The finite-temperature Hartree-Fock-Bogoliubov cranking equations are solved for the $i_{\frac{13}{2}}$ model. For any temperature below $k{T}_c=0.2\mathrm{}$ MeV, rotations induce a sharp first-order phase transition. When statistical fluctuations in the pair gap $\Delta$ are included, the phase transition is smoothed out for $\frac{1}{2}{T}_c<T<\mathrm{}{T}_c$. The rotation-aligned $i_{\frac{13}{2}}$ pair is unaffected by temperatures up to 0.5 MeV. The finite-temperature violation of the zero-temperature Hartree-Fock-Bogoliubov relation $R^2=R$ is given by the quasiparticle number fluctuation.

• Received 23 December 1983

DOI:https://doi.org/10.1103/PhysRevC.29.1887