Shell-model operator for K3-band splitting in odd-A nuclei

A shell-model operator is introduced that generates KJ-band splitting in odd-A nuclei, where KJ=KL+KS is the projection of the total angular momentum, J=L+S, on the principal symmetry axis of the system. An expression is given for the matrix elements of this KJ2 operator in angular-momentum-projected and spin-coupled basis states of the SU(3) scheme. Eigenvalues of the KJ2 operator in the leading normal-SU(3) symmetry for 25Mg and the leading pseudo-SU(3) symmetries for 159Dy and 165Er are compared with the corresponding quantum rotor results. Shell-model results for the ds-shell nucleus 21Ne with 17O single-particle energies and only the three residual interactions Q.Q, J2 and KJ2 are shown to compare favorably with experiment and an analysis based on a realistic (renormalized two-body form fit to experimental data) ds-shell interaction. The KJ2 operator is also the appropriate form for integral S≠0 configurations in even-A nuclei with matrix elements that reduce to those of the previously defined KL2 operator in S=0 states. (orig.)