Pavel Cejnar

Quantum phase transitions in the shapes of atomic nuclei

Signatures of criticality in the evolution of the nuclear ground-state shapes across the NxZ 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.

Excited state quantum phase transitions in many-body systems

Phenomena analogous to ground state quantum phase transitions have recently been noted to occur among states throughout the excitation spectra of certain many-body models. These excited state phase transitions are manifested as simultaneous singularities in the eigenvalue spectrum (including the gap or level density), order parameters, and wave function properties. In this article, the characteristics of excited state quantum phase transitions are investigated. The finite-size scaling behavior is determined at the mean-field level. It is found that excited state quantum phase transitions are universal to two-level bosonic and fermionic models with pairing interactions.

Quantum phase transitions in the interacting boson model

Abstract This review is focused on various properties of quantum phase transitions (QPTs) in the Interacting Boson Model (IBM) of nuclear structure. The model describes collective modes of motions in atomic nuclei at low energies, in terms of a finite number N of mutually interacting s and d bosons. Closely related approaches are applied in molecular physics. In the N → ∞ limit, the ground state is a boson condensate that exhibits shape–phase transitions between spherical (I), deformed prolate (II), and deformed oblate (III) forms when the interaction strengths are varied. Finite- N precursors of such behavior are verified by robust variations of nuclear properties (nuclear masses, excitation energies, transition probabilities for low lying levels) across the chart of nuclides. Simultaneously, the model serves as a theoretical laboratory for studying diverse general features of QPTs in interacting many-body systems, which differ in many respects from lattice models of solid-state physics. We outline the most important fields of the present interest: (a) The coexistence of first- and second-order phase transitions supports studies related to the microscopic origin of the QPT phenomena. (b) The competing quantum phases are characterized by specific dynamical symmetries, and novel symmetry related approaches are developed to also describe the transitional dynamical domains. (c) In some parameter regions, the QPT-like behavior can be ascribed also to individual excited states, which is linked to the thermodynamical and classical descriptions of the system. (d) The model and its phase structure can be extended in many directions: by separating proton and neutron excitations, considering odd-fermion degrees of freedom or different particle–hole configurations, by including other types of bosons, higher order interactions, and by imposing external rotation. All these aspects of IBM phase transitions are relevant in the interpretation of experimental data, and important for a fundamental understanding of the QPT phenomenon.

Facility and method for studying two-step γ cascades in thermal neutron capture☆

Abstract A dedicated facility for γ-γ coincidence studies of (n,γ) reactions at thermal neutron energies is described. The facility and the adopted method of data acquisition make it possible to determine intensities of two-step γ cascades proceeding from the neutron capturing state to a set of selected low-lying levels via resolved and unresolved intermediate levels occurring between the neutron capturing state and a final level of interest. A detailed description of the method for accumulating the γ-ray spectra, characterizing these two-step cascades, is given including procedures for corrections of these spectra for various kinds of backgrounds and distortions.

Monodromy and excited-state quantum phase transitions in integrable systems: collective vibrations of nuclei

Quantum phase transitions affecting the structure of ground and excited states of integrable systems with the Mexican-hat type potential are shown to be related to a singular torus of classical orbits passing the point of unstable equilibrium. As a specific example, we consider nuclear collective vibrations described by the O(6)–U(5) transitional Hamiltonian of the interacting boson model. While all states with zero values of the O(5) invariant undergo a continuous phase transition when crossing the energy of unstable equilibrium, the other states evolve in an analytic way.

Coulomb analogy for non-Hermitian degeneracies near quantum phase transitions.

Degeneracies near the real axis in a complex-extended parameter space of a Hermitian Hamiltonian are studied. We present a method to measure distributions of such degeneracies on the Riemann sheet of a selected level and apply it in classification of quantum phase transitions. The degeneracies are shown to behave similarly as complex zeros of a partition function.

Quantum chaos in the nuclear collective model: Classical-quantum correspondence.

Spectra of the geometric collective model of atomic nuclei are analyzed to identify chaotic correlations among nonrotational states. The model has been previously shown to exhibit a high degree of variability of regular and chaotic classical features with energy and control parameters. Corresponding signatures are now verified also on the quantum level for different schemes of quantization and with a variable classicality constant.

Thermodynamic analogy for quantum phase transitions at zero temperature

We propose a relationship between thermodynamic phase transitions and ground-state quantum phase transitions in systems with variable Hamiltonian parameters. It is based on a link between zeros of the canonical partition function at complex temperatures and branch points of a quantum Hamiltonian in the complex-extended parameter space. This approach is applied in the interacting boson model, where it is shown to properly distinguish the first- and second-order phase transitions.

Phase structure of interacting boson models in arbitrary dimension

We analyse the phase structure of a class of interacting boson models with two types of bosons, one scalar and one non-scalar, subject to one- and two-body interactions and with dynamic algebra U(n). To these models, we associate a classical description in terms of f = n − 1 variables. We show that, if the system is invariant under two- or three-dimensional rotations (for f ≥ 2 even or odd), the models have both first- and second-order phase transitions only if f = 5, 9, 13, .... In the other f ≥ 2 cases, the system has only second-order transitions. All phase transitions of this class of models belong to the cusp catastrophe in the classification of structurally unstable potentials.

On nuclear spin determinations from statistical feeding intensities in (particle, xn) fusion reactions

Abstract The 110 Cd nuclear levels were populated by the 108 Pd(α, 2nγ) reaction. Their statistical (side-feeding) population was shown to be spin and energy dependent, providing a new method of spin determination. The empirical regularities are reproduced by statistical evaporation-model calculations. This provides a new means to test the model and to set new constraints on its parameters.