  We consider the Casimir interaction, mediated by massless fermions, between a
spherical defect and a flat potential barrier, assuming hard (bag-type)
boundary conditions at both the barrier and the surface of the sphere. The
computation of the quantum interaction energy is carried out using the multiple
scattering approach, adapted here to the setup in question. We find an exact
integral formula for the energy, from which we extract both the large and short
distance asymptotic behaviour. At large distance the fermionic contribution is
found to scale as $L^{-3}$, in contrast to that of electromagnetic vacuum
fluctuations that, assuming perfectly conducting boundaries, scales as
$L^{-4}$. At short distance, we compute the leading and sub-leading
contribution to the vacuum energy. The leading one coincides with what it is
expected from the proximity force approximation, while the sub-leading term
gives, contrary to the electromagnetic case, a positive correction to the
proximity force result.
