Revisiting the Divergent Multipole Expansion of Atom-Surface Interactions: Hydrogen and Positronium, alpha-Quartz, and Physisorption

TL;DR

This paper revisits and corrects the multipole expansion of atom-surface interactions, providing refined asymptotic formulas, analyzing specific cases like hydrogen and positronium with alpha-quartz, and discussing implications for physisorption.

Contribution

It offers a revised derivation of multipole contributions, correcting previous results, and explores their significance in atom-surface interactions and related theoretical models.

Findings

Quadrupole correction is numerically significant.

The multipole expansion is an asymptotic, divergent series.

Analytic multipole polarizabilities are provided for hydrogen and positronium.

Abstract

We revisit the derivation of multipole contributions to the atom-wall interaction previously presented in [G. Lach et al., Phys. Rev. A 81, 052507 (2010)]. A careful reconsideration of the angular-momentum decomposition of the second-, third- and fourth-rank tensors composed of the derivatives of the electric-field modes leads to a modification for the results for the quadrupole, octupole and hexadecupole contributions to the atom-wall interaction. Asymptotic results are given for the asymptotic long-range forms of the multipole terms, in both the short-range and long-range limits. Calculations are carried out for hydrogen and positronium in contact with $\alpha$-quartz; a reanalysis of analytic models of the dielectric function of alpha-quartz is performed. Analytic results are provided for the multipole polarizabilities of hydrogen and positronium. The quadrupole correction is shown to be numerically significant for atom-surface interactions. The expansion into multipoles is shown to constitute a divergent, asymptotic series. Connections to van-der-Waals corrected density-functional theory and applications to physisorption are decribed.