Nuclear rotational inertia relative to a rigid sphere ($\mathcal{I}={\hslash }^{2}J(J+1)/(2E_J)$)

The excitation energy in an ideal $K=0$ nuclear rotational band determines an effective moment of inertia through the displayed equation. Comparing it with $2M{R}^2/5$ tests the rigid-sphere scale. A sequence of approximately constant $E_J/[J(J+1)]$ supports the rotational interpretation; systematic variation indicates that the effective inertia changes along the band. Collective rotation need not have a rigid-body inertia, notably when nuclear pairing is important.