Self-energy of a charged conducting droplet as an inversion problem

Abstract

The determination of fission barrier heights of charged clusters of alkali atoms requires the calculation of the electrostatic self-energy of arbitrarily shaped, conducting droplets. For axially symmetric shapes we propose to determine a charge distribution on the axis giving rise to the same electric field outside the droplet as the actual surface charge. This leads to an ill-posed inversion problem. We discuss its regularization and demonstrate the usefulness of the method in some examples.