  We extend previous work on the vacuum energy of a massless scalar field in
the presence of singular potentials. We consider a single sphere denoted by the
so-called "delta-delta prime" interaction. Contrary to the Dirac delta
potential, we find a nontrivial one-parameter family of potentials such that
the regularization procedure gives an unambiguous result for the Casimir
self-energy. The procedure employed is based on the zeta function
regularization and the cancellation of the heat kernel coefficient a_2. The
results obtained are in agreement with particular cases, such as the Dirac
delta or Robin and Dirichlet boundary conditions.
