Universal Features of Shape Transitions in Hot Rotating Nuclei

The Landau theory of shape transitions in hot rotating nuclei is introduced and the universal features of such transitions are derived. The phase diagram of the excitation energy versus angular momentum $J$ for nuclei with prolate ground states shows a transition line from triaxial to oblate shapes. The transition is first order for small values of $J$ and becomes second order above a certain value which is the analog of the tricritical point. Nuclear shapes change very rapidly from near prolate to oblate in the vicinity of this point. The theory is used to calculate the phase diagram of the ${}_{}{}^{166}{}_{}{}^{}\mathrm{Er}$ nucleus.