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

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.

13 pages; RevTeX

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Cited by in corpus (6)

• Comment on "Revisiting the divergent multipole expansion of atom-surface interactions: Hydrogen and positronium, $\alpha$-quartz, and physisorption" (arXiv:2308.04656v3)
• Retardation Effects in Atom-Wall Interactions
• Reply to Comment on "Revisiting the divergent multipole expansion of atom-surface interactions: Hydrogen and positronium, alpha-quartz, and physisorption" (arXiv:2501.14803)
• Coupled Oscillators and Dielectric Function
• Bound Deuteron-Antideuteron System (Deuteronium): Leading Radiative and Internal-Structure Corrections to Bound-State Energies
• Temperature-Dependent Dielectric Function of Calcium Fluoride