Nuclear Rotation: Cranking-Model Calculations and Their Relation to Other Treatments

The generalized cranking model is used to study the corrections to the nuclear rotational spectra that cause it to deviate from the $I(I+1\mathrm{})\mathrm{}$ rule. The fourth-order cranking corrections and the Coriolis-antipairing effect are treated as modes of a generalized vibration in the same way as the centrifugal stretching. The new form helps to explain the success of various two-parameter formulas used to fit the experimental energy levels and shows that they are equivalent. The parameters of such formulas are calculated here microscopically in a good- $j$ basis, and they agree reasonably well with experiment.