Interplay between shape-phase transitions and shape coexistence in the Zr isotopes

We investigate the evolution of structure in the zirconium isotopes where one of the most complex situations encountered in nuclear physics occurs. We demonstrate the role of two concurrent types of quantum phase transitions, sharing a common critical point. The first type, involves an abrupt crossing of coexisting normal and intruder configurations. The second type, involves a gradual shape-phase transition within the intruder configuration, changing from weakly-deformed to prolate-deformed and finally to gamma-unstable. Evidence for this scenario is provided by a detailed comparison with experimental data, using a definite algebraic framework.