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

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.