[Show abstract][Hide abstract] ABSTRACT: Pseudospin symmetry has been useful in understanding atomic nuclei. We review
the arguments that this symmetry is a relativistic symmetry. The condition for
this symmetry is that the sum of the vector and scalar potentials in the Dirac
Hamiltonian is a constant. We give the generators of pseudospin symmetry. We
review some of the predictions that follow from this insight into the
relativistic origins of pseudospin symmetry. Since in nuclei the sum of the
scalar and vector potentials is not zero but is small, we discuss preliminary
investigations into the conditions on the potentials to produce partial dynamic
pseudospin symmetry. Finally we show that approximate pseudospin symmetry in
nuclei predicts approximate spin symmetry in anti-nucleon scattering from
nuclei.
Journal of Physics Conference Series 10/2014; 580(1). DOI:10.1088/1742-6596/580/1/012036
[Show abstract][Hide abstract] ABSTRACT: Jerry Draayer has worked in approximate pseudospin and pseudo- U(3)
symmetry in nuclei in the non-relativistic shell model. We show that
pseudospin symmetry is a SU(2) relativistic symmetry of the Dirac
Hamiltonian for which the sum of the vector and scalar potentials is a
constant. We show that the Dirac Hamiltonian for which the sum of the
vector harmonic oscillator potential and a scalar harmonic oscillator is
a constant has a pseudo-U(3) symmetry and we derive the generators for
this symmetry.
Journal of Physics Conference Series 12/2012; 403(1):2004-. DOI:10.1088/1742-6596/403/1/012004
[Show abstract][Hide abstract] ABSTRACT: We show that pseudospin symmetry is a SU(2) symmetry of the Dirac
Hamiltonian for which the vector and scalar potentials are equal in
magnitude but opposite in sign. We give some experimental implications
of this insight for atomic nuclei. We show that the Dirac Hamiltonian
that has a vector harmonic oscillator potential equal but opposite in
sign of the scalar potential has a pseudo-U(3) symmetry and we derive
the generators for this symmetry.
[Show abstract][Hide abstract] ABSTRACT: We show that the pseudospin symmetry that Akito Arima discovered many
years ago (with collaborators) is a symmetry of the the Dirac
Hamiltonian for which the sum of the scalar and vector potentials are a
constant. In this paper we discuss some of the implications of this
relativistic symmetry and the experimental data that support these
predictions. In his original paper Akito also discussed pseudo-U(3)
symmetry. We show that pseudo-U(3) symmetry is a symmetry of the Dirac
Hamiltonian for which the sum of harmonic oscillator vector and scalar
potentials are equal to a constant, and we give the generators of
pseudo-U(3) symmetry. Going beyond the mean field we summarize new
results on non relativistic shell model Hamiltonians that have
pseudospin symmetry and pseudo-orbital angular momentum symmetry as a
dynamical symmetries.
[Show abstract][Hide abstract] ABSTRACT: 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 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.
Journal of Physics Conference Series 02/2011; 267(1):012037. DOI:10.1088/1742-6596/267/1/012037
[Show abstract][Hide abstract] ABSTRACT: We review some of the empirical and theoretical evidence supporting pseudospin symmetry in nuclei as a relativistic symmetry. We review the case that the eigenfunctions of realistic relativistic nuclear mean fields approximately conserve pseudospin symmetry in nuclei. We discuss the implications of pseudospin symmetry for magnetic dipole transitions and Gamow-Teller transitions between states in pseudospin doublets. We explore a more fundamental rationale for pseudospin symmetry in terms of quantum chromodynamics (QCD), the basic theory of the strong interactions. We show that pseudospin symmetry in nuclei implies spin symmetry for an anti-nucleon in a nuclear environment. We also discuss the future and what role pseudospin symmetry may be expected to play in an effective field theory of nucleons.
Journal of Physics Conference Series 12/2007; 87(1):012011. DOI:10.1088/1742-6596/87/1/012011
[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: 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: 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 gamma-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). DOI:10.1103/PhysRevC.71.064325 · 3.73 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). DOI:10.1103/PhysRevC.69.034318 · 3.73 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Pseudospin symmetry is a relativistic symmetry of the Dirac Hamiltonian. We show that the eigenfunctions of realistic relativistic nuclear mean fields approximately conserve pseudospin symmetry.
[Show abstract][Hide abstract] ABSTRACT: Pseudospin symmetry is an approximate relativistic symmetry of the nucleus as demonstrated by experimental data. This symmetry follows from the fact that the vector and scalar potentials of nucleons moving in a relativistic mean field are approximately equal in magnitude and opposite in sign. QCD sum rules in nuclear matter support this conclusion. Such an observation suggests a fundamental reason for pseudospin symmetry. We review the status of pseudospin symmetry conservation in the nucleon-nucleon interaction.
International Journal of Modern Physics E 02/2005; 14(1):105-110. DOI:10.1142/S0218301305002825 · 1.34 Impact Factor
[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. DOI:10.1103/PhysRevC.69.034303 · 3.73 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: We investigate Hamiltonians with attractive interactions between pairs of fermions coupled to angular momentum J. We show that pairs with spin J are reasonable building blocks for the low-lying states. For systems with only a J = Jmax pairing interaction, eigenvalues are found to be approximately integers for a large array of states, in particular for those with total angular momenta I le 2j. For I=0 eigenstates of four fermions in a single-j shell we show that there is only one non-zero eigenvalue. We address these observations using the nucleon pair approximation of the shell model and relate our results with a number of currently interesting problems. Comment: a latex text file and 2 figures, to be published
Physical Review C 05/2003; 68(4). DOI:10.1103/PhysRevC.68.044320 · 3.73 Impact Factor
[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
Physical Review C 01/2003; 68(1). DOI:10.1103/PhysRevC.68.014304 · 3.73 Impact Factor
[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 12/2002; 66(6). DOI:10.1103/PhysRevC.66.064312 · 3.73 Impact Factor