Publications (100)382.15 Total impact
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ABSTRACT: Jerry Draayer has worked in approximate pseudospin and pseudo U(3) symmetry in nuclei in the nonrelativistic 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 pseudoU(3) symmetry and we derive the generators for this symmetry.Journal of Physics Conference Series 12/2012; 403(1):2004.  [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 pseudospin limit for which pseudospin 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 nonrelativistic harmonic oscillator, each of these limits has a higher symmetry. For example, for the spherically symmetric oscillator, these limits have a U(3) and pseudoU(3) symmetry respectively. We shall discuss the eigenfunctions and eigenvalues of these two limits and derive the relativistic generators for the U(3) and pseudoU(3) symmetry. We also argue, that, if an antinucleon 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. 
Article: A relativistic symmetry in nuclei
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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 GamowTeller 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 antinucleon 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.  [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 pseudoU(3) symmetry. We derive the generators of the symmetry for each case.Physical Review Letters 01/2006; 95(25):252501. · 7.73 Impact Factor  [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 γunstable 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 nonrelativistic harmonic oscillator is discussed.Physical Review C 03/2005; 69. · 3.72 Impact Factor  [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 (quasidegenerate) have different radial quantum numbers and different orbital angular momenta, features that made the reason for their degeneracy difficult to penetrate.Nuclear Physics News 01/2005; 15(3):1316.  [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.Physics Reports 01/2005; 414:165261. · 22.93 Impact Factor  [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 nucleonnucleon interaction.International Journal of Modern Physics E 01/2005; 14:105110. · 0.63 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 pseudospin symmetry. Approximate pseudospin 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 pseudospin symmetry are derived and tested for realistic relativistic mean field eigenfunctions. Predictions for magnetic moments and GamowTeller transitions and nucleonnucleus scattering are reviewed. Pseudospin 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 antinucleon in a nuclear enviroment is discussed. The exact eigenfunctions and eigenenergies for the relativistic harmonic oscillator in this limit are derived.03/2004: pages 219237;  [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: 3D figures changed to 2D onesPhysical 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 flatbottomed potentials as encountered in a secondorder 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 nonrigid 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.06/2003;  [Show abstract] [Hide abstract]
ABSTRACT: At a critical point of a secondorder 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.Physical Review Letters 06/2003; 90(21):212501. · 7.73 Impact Factor 
Article: General pairing interactions and pair truncation approximations for fermions in a singlej shell
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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 lowlying 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 singlej shell we show that there is only one nonzero 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 publishedPhysical Review C 05/2003; · 3.72 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 nonrelativistic selfconsistent models as well as the harmonic oscillator model. Comment: 6 pages, 3 postscript figures, submitted to Phys. Rev. CPhysical Review C 01/2003; · 3.72 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: A generalized M1 sum rule for orbital magnetic dipole strength from excited symmetric states to mixed‐symmetry states is derived within the interacting boson model of even‐even nuclei. The applicability of the sum rule is investigated for the U(5)‐SO(6) transition region. By applying the sum rule to the recent extensive data on mixed‐symmetry states in 94Mo one obtains valuable structure information in a largely parameter‐independent way. © 2002 American Institute of PhysicsAIP Conference Proceedings. 11/2002; 638(1):257258.  [Show abstract] [Hide abstract]
ABSTRACT: The orthogonal transformation from the spin representation to the pseudospin representation for the nucleonnucleon 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 twonucleon interaction.Physical Review C 04/2002; 65(5). · 3.72 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We briefly review the evidence that pseudospin symmetry is an SU(2) symmetry of the Dirac Hamiltonian.AIP Conference Proceedings. 04/2002; 610(1).  [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.10/2001;
Publication Stats
2k  Citations  
382.15  Total Impact Points  
Top Journals
 Physical Review C (30)
 Nuclear Physics A (10)
 Physical Review Letters (9)
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 Physics Letters B (6)
Institutions

1982–2007

Los Alamos National Laboratory
 Theoretical Division
Los Alamos, California, United States


2001–2003

Hebrew University of Jerusalem
Yerushalayim, Jerusalem District, Israel


1997

European Centre for Theoretical Studies in Nuclear Physics and Related Areas
Trient, TrentinoAlto Adige, Italy


1992

University of Cologne
 Institute for Nuclear Physics
Köln, North RhineWestphalia, Germany 
Max Planck Institute for Nuclear Physics
Heidelburg, BadenWürttemberg, Germany
