Microscopic Analysis of Nuclear Quantum Phase Transitions in the N ∼ 90 region

Quantum Phase Transition (QPT) describes an abrupt change in the ground state of a many-body system due to its quantum fluctuations as the variation of a non-thermal control parameter at zero temperature. In the case of atomic nuclei, the first- and second-order QPT can occur between systems characterized by different ground-state shapes, and the corresponding control parameter is the number of nucleons. These shape phase transitions reflect the underlying modifications of single-nucleon shell structure and the interaction between valence nucleons as the number of nucleons changes. In the work, we analysis the shape transition in the region of Z = 60, 62, 64 with N ∼ 90. 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, to a good approximation, characterized by the X(5) critical-point symmetry of a first-order quantum phase transition. The shape phase transition is especially pronounced in 150Nd, where the microscopic potential energy surface displays a flat prolate minimum in the interval 0.2 < β < 0.4, and a parabolic dependence on γ, thus confirming the X(5) model assumption of a harmonic oscillator potential in γ. For the other two N = 90 isotones 152Sm and 154Gd, the spectra of the collective Hamiltonian and the E2 transition rates reproduce the data, but indicate that these two nuclei are located already past the critical point of shape phase transition.(author)