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Reviews of Modern Physics

Quantum phase transitions in the shapes of atomic nuclei

Pavel Cejnar, Jan Jolie, Richard F. Casten

Published Aug 5, 2010• 578 citations
Publisher

Abstract

Signatures of criticality in the evolution of the nuclear ground-state shapes across the $N\ifmmode\times\else\texttimes\fi{}Z$ plane are discussed. Attention is paid to specific data indicating sudden structural changes in various isotopic and isotonic chains of medium-mass and heavy even-even nuclei, as well as to diverse theoretical aspects of the models used to describe these changes. The interacting boson model and the geometric collective model, in particular, are discussed in detail, the former providing global predictions for the evolution of collective observables in nuclei between closed shells and the latter yielding a parameter-efficient description of nuclei at the critical points of shape transitions. Some issues related to the mechanism of first- and second-order quantum phase transitions in general many-body systems are also outlined.

DOI
10.1103/revmodphys.82.2155

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Signatures of criticality in the evolution of the nuclear ground-state shapes across the N\ifmmode×\else\texttimes\fiZN\ifmmode\times\else\texttimes\fi{}ZN\ifmmode×\else\texttimes\fiZ plane are discussed. Attention is paid to specific data indicating sudden structural changes in various isotopic and isotonic chains of medium-mass and heavy even-even nuclei, as well as to diverse theoretical aspects of the models used to describe these changes. The interacting boson model and the geometric collective model, in particular, are discussed in detail, the former providing global predictions for the evolution of collective observables in nuclei between closed shells and the latter yielding a parameter-efficient description of nuclei at the critical points of shape transitions. Some issues related to the mechanism of first- and second-order quantum phase transitions in general many-body systems are also outlined.
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We study quantum phase transitions between spherical, prolate, and oblate nuclear ground-state shapes using the interacting sd\mathrm{sd}sd-boson model (sd(sd(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.
A study of first and second order nuclear shape phase transitional behavior in yrast states of even-even nuclei in the context of the Interacting Boson Model-1 is presented. Finite boson number effects are identified using calculations with up to 150 bosons, and the role of the rotational degree of freedom of observables in first and second order quantum phase transitional nuclei is discussed. We aim to provide a first investigation of the angular momentum dependence of experimentally accessible phase transitional signatures in finite-sized quantum nuclear systems.
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Abstract. The mean-field approximation predicts pairing and shape phase transitions in nuclei as a function of temperature or excitation energy. However, in the finite nucleus the singularities of these phase transitions are smoothed out by quantal and thermal fluctuations. An interesting question is whether signatures of these transitions survive despite the large fluctuations. The shell model Monte Carlo (SMMC) approach enables us to calculate the statistical properties of nuclei beyond the mean-field approximation in model spaces that are many orders of magnitude larger than spaces that can be treated by conventional diagonalization methods. We have extended the SMMC method to heavy nuclei and used it to study the transition from vibrational (spherical) to rotational (deformed) nuclei in families of rare-earth isotopes. We have calculated collective enhancement factors of level densities as a function of excitation energy and found that the decay of the vibrational and rotational enhancements is well correlated with the pairing and shape phase transitions, respectively.