Shell-model operator for K-band splitting

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) contains 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) contains 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)containsSO(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. (orig.)