Skeleton boson realizations of collective subalgebras

Journal Article · Sun May 01 04:00:00 EDT 1988 · Phys. Rev. C; (United States)

DOI:https://doi.org/10.1103/PhysRevC.37.2176· OSTI ID:5372895

Kim, G; Vincent, C M

For an even number of nucleons, we consider collective motion based on any dynamical symmetry subalgebra A-italic-circumflex of the valence-shell bifermion algebra; the generators of A-italic-circumflex are coherent linear combinations of bifermion operators of the types a/sup dagger/a/sup dagger/, a/sup dagger/a, and aa. A boson algebra is obtained by Dyson mapping the whole valence-shell bifermion algebra, and then ''skeletonizing'' the resulting expressions by deleting all noncollective boson operators from them. This skeleton boson algebra is shown to have the same commutation relations as the collective bifermion algebra, provided that the bifermion algebra is self-conjugate. The resulting boson Hamiltonian is not Hermitian, but does resemble the Hamiltonian of the interacting boson model in containing only one- and two-body terms. Moreover, the skeleton boson algebra (when restricted to a collective boson subspace that is free of spurious states) is shown to be physically equivalent to the collective bifermion algebra. It is shown that by working solely with collective bosons one can identify spurious boson states unambiguously, although the procedure lacks convenience. The similarity transformation that connects conjugate versions of the skeleton boson mapping is discussed, and a general condition for hermiticity of the boson image of a Hermitian operator is given.

• Research Organization: Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
• OSTI ID: 5372895
• Journal Information: Phys. Rev. C; (United States), Journal Name: Phys. Rev. C; (United States) Vol. 37:5; ISSN PRVCA
• Country of Publication: United States
• Language: English

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73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ANNIHILATION
BASIC INTERACTIONS
BOSON EXPANSION
BOSONS
COLLECTIVE MODEL
DYSON REPRESENTATION
ELECTROMAGNETIC INTERACTIONS
FERMIONS
HAMILTONIANS
INTERACTING BOSON MODEL
INTERACTIONS
LIE GROUPS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
NUCLEAR MODELS
PARTICLE PRODUCTION
QUANTUM OPERATORS
SHELL MODELS
SO GROUPS
SO-8 GROUPS
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