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D. Lenis

Publications and source records attributed to D. Lenis.

34 records · Page 2Linked to original sources
arXiv2003

Sequence of Potentials Interpolating between the U(5) and E(5) Symmetries

It is proved that the potentials of the form $β^{2n}$ (with $n$ being integer) provide a ``bridge'' between the U(5) symmetry of the Bohr Hamiltonian with a harmonic oscillator potential (occuring for $n=1$) and the E(5) model of Iachello (Bohr Hamiltonian with an infinite well potential, materialized for infinite $n$). Parameter-free (up to overall scale factors) predictions for spectra and B(E2) transition rates are given for the potentials $β^4$, $β^6$, $β^8$, corresponding to $R_4=E(4)/E(2)$ ratios of 2.093, 2.135, 2.157 respectively, compared to the $R_4$ ratios 2.000 of U(5) and 2.199 of E(5). Hints about nuclei showing this behaviour, as well as about potentials ``bridging'' the E(5) symmetry with O(6) are briefly discussed. A note about the appearance of Bessel functions in the framework of E(n) symmetries is given as a by-product.

nucl-th↗
arXiv2003

Deformed Harmonic Oscillators for Metal Clusters and Balian-Bloch Theory

The predictions for the shell structure of metal clusters of the three-dimensional q-deformed harmonic oscillator (3D q-HO), utilizing techniques of quantum groups and having the symmetry Uq(3)$\supset$SOq(3), are compared to the restrictions imposed by the periodic orbit theory of Balian and Bloch, of electrons moving in a spherical cavity. It is shown that agreement between the predictions of the two models is established through the introduction of an additional term to the Hamiltonian of the 3D q-HO, which does not influence the predictions for supershells. This term preserves the Uq(3)$\supset$SOq(3) symmetry, while in addition it can be derived through a variational procedure, analogous to the one leading from the usual harmonic oscillator to the Morse oscillator by introducing the concept of the Variable Frequency Oscillator (VFO).

quant-ph↗
arXiv2003

Sequence of Potentials Lying Between the U(5) and X(5) Symmetries

Starting from the original collective Hamiltonian of Bohr and separating the beta and gamma variables as in the X(5) model of Iachello, an exactly soluble model corresponding to a harmonic oscillator potential in the beta-variable (to be called X(5)-$β^2$) is constructed. Furthermore, it is proved that the potentials of the form $β^{2n}$ (with n being integer) provide a ``bridge'' between this new X(5)-$β^2$ model (occuring for n=1) and the X(5) model (corresponding to an infinite well potential in the beta-variable, materialized for n going to infinity. Parameter-free (up to overall scale factors) predictions for spectra and B(E2) transition rates are given for the potentials $β^2$, $β^4$, $β^6$, $β^8$, corresponding to E(4)/E(2) ratios of 2.646, 2.769, 2.824, and 2.852 respectively, compared to the E(4)/E(2) ratios of 2.000 for U(5) and 2.904 for X(5). Hints about nuclei showing this behaviour, as well as about potentials ``bridging'' the X(5) symmetry with SU(3) are briefly discussed.

nucl-th↗
arXiv2002

Deformed Harmonic Oscillators for Metal Clusters: Analytic Properties and Supershells

The analytic properties of Nilsson's Modified Oscillator (MO), which was first introduced in nuclear structure, and of the recently introduced, based on quantum algebraic techniques, 3-dimensional q-deformed harmonic oscillator (3-dim q-HO) with Uq(3) > SOq(3) symmetry, which is known to reproduce correctly in terms of only one parameter the magic numbers of alkali clusters up to 1500 (the expected limit of validity for theories based on the filling of electronic shells), are considered. Exact expressions for the total energy of closed shells are determined and compared among them. Furthermore, the systematics of the appearance of supershells in the spectra of the two oscillators is considered, showing that the 3-dim q-HO correctly predicts the first supershell closure in alkali clusters without use of any extra parameter.

cond-mat↗
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

Symmetries of anisotropic harmonic oscillators with rational ratios of frequencies and their relations to U(N) and O(N+1)

