  We continue our study of intermittency for the parabolic Anderson equation
$\partial u/\partial t = \kappa\Delta u + \xi u$, where $u\colon \Z^d\times
[0,\infty)\to\R$, $\kappa$ is the diffusion constant, $\Delta$ is the discrete
Laplacian, and $\xi\colon \Z^d\times [0,\infty)\to\R$ is a space-time random
medium. The solution of the equation describes the evolution of a ``reactant''
$u$ under the influence of a ``catalyst'' $\xi$.
  In this paper we focus on the case where $\xi$ is exclusion with a symmetric
random walk transition kernel, starting from equilibrium with density $\rho\in
(0,1)$. We consider the annealed Lyapunov exponents, i.e., the exponential
growth rates of the successive moments of $u$. We show that these exponents are
trivial when the random walk is recurrent, but display an interesting
dependence on the diffusion constant $\kappa$ when the random walk is
transient, with qualitatively different behavior in different dimensions.
Special attention is given to the asymptotics of the exponents for
$\kappa\to\infty$, which is controlled by moderate deviations of $\xi$
requiring a delicate expansion argument.
  In G\"artner and den Hollander \cite{garhol04} the case where $\xi$ is a
Poisson field of independent (simple) random walks was studied. The two cases
show interesting differences and similarities. Throughout the paper, a
comparison of the two cases plays a crucial role.
