Abstract
We show that the linear energy weighted M1 sum rule is proportional to the summed E2 strength in the region of vibrational, transitional, and strongly deformed even-even nuclei using the proton-neutron interacting boson model. This general relation is compared with extensive data on M1 and E2 transition strength in rare-earth nuclei truncating the M1 sum rule to states below an excitation energy of 4 MeV. The above observation also implies a quadratic dependence on deformation (\ensuremath{\delta}) for the summed orbital M1 strength.
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