# Shape variables and the shell model

#### Abstract

The irreducible representation labels λ and μ of the SU(3) shell model are related to the shape variables β and γ of the collective model by invoking a linear mapping between eigenvalues of invariant operators of the two theories. All but one parameter of the theory is fixed if the shell-model result is required to reproduce the collective-model geometry. And for one special value of the remaining free parameter there is a simple linear relationship between the eigenvalues, λα, of the quadrupole matrix of the collective model and the SU(3) representation labels: {Mathematical expression} The correspondence between hamiltonians that describe rotations in each theory is also given. Results are shown for two cases,24Mg and168Er, to demonstrate that the simplest mapping yields excellent results for both energies and transition rates. For λ and/or μ large, the (β, γ)↔(λ,μ) correspondence introduced here reduces to the symplectic shell-model result. © 1988 Springer-Verlag.

*This paper has been withdrawn.*