Symmetries and deformations in the spherical shell model

Abstract

We discuss symmetries of the spherical shell model that make contact with the geometric collective model of Bohr and Mottelson. The most celebrated symmetry of this kind is SU(3), which is the basis of Elliott's model of rotation. It corresponds to a deformed mean field induced by a quadrupole interaction in a single major oscillator shell N and can be generalized to include several major shells. As such, Elliott's SU(3) model establishes the link between the spherical shell model and the (quadrupole component of the) geometric collective model. We introduce the analogue symmetry induced by an octupole interaction in two major oscillator shells N-1 and N, leading to an octupole-deformed solution of the spherical shell model. We show that in the limit of large oscillator shells (large N) the algebraic octupole interaction tends to that of the geometric collective model.

23 pages, 7 figures, 2 tables

References in corpus (5)

• Structure of A=10-13 nuclei with two- plus three-nucleon interactions from chiral effective field theory
• Three-body forces: From cold atoms to nuclei
• Overview of Neutron-Proton Pairing
• Nilsson-SU3 selfconsistency in heavy N=Z nuclei
• Algebraic models for shell-like quarteting of nucleons

Cited by in corpus (7)

• Shape coexistence in even-even nuclei: A theoretical overview
• Geometrical symmetries of nuclear systems: D(3h) and T(d) symmetries in light nuclei
• Nucleon-pair coupling scheme in Elliott's SU(3) model
• Quadrupole properties of the eight $SU(3)$ algebras in $(sdgi)$ space
• Symmetries and order in cluster nuclei
• Quadrupole-Octupole Residual Interaction in the Proxy-$SU(3)$ Scheme
• Inter-band B(E1) Strengths in Heavy Nuclei based on the Proxy-SU(3) Scheme