The 3-dimensional q-deformed harmonic oscillator and magic numbers of alkali metal clusters

  title={The 3-dimensional q-deformed harmonic oscillator and magic numbers of alkali metal clusters},
  author={Dennis Bonatsos and N. Karoussos and P. P. Raychev and R. P. Roussev and P. A. Terziev},
  journal={Chemical Physics Letters},
Abstract Magic numbers predicted by a 3-dimensional q-deformed harmonic oscillator with uq(3)⊃soq(3) symmetry are compared to experimental data for alkali metal clusters, 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. The 3-dimensional q-deformed harmonic oscillator correctly predicts all experimentally observed magic numbers up to 1500 (which is the expected limit of… 

Tables from this paper

Reproduction of metal-cluster magic numbers using a q-deformed, 3-dimensional, harmonic oscillator model
Abstract In this paper we review the main properties of the q -deformed, 3-dimensional harmonic oscillator ( Q3O ) and show how this model can be used for the description of metal cluster properties.
Derivation of shell effects and magic numbers in metal clusters by the application of Strutinsky's method to the Clemenger–Nilsson and q‐deformed 3‐D harmonic oscillator models
Strutinsky's standard averaging method is applied to metal clusters described by two different potentials—Clemenger–Nilsson (CN) and q-deformed 3-D (Q3D) harmonic oscillator (HO). In addition, a new
Theoretical study of the structure of silver clusters
Neutral silver cluster isomers Agn (n=2 to 12) were studied by Kohn–Sham density functional theory. There is a strong even-odd oscillation in cluster stability due to spin subshell closing.
Variation of the ℏω with the particle number and the appearance of “kinks” for atomic clusters
The dependence of the harmonic oscillator (HO) energy level spacing ℏω on the particle number N is studied analytically for atomic (metal) clusters on the basis of their electronic densities,
Statistical properties of the q-deformed relativistic Dirac oscillator in minimal length quantum mechanics
In this article, we introduce a two-dimensional Dirac oscillator in the presence of an external magnetic field in terms of q-deformed creation and annihilation operators in the framework of
What and How Physics Contributes to Understanding the Periodic Law
The current status of explanation worked out by Physics for the Periodic Law is considered from philosophical and methodological points of view. The principle gnosiological role of approximations and
Superalgebras for the 3D Harmonic Oscillator and Morse Quantum Potentials
Abstract In addition to obtaining supersymmetric structure related to the partner Hamiltonians, we get another supersymmetric structure via factorization method for both the 3D harmonic oscillator
A Pythagorean Approach to Problems of Periodicity in Chemical and Nuclear Physics
A Pythagorean approach to numerical sequences in both chemical and nuclear physics has allowed us to show geometrical analogies based on figurate numbers (three-dimensional forms of Mendeleev’s
Quantum deformations and q -boson operators
This Viewpoint relates to articles by L C Biedenharn (1989 J. Phys. A: Math. Gen . 22 L873) and A J Macfarlane (1989 J. Phys. A: Math. Gen . 22 4581) and was published as part of a series of
Why nuclear forces favor the highest weight irreducible representations of the fermionic SU(3) symmetry
The consequences of the attractive, short-range nucleon–nucleon (NN) interaction on the wave functions of the Elliott SU(3) and the proxy-SU(3) symmetry are discussed. The NN interaction favors the


An Application of the 3-dimensional q deformed harmonic oscillator to the nuclear shell model
A procedure for the construction of a q-deformed version of the Hamiltonian of the three-dimensional harmonic oscillator (HO), based on the application of q-deformed algebras, is presented. The
Observation of quantum supershells in clusters of sodium atoms
ATOMIC clusters of sodium and other simple metals are known to exhibit a shell structure, giving rise to enhanced stability at certain 'magic numbers' of constituent atoms1–3. Balian and Bloch have
WKB equivalent potentials for q-deformed harmonic and anharmonic oscillators
WKB equivalent potentials (WKB‐EP’s) giving the same WKB spectrum as the q‐deformed harmonic oscillator are determined in analytic form. For q being complex the WKB‐EP resembles the Poschl–Teller,
Dynamical algebra of the q‐deformed three‐dimensional oscillator
The q‐deformed three‐dimensional harmonic oscillator is defined in terms of the q‐bosons corresponding to the spherical components of a nondeformed three‐dimensional oscillator. It is shown that the
The physics of simple metal clusters: self-consistent jellium model and semiclassical approaches
The jellium model of simple metal clusters has enjoyed remarkable empirical success, leading to many theoretical questions. In this review, we first survey the hierarchy of theoretical approximations
The physics of simple metal clusters: experimental aspects and simple models
The study of simple metal clusters has burgeoned in the last decade, motivated by the growing interest in the evolution of physical properties from the atom to the bulk solid, a progression passing
Supershells in metal clusters.
The semiclassical interpretation of such a supershell structure, as proposed by Balian and Bloch in terms of interference of amplitudes associated with classical closed orbits, is found to be valid in the present case.
3n+l quantum number in the cluster problem.
  • Koch
  • Physics, Medicine
    Physical review. A, Atomic, molecular, and optical physics
  • 1996
This work investigates whether the conjectured quantum number 3n+l bears a similarity to the quantum numbers n+l and 2n-l, which characterize the hydrogen problem and the isotropic harmonic oscillator in three dimensions.
Evidence for quantized electronic level structure for 100–1300 electrons in metal-atomic clusters
Abstract Photoionization mass spectrometry experiments on cold and warm beams of Al N clusters reveal large, N -specific discontunuities in their cohesive and ionization properties. These can be
Alkali-atom shell model
Abstract An alkali-atom shell model for alkali microclusters is introduced, where the quantum constituent is the neutral atom itself considered as a heavy fermion in a central potential created by