  In this work we obtain analytical expressions for the non-additivity effects
in the dispersive interaction between two atoms and perfectly conducting
surface of arbitrary shape in the non-retarded regime. We show that this three
bodies quantum-mechanical problem can be solved by mapping it into a two-bodies
electrostatic one. We apply the general formulas developed in this paper in
several examples. Firstly we re-derive the London interaction as a particular
case of our formalism. Then we treat two atoms in the presence of a plane,
re-obtained the result displayed in the literature. After we add some new
examples. A particularly interesting one is two atoms inside a plate capacitor,
a situation where non-additivity is very manifest since the plates lead to the
exponentially suppression of the interaction of the atoms, provided the atoms
are separated by a distance of the order of the distance between the plates or
greater. Our results holds even in the presence of other atoms inside the plate
capacitor. As a last example we deal with two atoms in the presence of a
sphere, both grounded and isolated. We show that for realistic experimental
parameters the non-additivity may be relevant for the force in each atom.

Quantum Physics