Algebraic formulation of collective models III. The symplectic shell model of collective motion

Journal Article · Thu May 01 04:00:00 EDT 1980 · Ann. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1016/0003-4916(80)90180-3· OSTI ID:5206504

Rosensteel, G; Rowe, D J

The symplectic model is a microscopic theory which provides a practical technique for identifying the shell configurations necessary for the description of quadrupole and monopole vibrations as well as collective rotations of the nucleus. The model is based on the non-compact symplectic algebra sp(3, R) and is a natural generalization of Elliott's su(3) model to include many major oscillator shells in addition to core excitations. It is also simultaneously the shell model adaptation of the collective rotational (R/sup 5/)so(3), the Bohr-Mottelson cm(3)=R/sup 6/)sl(3) and the mass quadrupole collective MQC=R/sup 6/)gl(3) models. In contrast to the su(3) algebra, the sp(3, R) algebra makes no 0h..omega.. approximations and treats all observables in the algebra exactly, thereby achieving a microscopic theory of large amplitude collective motion. The observables in the algebra include the quadrupole and monopole moments, the kinetic energy, the harmonic oscillator Hamiltonian and the angular and vibrational momenta. Numerical results are reported for /sup 20/Ne using an 8 h..omega.. truncation and a phenomenological potential V(..beta..,..gamma..). Satisfactory agreement with experiment is obtained for the absolute B(E2) rates without resorting to an effective charge.

• Research Organization: Department of Physics, Tulane University, New Orleans, Louisiana 70118
• OSTI ID: 5206504
• Journal Information: Ann. Phys. (N.Y.); (United States), Journal Name: Ann. Phys. (N.Y.); (United States) Journal Issue: 2 Vol. 126:2; ISSN APNYA
• Country of Publication: United States
• Language: English

Related Subjects

651413 -- Nuclear Properties & Reactions
A=20-38
Theoretical-- Energy Levels & Transitions-- (-1987)
653007* -- Nuclear Theory-- Nuclear Models-- (-1987)
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ALGEBRA
COLLECTIVE MODEL
E2-TRANSITIONS
ENERGY-LEVEL TRANSITIONS
EVEN-EVEN NUCLEI
FUNCTIONS
HAMILTONIANS
HARMONIC OSCILLATOR MODELS
IRREDUCIBLE REPRESENTATIONS
ISOTOPES
LIE GROUPS
LIGHT NUCLEI
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATHEMATICS
MULTIPOLE TRANSITIONS
NEON 20
NEON ISOTOPES
NILSSON-MOTTELSON MODEL
NUCLEAR MODELS
NUCLEI
QUANTUM OPERATORS
SHELL MODELS
SP GROUPS
STABLE ISOTOPES
SYMMETRY GROUPS
WAVE FUNCTIONS