CASIMIR EFFECT FOR BODIES OF ARBITRARY SIZE

The usual expressions reported for the Casimir energy as a function of the characteristic size of system a are all divergent as a goes to ze ro. In this paper we make a careful revision of the calculations for t hree metallic systems (the parallel plates in one and three dimensions , and the spherical shell), introducing a cut-off frequency with a phy sical meaning and not merely as a mathematical tool; we thus obtain re sults that are valid for small sizes. The Casimir energy turns out to have an interesting behaviour for small a; in particular, in the case of the spherical shell it gives rise to an attractive force, as oppose d to the repulsive force proportional to a-2 reported in the literatur e. Some possible consequences of physical interest are briefly discuss ed.