Comment on "Revisiting the divergent multipole expansion of atom-surface interactions: Hydrogen and positronium, $\alpha$-quartz, and physisorption" (arXiv:2308.04656v3)

TL;DR

This paper critiques recent derivations of multipole corrections to atom-surface interactions, demonstrating that previous claims of significant effects are invalid within their proper application regimes, and confirming that these corrections are generally negligible.

Contribution

It clarifies the correct application ranges of multipole corrections in atom-surface interactions and shows that these corrections are negligible when properly applied.

Findings

Incorrect application areas were identified in previous work.

Within valid regimes, multipole corrections are negligibly small.

The critique aligns the theory with Lifshitz theory principles.

Abstract

Recently U. D. Jentschura [Phys. Rev. A $\bf 109$, 012802 (2024)] rederived the multipole corrections to the dipole part of the atom-wall interaction described by the Lifshitz theory using the concept of volume dielectric permittivity. These corrections were computed for the hydrogen and positronium atoms in close proximity to the $\alpha$-quartz wall and claimed to be numerically significant within the short-range regime. Here, it is shown that the application areas of the obtained expressions both in the short-and long-range asymptotic regimes are indicated incorrectly, in contradiction with those dictated by the Lifshitz theory. As a result, within the valid application areas, all multipole corrections to the Casimir-Polder dipole part of the atom-wall interaction turned out to be negligibly small.