318 research outputs found
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(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 -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 (-numbers, -analysis, -oscillators, -algebras),
the su(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
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
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 -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
- …