The concept of bisection of a harmonic oscillator or hydrogen atom, used in the past in establishing the connection between U(3) and O(4), is generalized into multisection (trisection, tetrasection, etc). It is then shown that all symmetries of the N-dimensional anisotropic harmonic oscillator with rational ratios of frequencies (RHO), some of which are underlying the structure of superdeformed and hyperdeformed nuclei, can be obtained from the U(N) symmetry of the corresponding isotropic oscillator with an appropriate combination of multisections. Furthermore, it is seen that bisections of the N-dimensional hydrogen atom, which possesses an O(N+1) symmetry, lead to the U(N) symmetry, so that further multisections of the hydrogen atom lead to the symmetries of the N-dim RHO. The opposite is in general not true, i.e. multisections of U(N) do not lead to O(N+1) symmetries, the only exception being the occurence of O(4) after the bisection of U(3).

nucl-th↗
arXiv1997

Symmetries in nuclei and molecules

Recent progress in two different fronts is reported. First, the concept of bisection of a harmonic oscillator (HO) or hydrogen atom (HA), used in the past in establishing the connection between U(3) and O(4), is generalized into multisection (trisection, tetrasection, etc). It is then shown that all symmetries of the N-dim anisotropic HO with rational ratios of frequencies (RHO), some of which are underlying the structure of superdeformed and hyperdeformed nuclei, can be obtained from the U(N) symmetry of the corresponding isotropic HO with an appropriate combination of multisections. Furthermore, it is seen that bisections of the N-dim HA, which possesses an O(N+1) symmetry, lead to the U(N) symmetry, so that further multisections of the HA lead to the symmetries of the N-dim RHO. Second, it is shown that there is evidence that the recently observed in superdeformed nuclear bands $ΔI=4$ bifurcation is also occuring in rotational bands of diatomic molecules. In addition there is evidence that a $ΔI=8$ bifurcation, of the same order of magnitude as the $ΔI=4$ one, is observed in superdeformed nuclear bands and rotational bands of diatomic molecules.

nucl-th↗
arXiv1996

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.

q-alg↗
arXiv1995

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.

nucl-th↗
arXiv1995

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 $α$-cluster model and possibly the shell structure in deformed atomic clusters.

nucl-th↗
arXiv1995

Quantum Algebraic Symmetries in Nuclear Structure

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 underlie the structure of superdeformed and hyperdeformed nuclei, the Bloch--Brink $α$-cluster model and possibly the shell structure in deformed atomic clusters.

nucl-th↗
arXiv1995

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 $α$-cluster model and possibly the shell structure in deformed atomic clusters.

q-alg↗
arXiv1994

Nonlinear extension of the u(2) algebra as the symmetry algebra of the planar anisotropic quantum harmonic oscillator with rational ratio of frequencies and ``pancake'' nuclei

The symmetry algebra of the two-dimensional anisotropic quantum harmonic oscillator with rational ratio of frequencies, which is characterizing ``pancake'' nuclei, is identified as a non-linear extension of the u(2) algebra. The finite dimensional representation modules of this algebra are studied and the energy eigenvalues are determined using algebraic methods of general applicability to quantum superintegrable systems. For labelling the degenerate states an ``angular momentum'' operator is introduced, the eigenvalues of which are roots of appropriate generalized Hermite polynomials. In the special case with frequency ratio 2:1 the resulting algebra is identified as the finite W algebra W$_3^{(2)}$.

nucl-th↗
arXiv1994

The symmetry algebra of the N-dimensional anisotropic quantum harmonic oscillator with rational ratios of frequencies and the Nilsson model

The symmetry algebra of the N-dimensional anisotropic quantum harmonic oscillator with rational ratios of frequencies is constructed by a method of general applicability to quantum superintegrable systems. The special case of the 3-dim oscillator is studied in more detail, because of its relevance in the description of superdeformed nuclei and nuclear and atomic clusters. In this case the symmetry algebra turns out to be a nonlinear extension of the u(3) algebra. A generalized angular momentum operator useful for labeling the degenerate states is constructed, clarifying the connection of the present formalism to the Nilsson model in nuclear physics.

hep-th↗