Interaction and charge transfer between dielectric spheres: exact and approximate analytical solutions

TL;DR

This paper derives exact and approximate analytical solutions for charge transfer and interaction energies between dielectric spheres, accounting for polarization effects, with applications in nanomaterials and astrophysics.

Contribution

It provides the first exact analytical solutions for dielectric sphere interactions and introduces simplified approximations for practical use.

Findings

Exact solutions include infinite polarization effects

Simplified formulas are effective for practical calculations

Dielectric properties significantly influence charge transfer processes

Abstract

We present exact analytical solutions for charge transfer reactions between two arbitrarily charged hard dielectric spheres. These solutions, and the corresponding exact ones for sphere-sphere interaction energies, include sums that describe polarization effects to infinite orders in the inverse of the distance between the sphere centers. In addition, we show that these exact solutions may be approximated by much simpler analytical expressions that are useful for many practical applications. This is exemplified through calculations of Langevin type cross sections for forming a compound system of two colliding spheres and through calculations of electron transfer cross sections. We find that it is important to account for dielectric properties and finite sphere sizes in such calculations, which for example may be useful for describing the evolution, growth, and dynamics of nanometer sized dielectric objects such as molecular clusters or dust grains in different environments including astrophysical ones.