Self-consistent assessment of Englert-Schwinger model on atomic properties

TL;DR

This paper evaluates the Englert-Schwinger (ES) statistical atom model, demonstrating its comparable accuracy to TFD-1/5vW models and its correction of near-nucleus Pauli potential issues, while highlighting limitations for low-Z atoms.

Contribution

It provides a self-consistent assessment of the ES model, benchmarking it against Kohn-Sham and orbital-free models, and identifies its strengths and limitations.

Findings

ES model matches TFD-1/5vW accuracy

ES corrects near-nucleus Pauli potential failure

Model struggles with low-Z atoms

Abstract

Our manuscript investigates a self-consistent solution of the statistical atom model proposed by Berthold-Georg Englert and Julian Schwinger (the ES model) and benchmarks it against atomic Kohn-Sham and two orbital-free models of the Thomas-Fermi-Dirac (TFD)-$\lambda$vW family. Results show that the ES model generally offers the same accuracy as the well-known TFD-$\frac{1}{5}$vW model; however, the ES model corrects the failure in Pauli potential near-nucleus region. We also point to the inability of describing low-$Z$ atoms as the foremost concern in improving the present model.