Ground-state shape phase transitions in nuclei:: Thermodynamic analogy and finite-N effects -: art. no. 034326

We study quantum phase transitions between spherical, prolate, and oblate nuclear ground-state shapes using the interacting sd-boson model (sd-IBM) and demonstrate the analogy between the IBM results (also results of any axially symmetric quadrupole collective model) and predictions of the Landau theory of phase transitions in classical thermodynamics. A detailed comparison of the two frameworks is performed exploiting the concept of "specific heat," introduced in four alternative ways in the quantum case. All these definitions (two of them based on spectroscopic features of the ground state, the others on a randomized version of the model) lead to similar peaked forms of the "specific heat" at the point of the quantum phase transition. We analyze the effect of an increasing boson number on these curves and observe convergence to the singular phase-transitional behavior in the classical limit. Other observable signatures of the IBM structural phase transitions are also discussed with the aim to facilitate the location of a particular nucleus in the parameter space (extended Casten triangle) near the transitions.