Van der Waals interaction between an atom with spherical plasma shell

TL;DR

This paper calculates the van der Waals energy of an atom near a spherical plasma shell, modeling fullerenes, using zeta-function regularization, and explores how the energy varies with distance and sphere size.

Contribution

It introduces a method to compute van der Waals energy for an atom near a finite-radius sphere with finite conductivity, extending Casimir-Polder results to spherical geometries.

Findings

Energy decreases as $d^{-3}$ near the sphere and $d^{-7}$ at large distances.

For hydrogen on C60, the energy is approximately 3.8 eV.

Fullerene polarizability scales with the cube of its radius.

Abstract

We consider the van der Waals energy of an atom near the infinitely thin sphere with finite conductivity which model the fullerene. We put the sphere into spherical cavity inside the infinite dielectric media, then calculate the energy of vacuum fluctuations in framework of the zeta-function approach. The energy for a single atom is obtained from this expression by consideration of the rare media. In the limit of the infinite radius of the sphere the Casimir-Polder expression for an atom and plate is recovered. For finite radius of sphere the energy of an atom monotonously falls down as $d^{-3}$ close to the sphere and $d^{-7}$ far from the sphere. For hydrogen atom on the surface of the fullerene $C_{60}$ we obtain that the energy is $3.8 eV$. We obtain also that the polarizability of fullerene is merely cube of its radius.