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D. Bonatsos

Publications and source records attributed to D. Bonatsos.

At least 37 records · Page 2Linked to original sources
arXiv2008

Analytical solutions of the Bohr Hamiltonian with the Morse potential

Analytical solutions of the Bohr Hamiltonian are obtained in the $γ$-unstable case, as well as in an exactly separable rotational case with $γ\approx 0$, called the exactly separable Morse (ES-M) solution. Closed expressions for the energy eigenvalues are obtained through the Asymptotic Iteration Method (AIM), the effectiveness of which is demonstrated by solving the relevant Bohr equations for the Davidson and Kratzer potentials. All medium mass and heavy nuclei with known $β_1$ and $γ_1$ bandheads have been fitted by using the two-parameter $γ$-unstable solution for transitional nuclei and the three-parameter ES-M for rotational ones. It is shown that bandheads and energy spacings within the bands are well reproduced for more than 50 nuclei in each case.

nucl-th↗
arXiv2006

Exactly separable version of X(5) and related models

One-parameter exactly separable versions of the X(5) and X(5)-beta^2 models, labelled as ES-X(5) and ES-X(5)-beta^2 respectively, are derived by using in the Bohr Hamiltonian potentials of the form u(beta)+u(gamma)/beta^2. Unlike X(5), in these models the beta_1 and gamma_1 bands are treated on equal footing. Spacings within the gamma_1 band are well reproduced by both models, while spacings within the beta_1 band are well reproduced only by ES-X(5)-beta^2, for which several nuclei with R_{4/2}=E(4_1^+)/E(2_1^+) ratios and [normalized to E(2_1^+)] beta_1 and gamma_1 bandheads corresponding to the model predictions have been found.

nucl-th↗
arXiv2006

Gamma-soft Analog of the Confined Beta-soft Rotor Model

A gamma-soft analog of the confined beta-soft (CBS) rotor model is developed, by using a gamma-independent displaced infinite well beta-potential in the Bohr Hamiltonian, for which exact separation of variables is possible. Level schemes interpolating between the E(5) critical point symmetry (with R(4/2)=E(4)/E(2)= 2.20) and the O(5) gamma-soft rotor (with R(4/2)=2.50) are obtained, exhibiting a crossover of excited 0+ bandheads which leads to agreement with the general trends of first excited 0+ states in this region and is observed experimentally in 128-Xe and 130-Xe.

nucl-th↗
arXiv2006

Nuclear collective motion with a coherent coupling interaction between quadrupole and octupole modes

A collective Hamiltonian for the rotation-vibration motion of nuclei is considered, in which the axial quadrupole and octupole degrees of freedom are coupled through the centrifugal interaction. The potential of the system depends on the two deformation variables $β_2$ and $β_3$. The system is considered to oscillate between positive and negative $β_3$-values, by rounding an infinite potential core in the $(β_2,β_3)$-plane with $β_2>0$. By assuming a coherent contribution of the quadrupole and octupole oscillation modes in the collective motion, the energy spectrum is derived in an explicit analytic form, providing specific parity shift effects. On this basis several possible ways in the evolution of quadrupole-octupole collectivity are outlined. A particular application of the model to the energy levels and electric transition probabilities in alternating parity spectra of the nuclei $^{150}$Nd, $^{152}$Sm, $^{154}$Gd and $^{156}$Dy is presented.

nucl-th↗
arXiv2006

E(5), X(5), and Prolate to Oblate Shape Phase Transitions in Relativistic Hartree Bogoliubov Theory

Relativistic mean field theory with the NL3 force is used for producing potential energy surfaces (PES) for series of isotopes suggested as exhibiting critical point symmetries. Relatively flat PES are obtained for nuclei showing the E(5) symmetry, while in nuclei corresponding to the X(5) case, PES with a bump are obtained. The PES corresponding to the Pt chain of isotopes suggest a transition from prolate to oblate shapes at 186-Pt.

nucl-th↗
arXiv2005

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).

nucl-th↗
arXiv2005

Analytical Special Solutions of the Bohr Hamiltonian

The following special solutions of the Bohr Hamiltonian are briefly described: 1) Z(5) (approximately separable solution in five dimensions with gamma close to 30 degrees), 2) Z(4) (exactly separable gamma-rigid solution in four dimensions with gamma = 30 degrees), 3) X(3) (exactly separable gamma-rigid solution in three dimensions with gamma =0). The analytical solutions obtained using Davidson potentials in the E(5), X(5), Z(5), and Z(4) frameworks are also mentioned.

