Spins and moment of inertia of superdeformed bands in the Pb isotopes

Abstract

A variable moment of inertia (VMI) inspired interacting boson model (IBM) is used to deduce the band-head spins of the SD bands in the odd-A Pb isotopes in the $A \sim 190$ mass region. We find that the calculated transition energies and band-head moment of inertia (MoI) explicitly depend upon the assigned band-head spin. The experimental and calculated transition energies and the band-head MoI of signature partners SD bands matches extremely well whenever an accurate spin is assigned to the SD band. The dynamic MoI is also deduced for the flat SD bands in the odd-A Pb isotopes, and its variation with the rotational frequency is explored. We observe that a competition between the pairing and anti-pairing effect is responsible for the flatness in the dynamic moment of inertia. Also, the role of the perturbation holding the $SO_{sdg}(5)$ (or $SU_{sdg}(5)$) symmetry on the dynamic MoI in the flat SD band is explored.