Critical-Point Structure in Finite Nuclei

Phase transitions associated with a change of shape are known to occur in dynamical systems such as nuclei. Recently, it has been recognized that such quantum shape-phase transitions are amenable to analytic descriptions at the critical points [1, 2]. For nuclei these analytic benchmarks of criticality were obtained in the geometric framework of a Bohr Hamiltonian for macroscopic quadrupole shapes. In particular, the E(5) [1] (X(5) [2]) benchmark is applicable to a second(first-) order shape-phase transition between spherical and deformed γ-unstable (axially-symmetric) nuclei. Empirical evidence of these benchmarks have been presented [3, 4]. An important issue concerning phase transitions in real nuclei is the role of a finite number of nucleons. This aspect can be addressed in the algebraic framework of the interacting boson model (IBM) [5] which describes low-lying quadrupole collective states in nuclei in terms of a system of N monopole (s) and quadrupole (d) bosons representing valence nucleon pairs. The three dynamical symmetry limits of the model: U(5), SU(3), and O(6), describe the dynamics of stable nuclear shapes: spherical, axially-deformed, and γ-unstable deformed. A geometric visualization of the model is obtained by an intrinsic energy surface defined by the expectation value of the Hamiltonian in the coherent (intrinsic) state [6, 7]