nucl-th↗
arXiv2001

Staggering effects in nuclear and molecular spectra

It is shown that the recently observed Delta J = 2 staggering effect (i.e. the relative displacement of the levels with angular momenta J, J+4, J+8, ..., relatively to the levels with angular momenta J+2, J+6, J+10, ...) seen in superdeformed nuclear bands is also occurring in certain electronically excited rotational bands of diatomic molecules (YD, CrD, CrH, CoH), in which it is attributed to interband interactions (bandcrossings). In addition, the Delta J = 1 staggering effect (i.e. the relative displacement of the levels with even angular momentum J with respect to the levels of the same band with odd J) is studied in molecular bands free from Delta J = 2 staggering (i.e. free from interband interactions/bandcrossings). Bands of YD offer evidence for the absence of any Delta J = 1 staggering effect due to the disparity of nuclear masses, while bands of sextet electronic states of CrD demonstrate that Delta J = 1 staggering is a sensitive probe of deviations from rotational behaviour, due in this particular case to the spin-rotation and spin-spin interactions.

physics.chem-ph↗
arXiv2001

"Beat" patterns for the odd-even staggering in octupole bands from a quadrupole-octupole Hamiltonian

We propose a collective Hamiltonian which incorporates the standard quadrupole terms, octupole terms classified according to the irreducible representations of the octahedron group, a quadrupole-octupole interaction, as well as a term for the bandhead energy linear in K (the projection of angular momentum on the body-fixed z-axis). The energy is subsequently minimized with respect to K for each given value of the angular momentum I, resulting in K values increasing with I within each band, even in the case in which K is restricted to a set of microscopically plausible values. We demonstrate that this Hamiltonian is able to reproduce a variety of ``beat'' patterns observed recently for the odd-even staggering in octupole bands of light actinides.

nucl-th↗
arXiv2001

Rotations of nuclei with reflection asymmetry correlations

We propose a collective Hamiltonian which incorporates interactions capable to generate rotations in nuclei with simultaneous presence of octupole and quadrupole deformations. It is demonstrated that the model formalism could be applied to reproduce the staggering effects observed in nuclear octupole bands. On this basis we propose that the interactions involved would provide a relevant handle in the study of collective phenomena in nuclei and other quantum mechanical systems with reflection asymmetry correlations.

nucl-th↗
arXiv2001

Delta I = 1 staggering in octupole bands of light actinides: "Beat" patterns

The Delta I = 1 staggering (odd--even staggering) in octupole bands of light actinides is found to exhibit a ``beat'' behaviour as a function of the angular momentum I, forcing us to revise the traditional belief that this staggering decreases gradually to zero and then remains at this zero value. Various algebraic models (spf-Interacting Boson Model, spdf-IBM, Vector Boson Model, Nuclear Vibron Model) are shown to predict in their su(3) limits constant staggering for this case, being thus unable to describe the ``beat'' behaviour. An explanation of the ``beat'' behaviour is given in terms of two Dunham expansions (expansions in terms of powers of I(I+1)) with slightly different sets of coefficients for the ground state band and the negative parity band, the difference in the values of the coefficients being attributed to Coriolis couplings to other negative parity bands. Similar ``beat'' patterns have already been seen in rotational bands of some diatomic molecules, like AgH.

nucl-th↗
arXiv2001

Symmetries and staggering effects in nuclear rotational spectra

We study the fine structure of nuclear rotational spectra on the basis of both dynamical and discrete symmetry approaches. In this framework we show that the odd--even (Delta I = 1) staggering effects observed in various rotational bands carry detailed information about the collective band-mixing interactions and the collective shape properties of heavy nuclei.

nucl-th↗
arXiv2001

Quantum algebraic symmetries in atomic clusters, molecules and nuclei

Quantum algebras (also called quantum groups) are deformed versions of the usual Lie algebras, to which they reduce when the deformation parameter q is set equal to unity. From the mathematical point of view they are Hopf algebras. Their use in physics became popular with the introduction of the q-deformed harmonic oscillator as a tool for providing a boson realization of the quantum algebra SUq(2), although similar mathematical structures had already been known. Initially used for solving the quantum Yang-Baxter equation, quantum algebras have subsequently found applications in several branches of physics, as, for example, in the description of spin chains, squeezed states, hydrogen atom and hydrogen-like spectra, rotational and vibrational nuclear and molecular spectra, and in conformal field theories. By now much work has been done on the q-deformed oscillator and its relativistic extensions, and several kinds of generalized deformed oscillators and SU(2) algebras have been introduced. Here we shall confine ourselves to a list of applications of quantum algebras in nuclear structure physics and in molecular physics and, in addition, a recent application of quantum algebraic techniques to the structure of atomic clusters will be discussed in more detail.

quant-ph↗
arXiv2001

Unified description of magic numbers of metal clusters in terms of the 3-dimensional q-deformed harmonic oscillator

