Ground-state shape phase transitions in nuclei: Thermodynamic analogy and finite- N effects
Pavel Cejnar, Stefan G. Heinze, Jan Jolie
We study quantum phase transitions between spherical, prolate, and oblate nuclear ground-state shapes using the interacting $\mathrm{sd}$-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.
Physical Review C•Sep 23, 2003•54 citations