28 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

### 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 $\gamma$-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.Comment: 10 pages, 3 figures, Proc. Int. Conf. on "Symmetry in Physics", March
23-30, 2003, Erice, Ital

### U(3) and Pseudo-U(3) Symmetry of the Relativistic Harmonic Oscillator

We show that a Dirac Hamiltonian with equal scalar and vector harmonic
oscillator potentials has not only a spin symmetry but an 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.Comment: 8 pages, 0 figures, pusblished in Physical Review Letters 95, 252501
(2005

### 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

### 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

### Hermitian boson mapping and finite truncation

Starting from a general, microscopic fermion-to-boson mapping that preserves
Hermitian conjugation, we discuss truncations of the boson Fock space basis. We
give conditions under which the exact boson images of finite fermion operators
are also finite (e.g., a 1+2-body fermion Hamiltonian is mapped to a 1+2-body
boson Hamiltonian) in the truncated basis. For the most general case, where the
image is not necessarily exactly finite, we discuss how to make practical and
controlled approximations.Comment: 12 pages in RevTex with no figures, Los Alamos preprint #
LA-UR-94-146