288 research outputs found

### 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

### 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, $V_V = - V_S$. 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

### Violation of pseudospin symmetry in nucleon-nucleus scattering: exact relations

An exact determination of the size of the pseudospin symmetry violating part
of the nucleon-nucleus scattering amplitude from scattering observables is
presented. The approximation recently used by Ginocchio turns out to
underestimate the violation of pseudospin symmetry. Nevertheless the conclusion
of a modestly broken pseudospin symmetry in proton-208Pb scattering at
EL=800MeV remains valid.Comment: 8 pages, 2 figure

### Test of Nuclear Wave Functions for Pseudospin Symmetry

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.Comment: 11 pages, 4 figures, minor changes in text and figures to conform
with PRL requirement

### Isospin relations for four nucleons in a single j shell

We had previously used techniques involving isospin to count the number of
states for three identical fermions in a single j shell with total angular
momentum I=j. We generalize this to all I, but the main thrust of this work is
to consider now a 4-fermion system. As before, one evaluates the eigenvalues of
the Hamiltonian \sum_{i<j}[a + bt(i)t(j)] both from an isospin point of view
and an angular momentum point of view. In the 4-particle case, we get a more
limited result than in the 3-particle case, namely the number of T=0 states
minus twice the number of T=2 states, all of a given angular momentum I.Comment: 6 pages, RevTex

### An intrinsic state for an extended version of the interacting boson model

An intrinsic-state formalism for IBM-4 is presented. A basis of deformed
bosons is introduced which allows the construction of a general trial wave
function which has Wigner's spin-isospin SU(4) symmetry as a particular limit.
Intrinsic-state calculations are compared with exact ones showing good
agreement.Comment: 12 pages, TeX (ReVTeX). Content changed. Accepted in Phys. Rev.

### Relativistic U(3) Symmetry and Pseudo-U(3) Symmetry of the Dirac Hamiltonian

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 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.Comment: Submitted to the Proceedings of "Tenth International Spring
Seminar-New Quests in Nuclear Structure", 6 page

### Alternate Derivation of Ginocchio-Haxton relation [(2j+3)/6]

We address the problem, previously considered by Ginocchio and Haxton (G-H),
of the number of states for three identical particles in a single j-shell with
angular momentum J=j. G-H solved this problem in the context of the quantum
Hall effect. We address it in a more direct way. We also consider the case
J=j+1 to show that our method is more general, and we show how to take care of
added complications for a system of five identical particles.Comment: 7 pages, RevTeX4; submitted to Phys. Rev.

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