and in-between these limits. Lastly, the sum rule is applied to the new data on mixed-symmetry states of 94Mo and a quadrupole d-boson ratio $nd(0^+_1)/nd(2^+_2) \approx 0.6$ is obtained in a largely parameter-independent way Comment: 19 pages, 3 figures, Revtex
[show abstract][hide abstract] ABSTRACT: The identification of pseudospin symmetry as a relativistic symmetry of the Dirac Hamiltonian is used to explain the structure of radial nodes occurring in pseudospin doublets and to illuminate the special status of nodeless intruder states in nuclei.
[show abstract][hide abstract] ABSTRACT: Experimental data indicate small spin-orbit splittings in hadrons. For heavy-light mesons we identify a relativistic symmetry that suppresses these splittings. We suggest an experimental test in electron-positron annihilation. Furthermore, we argue that the dynamics necessary for this symmetry are possible in QCD.