Microscopic analysis of nuclear quantum phase transitions in the N≈90 region

The analysis of shape transitions in Nd isotopes, based on the framework of relativistic energy-density functionals and restricted to axially symmetric shapes in T. Niksic, D. Vretenar, G. A. Lalazissis, and P. Ring [Phys. Rev. Lett. 99, 092502 (2007)], is extended to the region Z=60,62,64 with N approximate to 90 and includes both beta and gamma deformations. Collective excitation spectra and transition probabilities are calculated starting from a five-dimensional Hamiltonian for quadrupole vibrational and rotational degrees of freedom, with parameters determined by constrained self-consistent relativistic mean-field calculations for triaxial shapes. The results reproduce available data and show that there is an abrupt change of structure at N=90 that can be approximately characterized by the X(5) analytic solution at the critical point of the first-order quantum phase transition between spherical and axially deformed shapes.