Deformed Harmonic Oscillators for Metal Clusters: Analytic Properties and Supershells

TL;DR

This paper compares the analytic properties of Nilsson's Modified Oscillator and a 3D q-deformed harmonic oscillator, demonstrating that the latter accurately predicts supershell closures in alkali clusters with minimal parameters.

Contribution

It introduces a quantum algebraic approach to harmonic oscillators, showing improved predictions of supershells in metal clusters over traditional models.

Findings

3D q-deformed harmonic oscillator accurately predicts supershell closures.

Exact energy expressions for closed shells are derived and compared.

The q-deformed oscillator reproduces magic numbers up to 1500 alkali atoms.

Abstract

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.