Retardation Effects in Atom-Wall Interactions

TL;DR

This paper investigates how retardation effects influence atom-wall interactions, showing the transition from van der Waals to Casimir regimes depends on atomic and material properties, with transition distances around 10 nm for simple atoms.

Contribution

It provides a detailed analysis of the transition range from short-range to retarded atom-wall interactions, including a simple estimate for the critical distance based on atomic polarizability.

Findings

Transition to retarded regime occurs around 10 nm for simple atoms.

Transition distance depends on atomic polarizability and material dielectric properties.

A formula for critical distance z_cr is derived based on atomic parameters.

Abstract

The onset of retardation effects in atom-wall interactions is studied. It is shown that the transition range from the 1/z^3 short-range (van der Waals) interaction to the 1/z^4 long-range (Casimir) retarded interaction critically depends on the atomic properties and on the dielectric function of the material. For simple non-alkali atoms (e.g., ground-state hydrogen and ground-state helium) interacting with typical dielectric materials such as intrinsic silicon, the transition to the retarded regime is shown to proceed at a distance of about 10 nm (200 Bohr radii). This is much shorter than typical characteristic absorption wavelengths of solids. Larger transition regimes are obtained for atoms with a large static polarizability such as metastable helium. We present a simple estimate for the critical distance, z_cr=137*(\alpha(0)/Z)^(1/2) atomic units, where alpha(0) is the static polarizability (expressed in atomic units) and Z is the number of electrons of the atom.