  Rydberg atoms and beams of ultracold polar molecules have become highly
useful experimental tools in recent years. There is therefore a need for
accessible calculations of interaction potentials between such particles and
nearby surfaces and structures, bearing in mind that the particles are far out
of thermal equilibrium with their environment and that their interaction is
predominantly non-retarded. Based on a new perturbative expansion with respect
to the inverse speed of light and the inverse conductivity, we derive a simple,
closed-form expression for the interaction potential (i.e., the particle energy
level shifts) of a particle and a metallic sphere that is is accurate at better
than 1% level for typical experimental set-ups at room temperature and above,
and off by no more than a few percent at any temperature including zero. Our
result illuminates the influence of retardation and imperfect conductivity and
the interplay of these effects with geometry. The method developed for the
present study may be applied to other, more complex geometries.
