Simple systematics of the shape transitions in hot rare-earth nuclei

The Landau theory of shape transitions in hot rotating nuclei is applied to even-even rare-earth nuclei from cerium to hafnium. The parameters of the Landau expansion are extracted from microscopic calculations based on the Nilsson-Strutinsky procedure, and are shown to follow simple systematics. In particular, the systematics of the critical temperature and the critical angular momentum of the shape transitions as functions of neutron and proton number are investigated. Simple rules are provided for the behavior of these quantities.