1,522 research outputs found
A Relativistic Symmetry in Nuclei: Its origins and consequences
We review the status of quasi-degenerate doublets in nuclei, called
pseudospin doublets, which were discovered about thirty years ago and the
origins of which have remained a mystery, until recently. We show that
pseudospin doublets originate from an SU(2) symmetry of the Dirac Hamiltonian
which occurs when the sum of the scalar and vector potentials is a constant.
Furthermore, we survey the evidence that pseudospin symmetry is approximately
conserved in nuclear spectra and eigenfunctions and in nucleon-nucleus
scattering for a Dirac Hamiltonian with realistic nuclear scalar and vector
potentials.Comment: Invited Talk for "Nuclei and Nucleons", Darmstadt, Germany, Oct.
11-13,2000; International Symposium on the occasion of Achim Richter's 60th
Birthda
Pseudo-spin symmetry in density-dependent relativistic Hartree-Fock theory
The pseudo-spin symmetry (PSS) is investigated in the density-dependent
relativistic Hartree-Fock theory by taking {the} doubly magic nucleus
Sn as a representative. It is found that the Fock terms bring
significant contributions to the pseudo-spin orbital potentials (PSOP) and make
it comparable to the pseudo-centrifugal barrier (PCB). However, these Fock
terms in the PSOP are counteracted by other exchange terms due to the
non-locality of the exchange potentials. The pseudo-spin orbital splitting
indicates that the PSS is preserved well for the partner states \lrb{\nu
3s_{1/2}, \nu2d_{3/2}} of Sn in the relativistic Hartree-Fock theory.Comment: 6 figue
Dynamical symmetries of two-dimensional systems in relativistic quantum mechanics
The two-dimensional Dirac Hamiltonian with equal scalar and vector potentials
has been proved commuting with the deformed orbital angular momentum . When
the potential takes the Coulomb form, the system has an SO(3) symmetry, and
similarly the harmonic oscillator potential possesses an SU(2) symmetry. The
generators of the symmetric groups are derived for these two systems
separately. The corresponding energy spectra are yielded naturally from the
Casimir operators. Their non-relativistic limits are also discussed.Comment: 3 pages, Accepted by Annals of Physics (New York
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
Critical Points in Nuclei and Interacting Boson Model Intrinsic States
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 -unstable nuclei. We
show that intrinsic states with an effective -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 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.Comment: 10 pages, 3 figures, Proc. Int. Conf. on "Symmetry in Physics", March
23-30, 2003, Erice, Ital
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, . 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
Confinement of spinless particles by Coulomb potentials in two-dimensional space-time
The problem of confinement of spinless particles in 1+1 dimensions is
approached with a linear potential by considering a mixing of Lorentz vector
and scalar couplings. Analytical bound-states solutions are obtained when the
scalar coupling is of sufficient intensity compared to the vector coupling.Comment: 14 pages, 2 figure
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