  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.
