Joseph N. Ginocchio

Pseudospin as a Relativistic Symmetry

We show that pseudospin symmetry in nuclei could arise from nucleons moving in a relativistic mean field which has an attractive scalar and repulsive vector potential nearly equal in magnitude. {copyright} {ital 1997} {ital The American Physical Society}

An intrinsic state for the interacting boson model and its relationship to the Bohr-Mottelson model☆

Abstract Within the interacting boson model, an intrinsic state is defined, in terms of quadrupole shape variables, from which all eigenstates of the interacting boson model can be projected by appropriately averaging over these shape variables and the orientations of the intrinsic state. With this intrinsic state, an energy surface and a Bohr hamiltonian can be derived for any boson hamiltonian in terms of these quadrupole variables.

A schematic model for monopole and quadrupole pairing in nuclei

Abstract A schematic Hamiltonian with a pairing interaction plus a quadrupole-quadrupole interaction between nucleons is presented. It is shown that all the states of the fermion system can be classified according to the number of nucleons u not coupled to coherent monopole or quadrupole pairs. The states with u = 0 are shown to have a one-to-one correspondence to the states of the interacting boson model. The spectra for these states are derived analytically for various limits of the pairing strength and the quadrupole strength. Analytical forms for the matrix elements of operators are derived for these limits. The operators in fermion space are mapped onto boson operators. The matrix elements of operators in the fermion space are shown to be equal to matrix elements of the boson operators multiplied by analytical Pauli factors which are state dependent. The two-nucleon transfer strength is calculated in two limits and is compared to experimental values.

RELATIVISTIC SYMMETRY SUPPRESSES QUARK SPIN-ORBIT SPLITTING

Experimental data indicate small spin-orbit splittings in hadrons. For heavy-light mesons we identify a relativistic symmetry that suppresses these splittings. We suggest an experimental test in electron-positron annihilation. Furthermore, we argue that the dynamics necessary for this symmetry are possible in QCD.

On the relativistic foundations of pseudospin symmetry in nuclei

Abstract 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.

A CLASS OF EXACTLY SOLVABLE POTENTIALS. I. ONE-DIMENSIONAL SCHRODINGER EQUATION

Abstract The one-dimensional Schrodinger equation is solved for a new class of potentials with varying depths and shapes. The energy eigenvalues are given in algebraic form as a function of the depth and shape of the potential. The eigenfunctions and scattering function are also given in closed form. For certain shapes these potentials resemble the mean field of an atomic nucleus.

Test of pseudospin symmetry in deformed nuclei

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.

Pseudospin symmetry and relativistic single-nucleon wave functions

We show that the occurrence of approximate pseudospin symmetry in nuclei is connected with certain similarities in the relativistic single-nucleon wave functions of the corresponding pseudospin doublets. We perform a case study in which several examples and the systematics of this connection are explored. {copyright} {ital 1998} {ital The American Physical Society}

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 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.

On a generalization of quasispin to monopole and quadrupole pairing

Abstract A generalization of the quasispin group for monopole pairing to a group which includes both monopole and quadrupole pairing is discussed. Shell model hamiltonians with monopole and quadrupole pairing are shown to have a rich variety of eigenspectra.