Spherical image states for one- and two-electron atoms

The interaction between a system of charged particles can be strongly affected by the surrounding
media. While for free particles in vacuum, the interaction is described by the Coulomb potential, the
presence of polarizable surfaces introduces surface-particle forces, thus modifying interparticle
interactions. In a recent communication [Randazzo et al., 2024, Proc. R. Soc. A 480: 20240357],
these interactions are described by integrating the electromagnetic energy density of the electrical
system in a stationary approximation, a procedure which recovers the Coulomb interaction for free
particles in vacuum. As an illustration, concave and convex spherical conductor surface cases have
been considered, and analytical expressions could be derived.

In this work, we present the results of one- and two-electron atoms interacting with spherical conductor
surfaces. First, the dynamics of a single electron confined in a spherical cavity in a conductor and
surrounding a conductive sphere is considered. It is shown that for large surface radii, eigenstates
and eigenvalues can be accurately described by analytical expressions.
Then, one- and two-electron atomic systems are investigated. When compared to the corresponding
unconfined systems, the level structure and the charge density distributions are drastically changed
(see Morcillo-Arencibia et al. [2025, Proc. R. Soc. A, in press] for a case of a spherical cavity
in a conductor). This is also the case for the conducting sphere. The influence of such confinement is
also illustrated by studying the photoionization of electron nano sphere states.