  A multiple scattering formulation is used to calculate the force, arising
from fluctuating scalar fields, between distinct bodies described by
$\delta$-function potentials, so-called semitransparent bodies. (In the limit
of strong coupling, a semitransparent boundary becomes a Dirichlet one.) We
obtain expressions for the Casimir energies between disjoint parallel
semitransparent cylinders and between disjoint semitransparent spheres. In the
limit of weak coupling, we derive power series expansions for the energy, which
can be exactly summed, so that explicit, very simple, closed-form expressions
are obtained in both cases. The proximity force theorem holds when the objects
are almost touching, but is subject to large corrections as the bodies are
moved further apart.
