Shape Transition in Rare-Earth Nuclei in Relativistic Mean Field Theory

A systematic study of the temperature dependence of the shapes and pairing gaps of some isotopes in the rare-earth region is made in the relativistic Hartree-BCS theory. Thermal response to these nuclei is always found to lead to a phase transition from the superfluid to the normal phase at a temperature $T_{\Delta}\sim 0.4 - 0.8$ MeV and a shape transition from prolate to spherical shapes at $T_c\sim 1.0 - 2.5$ MeV. These shape transition temperatures are appreciably higher than the corresponding ones calculated in the non-relativistic framework with the pairing plus quadrupole interaction. Study of nuclei with continued addition of neutron pairs for a given isotope shows that with increased ground state deformation, the transition to the spherical shape is delayed in temperature. A strong linear correlation between $T_{\Delta}$ and the ground state pairing gap $\Delta^0$ is observed; a well- marked linear correlation between $T_c$ and the ground state quadrupole defromation $\beta_2^{0}$ is also seen. The thermal evolution of the hexadecapole deformation is further presented in the paper.