  In earlier papers we have applied multiple scattering techniques to calculate
Casimir forces due to scalar fields between different bodies described by delta
function potentials. When the coupling to the potentials became weak,
closed-form results were obtained. We simplify this weak-coupling technique and
apply it to the case of tenuous dielectric bodies, in which case the method
involves the summation of van der Waals (Casimir-Polder) interactions. Once
again exact results for finite bodies can be obtained. We present closed
formulas describing the interaction between spheres and between cylinders, and
between an infinite plate and a retangular slab of finite size. For such a
slab, we consider the torque acting on it, and find non-trivial equilibrium
points can occur.
