Superfluid to normal phase transition and extreme regularity of superdeformed bands

We derive the exact semiclassical expression for the second inertial parameter $\cal B$ for the superfluid and normal phases. Interpolation between these limiting values shows that the function ${\cal B}(I)$ changes sign at the spin $I_c$, which is critical for a rotational spectrum. The quantity $\cal B$ turns out to be a sensitive measure of the change in static pairing correlations. The superfluid-to-normal transition reveals itself in the specific variation of the ratio ${\cal B}/{\cal A}$ versus spin $I$ with the plateau characteristic of the normal phase. We find this dependence to be universal for normal deformed and superdeformed bands. The long plateau with a small value ${\cal B}/{\cal A}\sim A^{-8/3}$ explains the extreme regularity of superdeformed bands.