On the relative quality of the spin expansion and frequency expansion for the description of rotational level energies

The expansions in terms of angular momentum I or angular frequency ω that describe the energies of the levels in the ground-state rotational bands with Ksup(π)=O+ are generally not equivalent unless n1=n2=1 or infinity. A method is proposed to characterise this non-equivalency quantitatively. It was found that in some nuclei, like 248Cm and 166Er, the I(I + 1) expansion is better than the ω2 expansion, whereas in the majority of nuclei the ω2 expansion is better. The data demonstrate that the rates of convergence of the I(I + 1) and ω2 expansions for Esub(rot) depend on the individual properties of the nuclei. (author)