Shape transition in some 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 similar to 0.4-0.8 MeV and a shape transition from prolate to spherical shapes at T-c similar to 1.0-2.5 MeV. These shape transition temperatures are appreciably higher than the corresponding ones calculated in the nonrelativistic 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 (0)(2) is also seen. The thermal evolution of the hexadecapole deformation is further presented in the paper.