Algebraic formulation of collective models. I. The mass quadrupole collective model

Journal Article · Thu Nov 01 04:00:00 EST 1979 · Ann. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1016/0003-4916(79)90264-1· OSTI ID:5482356

Rosensteel, G; Rowe, D J

This paper is the first in a series of three which together present a microscopic formulation of the Bohr--Mottelson (BM) collective model of the nucleus. In this article the mass quadrupole collective (MQC) model is defined and shown to be a generalization of the BM model. The MQC model eliminates the small oscillation assumption of BM and also yields the rotational and CM (3) submodels by holonomic constraints on the MQC configuration space. In addition, the MQC model is demonstrated to be an algebraic model, so that the state space of the MQC model carries an irrep of a Lie algebra of microscopic observables, the MQC algebra. An infinite class of new collective models is then given by the various inequivalent irreps of this algebra. A microscopic embedding of the BM model is achieved by decomposing the representation of the MQC algebra on many-particle state space into its irreducible components. In the second paper this decomposition is studied in detail. The third paper presents the symplectic model, which provides the realization of the collective model in the harmonic oscillator shell model.

• Research Organization: Department of Physics, Tulane University, New Orleans, Louisiana 70118
• OSTI ID: 5482356
• Journal Information: Ann. Phys. (N.Y.); (United States), Journal Name: Ann. Phys. (N.Y.); (United States) Vol. 123:1; ISSN APNYA
• Country of Publication: United States
• Language: English

Related Subjects

653007* -- Nuclear Theory-- Nuclear Models-- (-1987)
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ALGEBRA
COLLECTIVE MODEL
ENERGY
IRREDUCIBLE REPRESENTATIONS
KINETIC ENERGY
LIE GROUPS
MATHEMATICAL MODELS
MATHEMATICS
MOTION
NUCLEAR MODELS
QUADRUPOLE MOMENTS
ROTATION
SYMMETRY GROUPS