  Let $\FRAK{g}$ be a classical simple Lie superalgebra. To every nilpotent
orbit $\cal O$ in $\FRAK{g}_0$ we associate a Clifford algebra over the field
of rational functions on $\cal O$. We find the rank, $k(\cal O)$ of the
bilinear form defining this Clifford algebra, and deduce a lower bound on the
multiplicity of a $U(\FRAK{g})$-module with $\cal O$ or an orbital subvariety
of $\cal O$ as associated variety. In some cases we obtain modules where the
lower bound on multiplicity is attained using parabolic induction. The
invariant $k(\cal O)$ is in many cases, equal to the odd dimension of the orbit
$G\cdot\cal O$ where $G$ is a Lie supergroup with Lie superalgebra ${\mathfrak
g.}$
