Modified Nilsson model for large sodium clusters

Abstract

Abstract. We propose a modified Nilsson model for spheroidal sodium clusters and investigate the modification of shell structure by deformation for sizes up to N = 850. For spherical clusters, our potential is fitted to the single-particle spectra obtained from microscopically selfconsistent Kohn-Sham calculations using the jellium model and the local density approximation. Employing Strutinsky's shell-correction method, the surface energy of the jetlium model is renormalized to its experimental value. We find good agreement between our theoretically predicted deformed magic numbers and the experimentally observed ones extracted from recent sodium mass abundance spectra.

Spheroidally deformed sodium clusters in the selfconsistent jellium model

“…the choice of the diffusivity in the definition of V,(z,e), which implies an angular dependence d ( Q ) in our calculations different to, e.g., the definition in [22]. Nevertheless, comparing the results with those of [24] and [52], prolate-to-oblate transitions are kept at about the same particle number in all three models. The absolute value of the deformation strength 6 increases from Na-10 to Na-14.…”

“…Clemenger introduced a different parameter 6, to describe axial deformations [7], which is related to q by and is only useful for 6 1 4 2 . Another definition (see, e.g., [52]) is…”

“…[52] fitted the Nilsson Hamiltonian to the selfconsistent spherical spectrum, thus keeping some selfconsistency to the results. Although the schematic results are in quite good qualitative agreement, they certainly cannot reproduce the effects of selfconsistency, e.g.…”

Electronic shell structure of large metallic clusters in the modified harmonic oscillator

“…For b = 2 the emerging shell structure is confined to the very low end of the spectrum and to rather small values of λ. where the applicability of the model is no longer certain. For example, in [12] it was found that for large spherical clusters (A = 676 and 832) the energy minima are more pronounced than in the KS calculations, which is an artifact. In other words, while in the axial MHO potential the re-emergence of order and hence shell structure is a fact for large Λ, its physical impact cannot be assessed from this model alone.…”

“…In practical applications the study of the more realistic deformed WS potential is complicated due to the effective occurrence of many multipoles; this is the subject of a future paper. Since the MHO is being used widely for the interpretation of data [1,12,27,28,42] we expand in the present paper the preliminary classical analysis of the MHO potential [41] and demonstrate its connection with quantum-mechanical single particle orbitals. One particular result of the classical analysis is a kind of scaling relationship between energy range and the strength λ of the ( L) 2 term in the MHO potential.…”