Free energies of triply and quadruply degenerate electron ladder spectra

TL;DR

This paper calculates electronic free energies in metal clusters using ladder spectra with degeneracies three and four, extending known results for lower degeneracies, and reveals that free energy differences do not vanish at high energies.

Contribution

It introduces a generalized approach for calculating free energies in ladder spectra with arbitrary degeneracies, expanding beyond previous models.

Findings

Free energy differences remain non-zero at high energies for size-independent Fermi energies.

Derived low and high temperature asymptotic results for any degeneracy.

Compared free energies across different degeneracy levels in metal clusters.

Abstract

The electronic free energies in metal clusters are calculated based on a simple ladder spectrum for the level degeneracies three and four, and compared with the known results for degeneracies one and two. The low temperature and the asymptotic high temperature results for free energy differences are generalized to ladder spectra of any degeneracy. Remarkably, free energy differences do not approach zero at high energies for size-independent Fermi energies.