The shape phase transition between spherical U (5) and axially deformed SU (3) nuclei is investigated systemically for the rare-earth region nuclei by the constrained relativistic mean field theory with the interactions NL3. The properties of ground state for Nd , Gd and Dy isotopes are described fairly well as compared with experiments. By examining the potential energy curve and quadruple deformation β2 obtained with this microscopic approach, the possible critical point nuclei are suggested to be 148,150 Nd for Nd isotopes, but 148 Nd is the best candidate, and 150 Nd is slightly to the rotor side of the phase transition. For Gd and Dy isotopes, 150,152 Gd and 152,154 Dy are suggested to be the critical point nuclei. Similar conclusions are also drawn from the microscopic neutron single particle spectra.
Relativistic mean-field theory equation of state of neutron star matter and a Maxwellian phase transition to strange quark matter