Shape phase transition in γ-rigid prolate nuclei

Abstract

A γ-rigid prolate version of the Bohr-Hamiltonian is quasi-exactly solved for a sextic oscillator potential. Both energies and wave functions are obtained in analytical form depending, up to a scale factor, on a single free parameter. Moreover, due to the special properties of the sextic potential, a shape evolution can be covered from a γ-rigid prolate harmonic vibrator to an anharmonic one crossing a critical region where the potential is flat. Experimental evidence of this type of shape transition has been found in the isotopic chains of Ru, Xe and Nd with the following candidates for the critical points: 104Ru, 120,126Xe and 148Nd, respectively. Other two candidates for the critical region can be considered to be 196Pt and 172Os, even if no such shape phase transition have been observed in their corresponding isotopic chains.