  We obtain analytically the exact non-retarded dispersive interaction energy
between an atom and a perfectly conducting disc. We consider the atom in the
symmetry axis of the disc and assume the atom is predominantly polarizable in
the direction of this axis. For this situation we discuss the finite size
effects on the corresponding interaction energy. We follow the recent procedure
introduced by Eberlein and Zietal together with the old and powerful
Sommerfeld's image method for non-trivial geometries. For the sake of clarity
we present a detailed discussion of Sommerfeld's image method. Comparing our
results form the atom-disc system with those recently obtained for an atom near
a conducting plane with a circular aperture, we discus the non-additivity of
the van der Waals interactions involving an atom and two complementary
surfaces. We show that there is a given ratio z/a between the distance z from
the atom to the center of the disc (aperture) and the radius of the disc a
(aperture) for which non-additivity effects vanish. Qualitative arguments
suggest that this quite unexpected result will occur not only for a circular
hole, but for anyother symmetric hole.
