Phase Transitions: Summary of Discussion Session II of Camerino 2005

A brief report of the topics which received attention during the discussion session II of the International Workshop on Symmetries and Low-Energy Phase Transitions in Nuclear-Structure Physics, held in Camerino on 9-11 October 2005, is given. These include special solutions of the Bohr Hamiltonian for various potentials, the study of triaxial shapes and of degrees of freedom other than the quadrupole one (octupole, scissors), as well as the search for experimental manifestations of the critical point symmetries E(5) and X(5), and of the recently proposed critical point supersymmetry E(5/4).Comment: 6 pages, LaTeX. To appear in the Proceedings of the Workshop on Symmetries and Low-Energy Phase Transitions in Nuclear-Structure Physics (Camerino, October 9-11, 2005

Special Solutions of the Bohr Hamiltonian Related to Shape Phase Transitions in Nuclei

Nuclei exhibit quantum phase transitions (earlier called ground state phase transitions) between different shapes as the number of nucleons is modified, resulting in changes in the ground and low lying nuclear states. Special solutions of the Bohr Hamiltonian appropriate for the critical point of such shape phase transitions, as well as other special solutions applicable to relevant nuclear regions are described.Comment: 17 pages, LaTeX. To be published in a special issue of the Romanian Reports in Physics devoted to Dorin Poenaru's 70th Anniversar

Various aspects of the Deformation Dependent Mass model of nuclear structure

Recently, a variant of the Bohr Hamiltonian was proposed where the mass term is allowed to depend on the beta variable of nuclear deformation. Analytic solutions of this modified Hamiltonian have been obtained using the Davidson and the Kratzer potentials, by employing techniques from supersymmetric quantum mechanics. Apart from the new set of analytic solutions, the newly introduced Deformation-Dependent Mass (DDM) model offered a remedy to the problematic behaviour of the moment of inertia in the Bohr Hamiltonian, where it appears to increase proportionally to the square of beta. In the DDM model the moments of inertia increase at a much lower rate, in agreement with experimental data. The current work presents an application of the DDM-model suitable for the description of nuclei at the point of shape/phase transitions between vibrational and gamma-unstable or prolate deformed nuclei and is based on a method that was successfully applied before in the context of critical point symmetries.Comment: 8 pages, 6 figures, 1 tabl

Bohr Hamiltonian with a deformation-dependent mass term: physical meaning of the free parameter

Embedding of the 5-dimensional (5D) space of the Bohr Hamiltonian with a deformation-dependent mass (DDM) into a 6-dimensional (6D) space shows that the free parameter in the dependence of the mass on the deformation is connected to the curvature of the 5D space, with the special case of constant mass corresponding to a flat 5D space. Comparison of the DDM Bohr Hamiltonian to the 5D classical limit of Hamiltonians of the 6D interacting boson model (IBM), shows that the DDM parameter is proportional to the strength of the pairing interaction in the U(5) (vibrational) symmetry limit, while it is proportional to the quadrupole-quadrupole interaction in the SU(3) (rotational) symmetry limit, and to the difference of the pairing interactions among s, d bosons and d bosons alone in the O(6) (gamma-soft) limit. The presence of these interactions leads to a curved 5D space in the classical limit of IBM, in contrast to the flat 5D space of the original Bohr Hamiltonian, which is made curved by the introduction of the deformation-dependent mass.Comment: 21 pages, 1 figur

Electric quadrupole transitions of the Bohr Hamiltonian with the Morse potential

Eigenfunctions of the collective Bohr Hamiltonian with the Morse potential have been obtained by using the Asymptotic Iteration Method (AIM) for both gamma-unstable and rotational structures. B(E2) transition rates have been calculated and compared to experimental data. Overall good agreement is obtained for transitions within the ground state band, while some interband transitions appear to be systematically underpredicted in gamma-unstable nuclei and overpredicted in rotational nuclei.Comment: LaTeX, 19 page

W(5): Wobbling Mode in the Framework of the X(5) Model

Using in the Bohr Hamiltonian the approximations leading to the Bohr and Mottelson description of wobbling motion in even nuclei, a W(5) model for wobbling bands, coexisting with a X(5) ground state band, is obtained. Separation of variables is achieved by assuming that the relevant potential has a sharp minimum at gamma_0, which is the only parameter entering in the spectra and B(E2) transition rates (up to overall scale factors). B(E2) transition rates exhibit the features expected in the wobbling case, while the spectrum for gamma_0=20 degrees is in good agreement with experimental data for Dy-156.Comment: 14 pages, LaTeX, 3 postscript figure

The Use of Quantum Groups in Nuclear Structure Problems

Various applications of quantum algebraic techniques in nuclear structure physics, such as the su$_q$(2) rotator model and its extensions, the use of deformed bosons in the description of pairing correlations, and the construction of deformed exactly soluble models (Interacting Boson Model, Moszkowski model) are briefly reviewed. Emphasis is put in the study of the symmetries of the anisotropic quantum harmonic oscillator with rational ratios of frequencies, which underly the structure of superdeformed and hyperdeformed nuclei, the Bloch--Brink $\alpha$-cluster model and possibly the shell structure in deformed atomic clusters.Comment: LaTeX, 15 pages Invited lecture at the Predeal International Summer School on Collective Motion and Nuclear Dynamics (Predeal, Romania, 28 August - 9 September 1995

Quantum Algebras in Nuclear Structure

Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical tools ($q$-numbers, $q$-analysis, $q$-oscillators, $q$-algebras), the su$_q$(2) rotator model and its extensions, the construction of deformed exactly soluble models (Interacting Boson Model, Moszkowski model), the use of deformed bosons in the description of pairing correlations, and the symmetries of the anisotropic quantum harmonic oscillator with rational ratios of frequencies, which underly the structure of superdeformed and hyperdeformed nuclei, are discussed in some detail. A brief description of similar applications to molecular structure and an outlook are also given.Comment: LaTeX, 86 pages; Review article to appear in a special volume of the Romanian Journal of Physics devoted to the International Summer School on Collective Motion and Nuclear Dynamics (Predeal, Romania, 28 August - 9 September 1995. 324 reference

Quantum Algebraic Symmetries in Nuclei and Molecules

Various applications of quantum algebraic techniques in nuclear and molecular physics are briefly reviewed. Emphasis is put in the study of the symmetries of the anisotropic quantum harmonic oscillator with rational ratios of frequencies, which underly the structure of superdeformed and hyperdeformed nuclei, the Bloch--Brink $\alpha$-cluster model and possibly the shell structure in deformed atomic clusters.Comment: LaTeX, 8 pages; Invited lecture at the VIIth International Conference on Symmetry Methods in Physics (Dubna, 10-16 July 1995

Representations of the deformed U(su(2)) and U(osp(1,2)) algebras

The polynomial deformations of the Witten extensions of the U(su(2)) and U(osp(1,2)) algebras are three generator algebras with normal ordering, admitting a two generator subalgebra. The modules and the representations of these algebras are based on the construction of Verma modules, which are quotient modules, generated by ideals of the original algebra. This construction unifies a large number of the known algebras under the same scheme. The finite dimensional representations show new features such as the multiplicity of representations of the same dimensionality, or the existence of finite dimensional representations only for some dimensions.Comment: LaTeX file, LaTeX twice, 10 page