Divergencies in the Casimir energy for a medium with realistic ultravioletbehaviour

We consider a dielectric medium with an ultraviolet behaviour as follows fr om the Drude model. Compared with dilute models, this has the advantage tha t, for large frequencies, two different media behave in the same way. As a result one expects the Casimir energy to contain fewer divergencies than fo r the dilute media approximation. We show that the Casimir energy of a sphe rical dielectric ball contains just one divergent term, a volume one, which can be renormalized by introducing a contact term analogous to the volume energy counterterm needed in bag models.