Empirical evidence of a superrigid structure of “flat” superdeformed bands

Abstract

For the first time, we present the empirical evidence of superrigid character of the ``flat'' superdeformed bands in the Tl and Pb isotopes. For this purpose, we have used various rotational energy formulas. The free parameters of superdeformed (SD) bands in the Tl and Pb isotopes have been extracted and systematically studied to obtain the proposed empirical evidence. In particular, the intraband transition energies of the SD bands have been split into rotational and shape fluctuation energies. The role of the vibrational factor in the evolution of dynamic moment of inertia, softness parameter, alignment, and effective pairing gap parameter of the flat SD bands has been studied. Using these models, two distinct natures have been identified for the SD bands in the Tl and Pb isotopes. Our study establishes the role of shape fluctuations, vibrational effect, deformation, and pairing correlations for the unusual behavior of the dynamic moment of inertia in the flat SD bands of the $A\ensuremath{\approx}190$ mass region.