Extended M1 sum rule for excited symmetric and mixed-symmetry states in nuclei

A generalized M1 sum rule for orbital magnetic dipole strength from excited symmetric states to mixed-symmetry states is considered within the proton-neutron interacting boson model of even-even nuclei. Analytic expressions for the dominant terms in the B(M1) transition rates from the 2_1.2⁺ states are derived in the U(5) and SO(6) dynamic symmetry limits of the model, and the applicability of a sum rule approach is examined at and between these limits. Lastly, the sum rule is applied to the new data on mixed-symmetry states of ⁹⁴Mo and a quadrupole d-boson ratio n_d(0₁⁺)/n_d(2₂⁺ )≈0.6 is obtained in a largely parameter-independent way.