Magic numbers predicted by a 3-dimensional q-deformed harmonic oscillator with Uq(3)>SOq(3) symmetry are compared to experimental data for atomic clusters of alkali metals (Li, Na, K, Rb, Cs), noble metals (Cu, Ag, Au), divalent metals (Zn, Cd), and trivalent metals (Al, In), as well as to theoretical predictions of jellium models, Woods-Saxon and wine bottle potentials, and to the classification scheme using the 3n+l pseudo quantum number. In alkali metal clusters and noble metal clusters the 3-dimensional q-deformed harmonic oscillator correctly predicts all experimentally observed magic numbers up to 1500 (which is the expected limit of validity for theories based on the filling of electronic shells), while in addition it gives satisfactory results for the magic numbers of clusters of divalent metals and trivalent metals, thus indicating that Uq(3), which is a nonlinear extension of the U(3) symmetry of the spherical (3-dimensional isotropic) harmonic oscillator, is a good candidate for being the symmetry of systems of several metal clusters. The Taylor expansions of angular momentum dependent potentials approximately producing the same spectrum as the 3-dimensional q-deformed harmonic oscillator are found to be similar to the Taylor expansions of the symmetrized Woods-Saxon and wine-bottle symmetrized Woods-Saxon potentials, which are known to provide successful fits of the Ekardt potentials.

physics.atm-clus↗
arXiv1997

Broken SU(3) symmetry in deformed even-even nuclei

A collective vector-boson model with broken SU(3) symmetry, in which the ground state band and the lowest $γ$ band belong to the same irreducible representation but are non-degenerate, is applied to several deformed even-even nuclei. The model description of ground and $γ$ bands together with the corresponding B(E2) transition probabilities is investigated within a broad range of SU(3) irreducible representations $(λ,μ)$. The calculations show that the $(λ,μ)$ characteristics of rotational nuclei depend to a great extent on the magnitude of the SU(3) splitting between the ground and $γ$ bands. It is found that for weakly split spectra, the ground--$γ$ band coupling scheme is realized relevantly within narrow regions of ``favored'' $(λ,μ)$ multiplets, while in the cases of strong splitting a description in which the ground band is situated alone in an irreducible representation is favored. The obtained results are analyzed in terms of the bandmixing interactions. The possibility for a transition between the different collective SU(3) schemes is discussed.

nucl-th↗
arXiv1997

Nonlinear deformed su(2) algebras involving two deforming functions

The most common nonlinear deformations of the su(2) Lie algebra, introduced by Polychronakos and Ro\v cek, involve a single arbitrary function of J_0 and include the quantum algebra su_q(2) as a special case. In the present contribution, less common nonlinear deformations of su(2), introduced by Delbecq and Quesne and involving two deforming functions of J_0, are reviewed. Such algebras include Witten's quadratic deformation of su(2) as a special case. Contrary to the former deformations, for which the spectrum of J_0 is linear as for su(2), the latter give rise to exponential spectra, a property that has aroused much interest in connection with some physical problems. Another interesting algebra of this type, denoted by ${\cal A}^+_q(1)$, has two series of (N+1)-dimensional unitary irreducible representations, where N=0, 1, 2, .... To allow the coupling of any two such representations, a generalization of the standard Hopf axioms is proposed. The resulting algebraic structure, referred to as a two-colour quasitriangular Hopf algebra, is described.

q-alg↗
arXiv1997

A nonlinear deformed su(2) algebra with a two-colour quasitriangular Hopf structure

Nonlinear deformations of the enveloping algebra of su(2), involving two arbitrary functions of J_0 and generalizing the Witten algebra, were introduced some time ago by Delbecq and Quesne. In the present paper, the problem of endowing some of them with a Hopf algebraic structure is addressed by studying in detail a specific example, referred to as ${\cal A}^+_q(1)$. This algebra is shown to possess two series of (N+1)-dimensional unitary irreducible representations, where N=0, 1, 2, .... To allow the coupling of any two such representations, a generalization of the standard Hopf axioms is proposed by proceeding in two steps. In the first one, a variant and extension of the deforming functional technique is introduced: variant because a map between two deformed algebras, su_q(2) and ${\cal A}^+_q(1)$, is considered instead of a map between a Lie algebra and a deformed one, and extension because use is made of a two-valued functional, whose inverse is singular. As a result, the Hopf structure of su_q(2) is carried over to ${\cal A}^+_q(1)$, thereby endowing the latter with a double Hopf structure. In the second step, the definition of the coproduct, counit, antipode, and R-matrix is extended so that the double Hopf algebra is enlarged into a new algebraic structure. The latter is referred to as a two-colour quasitriangular Hopf algebra because the corresponding R-matrix is a solution of the coloured Yang-Baxter equation, where the `colour' parameters take two discrete values associated with the two series of finite-dimensional representations.

q-alg↗