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Joseph N. Ginocchio

Publications and source records attributed to Joseph N. Ginocchio.

15 recordsLinked to original sources
arXiv2010

Pseudospin Conserving Shell Model Interactions

Pseudospin symmetry is approximately conserved in nuclei. Normally shell model interactions are written in terms of spin an orbital angular momentum operators, not in terms of pseudospin and pseudo-orbital angular momentum operators. We determine the shell model interactions which conserve pseudospin symmetry and pseudo-orbital angular momentum symmetry and write them in terms of spin and orbital angular momentum operators including the tensor interaction. We show that, although the tensor interaction by itself does not conserve pseudo-orbital angular momentum, certain combinations of the tensor interaction with the two body angular momentum squared interaction and the two body spin orbit interaction do conserve pseudo-orbital angular momentum.

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arXiv2005

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.

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arXiv2005

Relativistic Harmonic Oscillator with Spin Symmetry

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 non-relativistic harmonic oscillator is discussed.

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arXiv2003

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 $γ$-unstable nuclei. We show that intrinsic states with an effective $β$-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.

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arXiv2000

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.

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arXiv1999

The Resurrection of a Symmetry in Nucleon - Nucleus Scattering

We re-examine a symmetry in nucleon - nucleus scattering that previously had been proclaimed to be dead. We show that this symmetry is the continuum analog of pseudospin symmetry, a relativistic symmetry which manifests itself in the spectra of nuclei. Using experimental data only we show that pseudospin symmetry in nucleon - nucleus scattering is not dead but only modestly broken for 800 MeV proton scattering on nuclei.

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arXiv1999

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 $^{39}K$.

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arXiv1998

A Relativistic Symmetry in Nuclei

We review the status of a 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 scalar and vector potentials are opposite in sign but equal in magnitude. Furthermore, we survey the evidence that pseudospin symmetry is approximately conserved for a Dirac Hamiltonian with realistic scalar and vector potentials. We briefly discuss the relationship of pseudospin symmetry with chiral symmetry and the implications of pseudospin symmetry for the antinucleon spectrum in nuclei.

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arXiv1997

Pseudo-spin Symmetry and Relativistic Single-nucleon Wave Functions

We show that the occurrence of approximate pseudo-spin symmetry in nuclei is connected with certain similarities in the relativistic single-nucleon wave functions of the corresponding pseudo-spin doublets. We perform a case study in which several examples and the systematics of this connection are explored.

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arXiv1996

Pseudo-spin as a Relativistic Symmetry

We show that pseudo - spin 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.

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arXiv1994

Theory of fermion to boson mappings: old wine in new bottles

After a brief review of various mappings of fermion pairs to bosons, we rigorously derive a general approach. Following the methods of Marumori and Otsuka, Arima, and Iachello, our approach begins with mapping states and constructs boson representations that preserve fermion matrix elements. In several cases these representations factor into finite, Hermitian boson images times a projection or norm operator that embodies the Pauli principle. We pay particular attention to truncated boson spaces, and describe general methods for constructing Hermitian and approximately finite boson image Hamiltonians, including effective operator theory to account for excluded states. This method is akin to that of Otsuka, Arima, and Iachello introduced in connection with the Interacting Boson Model, but is more rigorous, general, and systematic.

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arXiv1994

Fermion to boson mappings revisited

We briefly review various mappings of fermion pairs to bosons, including those based on mapping operators, such as Belyaev-Zelevinskii, and those on mapping states, such as Marumori; in particular we consider the work of Otsuka-Arima-Iachello, aimed at deriving the Interacting Boson Model. We then give a rigorous and unified description of state-mapping procedures which allows one to systematically go beyond Otsuka-Arima-Iachello and related approaches, along with several exact results.

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arXiv1994

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.

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arXiv1993

Exact, finite, and Hermitian fermion-pair-to-boson mapping

We discuss a general, exact (in that matrix elements are preserved) mapping of fermion pairs to bosons, and find a simple factorization of the boson representation of fermion operators. This leads to boson Hamiltonians that are Hermitian and finite, with no more than two-body operators if the fermion Hamiltonian has at most two-body operators, and one-body boson transition operators if the fermion transition operator is one-body.

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