Relation between the Scissors Mode and the Interacting Boson Model Deformation

An interacting boson model sum rule for the strength of exciting the magnetic dipole scissors mode is used to relate this strength to the quadrupole deformation, resulting in a parameter-free description of the $M1\mathrm{}$ transition strength over the entire range of nuclei from Nd to W studied experimentally. Also, the experimentally established quadratic dependence on the quadrupole ground state deformation is quantitatively reproduced for nuclei up to Yb, but systematic deviations are predicted for heavier nuclei.