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Systematic study of the rotational bands in the $A\sim 250$ mass region

For the first time, we conducted a comprehensive analysis of the rotational bands in the \( A\sim250 \) mass region. Utilizing a variety of rotational energy models and formulas, we have extracted free parameters for 36 rotational bands within this mass region, encompassing neutron numbers from N = 148 to 152. A significant enhancement has been made to the vibrational distortion model, leading to an exceptional match with the experimental data on dynamic moment of inertia across most of the rotational bands studied. Through the application of this revised model, we have categorized the dynamic moment of inertia into three distinct groups. The implications of the modified vibrational distortion term and how it evolves with changes in rotational frequency is also investigated. Our systematic investigation brings to light the peculiar behavior of Pu isotopes, especially in ground state bands of \( ^{242,244}\text{Pu}\), within this mass region. We provide a thorough discussion on various aspects such as the role of shape-fluctuation energy, the softness parameter, band-head and average moment of inertia, the prominence of the anti-pairing effect, and the transition from pairing to anti-pairing effects in Pu isotopes. Moreover, these findings are compared with other isotones, offering a comprehensive understanding of their unique characteristics.