Image method in the calculation of the van der Waals force between an atom and a conducting surface

TL;DR

This paper reviews a classical electrostatic image method combined with a quantum approach to efficiently compute van der Waals forces between an atom and conducting surfaces of arbitrary shape, including new specific examples.

Contribution

It demonstrates how electrostatic image methods can be integrated with the Eberlein and Zietal approach to calculate dispersion forces for complex geometries.

Findings

Effective use of image method for atom-surface van der Waals calculations

Application to atom-sphere system with explicit force calculation

Novel result: van der Waals force with a grounded conducting boss hat

Abstract

Initially, we make a detailed historical survey of van der Waals forces, collecting the main references on the subject. Then, we review a method recently proposed by Eberlein and Zietal to compute the dispersion van der Waals interaction between a neutral but polarizable atom and a perfectly conducting surface of arbitrary shape. This method has the advantage of relating the quantum problem to a corresponding classical one in electrostatics so that all one needs is to compute an appropriate Green function. We show how the image method of electrostatics can be conveniently used together with the Eberlein and Zietal mehtod (when the problem admits an image solution). We then illustrate this method in a couple of simple but important cases, including the atom-sphere system. Particularly, in our last example, we present an original result, namely, the van der Waals force between an atom and a boss hat made of a grounded conducting material.