# Shell-model operator for K-band splitting

#### Abstract

A microscopic shell-model operator that generates K-band splitting is introduced. An analytic matrix representation for this K2 operator is given in angular momentum projected states of the SU(3) ⊃ SO(3) group reduction. The K2 operator can also be used to resolve multiple occurrences of L-values in SU(3) representations, that is, it provides for a resolution of the SU(3) ⊃ SO(3) state labelling problem. Results for the leading SU(3) representations of 24Mg and 168Er, with (λ, μ) = (8, 4) and (30, 8) respectively, are presented to show that K2 is very nearly diagonal in an angular momentum projected SU(3) ⊃ SO(3) basis. An analysis of K-band splitting for 24Mg and 168Er is used to demonstrate the utility of the theory for carrying out shell-model calculations. © 1990.

*This paper has been withdrawn.*