Multiple pairing gap structures in rare earth nuclei

Detailed experimental studies using multiple spectroscopic techniques reveal two extensive families of rotational bands in $^{152}$Sm that are remarkably similar. This result suggests that there are two coexisting shapes which strongly mix. Experimental results and a prescription of two-state mixing calculations are presented which describe the level energies of the ground-state and first excited ($0^+$ state) rotational bands, electric monopole transition rates, electric quadrupole matrix elements, and the isomer shift of the first excited $2^+$ state.