Microscopic analysis of shape-phase transitions in even-even N~90 rotating nuclei

We study in cranked Nilsson plus random phase approximation shape transitions in fast rotating nuclei undergoing backbending, more specifically 156Dy and 162Yb. We found that a backbending in 156Dy is correlated with the disappearance of the collective, positive signature gamma-vibrational mode in the rotating frame, and, a shape transition (from axial to nonaxial) is accompanied with a large acquiring of the gamma-deformation. We show that such a shape transition can be considered as a phase transition of the first order. In 162Yb the quasiparticle alignment dominates in the backbending and the shape transition (from axial to nonaxial) is accompanied with a smooth transition from zero to nonzero values of the gamma-deformation. We extend the classical Landau theory for rotating nuclei and show that the backbending in 162Yb is identified with the second order phase transition. A description of spectral and decay properties of the yrast states and low-lying excitations demonstrates a good agreement between our results and experimental data