  We present calculations of ground state properties of spherical, doubly
closed-shell nuclei from $^{16}$O to $^{208}$Pb employing the techniques of
many-body perturbation theory using a separable density dependent monopole
interaction. The model gives results in Hartree-Fock order which are of similar
quality to other effective density-dependent interactions. In addition, second
and third order perturbation corrections to the binding energy are calculated
and are found to contribute small, but non-negligible corrections beyond the
mean-field result. The perturbation series converges quickly, suggesting that
this method may be used to calculate fully correlated wavefunctions with only
second or third order perturbation theory. We discuss the quality of the
results and suggest possible methods of improvement.
