scholarly journals The 3-Dimensional g-Deformed Harmonic Oscillator and a Unified Description of Magic Numbers of Metal Clusters

2019 ◽  
Vol 10 ◽  
pp. 215
Author(s):  
N. Karoussos ◽  
Dennis Bonatsos ◽  
P. P. Raychev ◽  
R. P. Roussev
Keyword(s):  
Harmonic Oscillator ◽  
Noble Metals ◽  
Alkali Metals ◽  
Metal Clusters ◽  
Magic Numbers ◽  
Divalent Metals ◽  
3 Dimensional ◽  
Theoretical Predictions ◽  
Alkali Metal Clusters ◽  
Trivalent Metals

Magic numbers predicted by a 3-dimensional (/-deformed harmonic oscillator with u9(3) D 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 + / pseudo quantum number. In alkali metal clusters and noble metal clusters the 3-dimensional çr-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 ug(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.

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

1999 ◽  
Vol 302 (5-6) ◽  
pp. 392-398 ◽  
Author(s):  
Dennis Bonatsos ◽  
N. Karoussos ◽  
P.P. Raychev ◽  
R.P. Roussev ◽  
P.A. Terziev
Keyword(s):  
Alkali Metal ◽  
Harmonic Oscillator ◽  
Metal Clusters ◽  
Magic Numbers ◽  
3 Dimensional ◽  
Alkali Metal Clusters

scholarly journals Unified description of magic numbers of metal clusters in terms of the three-dimensionalq-deformed harmonic oscillator

2000 ◽  
Vol 62 (1) ◽  
Author(s):  
Dennis Bonatsos ◽  
N. Karoussos ◽  
D. Lenis ◽  
P. P. Raychev ◽  
R. P. Roussev ◽  
...  
Keyword(s):  
Harmonic Oscillator ◽  
Metal Clusters ◽  
Magic Numbers ◽  
Unified Description

scholarly journals Quantum Groups in Nuclear Spectra and in Metal Clusters

2019 ◽  
Vol 11 ◽  
Author(s):  
Dennis Bonatsos ◽  
B. A. Kotsos ◽  
P. P. Raychev ◽  
P. A. Terziev
Keyword(s):  
Quantum Groups ◽  
Metal Clusters ◽  
Good Description ◽  
Magic Numbers ◽  
Irreducible Tensor ◽  
Physical Systems ◽  
3 Dimensional ◽  
Rotational Spectra ◽  
Nuclear Models ◽  
Rotationally Invariant

Quantum algebras (quantum groups), which are nonlinear generalizations of the usual Lie algebras, provide a rich variety of symmetries finding applications in the description of several physical systems [1]. Using irreducible tensor operators under sug(2) a rotationally invariant Hamiltonian which provides a good description of nuclear rotational spectra is constructed and its relation to existing nuclear models is considered. Using the same techniques a 3-dimensional ç-deformed harmonic oscillator with ug(3)Dsoq(3) symmetry is constructed, compared to the modified oscillator of Nilsson, and used for the successful description of magic numbers [2] and supershells [3] in metal clusters.

scholarly journals A mechanism for shape coexistence

2021 ◽  
Vol 252 ◽  
pp. 02005
Author(s):  
Andriana Martinou
Keyword(s):  
Harmonic Oscillator ◽  
Shell Model ◽  
Magic Numbers ◽  
Shape Coexistence ◽  
Spin Orbit ◽  
Nuclear Shell Model ◽  
Different Types ◽  
Theoretical Predictions ◽  
Different Shapes ◽  
Nuclear Shell

The phenomenon of shape coexistence in a nucleus is about the occurence of two different nuclear states with drastically different shapes, lying close in energy. It is commonly seen in the data, that such coexisting states manifest in specific nuclei, which lie within certain islands on the nuclear chart, the islands of shape coexistence. A recently introduced mechanism predicts that these islands derive from the coexistence of two different types of magic numbers: the harmonic oscillator and the spin-orbit like. The algebraic realization of the nuclear Shell Model, the Elliott SU(3) symmetry, along with its extension, the proxy-SU(3) symmetry , are used for the parameter-free theoretical predictions of the islands of shape coexistence

Control of wavepacket dynamics in mixed alkali metal clusters by optimally shaped fs pulses

2001 ◽  
Vol 16 (1) ◽  
pp. 127-131 ◽  
Author(s):  
A. Bartelt ◽  
S. Minemoto ◽  
C. Lupulescu ◽  
Š. Vajda ◽  
L. Wöste
Keyword(s):  
Alkali Metal ◽  
Metal Clusters ◽  
Mixed Alkali ◽  
Wavepacket Dynamics ◽  
Alkali Metal Clusters

The symmetric group and the method of diatomics in molecules: an application to small lithium clusters

1973 ◽  
Vol 333 (1592) ◽  
pp. 69-87 ◽  
Keyword(s):  
Alkali Metal ◽  
Symmetric Group ◽  
Metal Clusters ◽  
Basis Functions ◽  
Basis Set ◽  
Irreducible Representations ◽  
Secular Equations ◽  
Alkali Metal Clusters ◽  
Lithium Clusters

A new ‘most economical’ algorithm for the construction of diatomics in molecules secular equations is described. The method does not require the basis functions to be written down explicitly, since overlap may be factored out of the equations entirely. The theory is presented in detail for the particular case of homogeneous alkali metal clusters. A knowledge of the irreducible representations of the symmetric group for the Jahn-Serber basis set is necessary. The irreducible representations are derived by a genealogical procedure. Some preliminary calculations are presented for the molecules Li 3 through Li 6 , Li + 3 and Li + 4 . The lithium clusters are found to be stable with respect to all possible dissociations, and the i.ps of Li 3 and Li 4 are in agreement with the trends for the species Na 3 , Na 4 , K 3 , K 4 , etc., whose i.ps have been measured experimentally.

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