  A numerical simulation of silica aerogels is performed using
diffusion-limited cluster-cluster aggregation of spheres inside a cubic box
(with periodic boundary conditions). The volume fraction $c$ is taken to be
sufficiently large to get a gel structure at the end of the process. In the
case of monodisperse spheres, the wavevector dependent scattered intensity
$I(q)$ is calculated from the product of the form factor $P(q)$ of a sphere by
the structure factor $S(q)$, which is related to the Fourier transform of
$g(r)-1$, where $g(r)$ is the pair correlation function between sphere centers.
The structure factor $S(q)$ exhibits large-$q$ damped oscillations
characteristics of the short range (intra-aggregate) correlations between
spheres. These oscillations influence the $I(q)$ curve in the $q$-region
between the fractal regime and the Porod regime and quantitative comparisons
are made with experiments on colloidal aerogels. Moreover, at small-$q$ values,
$S(q)$ goes through a maximum characteristic of large range (inter-aggregate)
correlations. Quantitative fits of the maximum in the experimental $I(q)$
curves of base-catalyzed aerogel are presented. In the case of polydisperse
spheres, $I(q)$ is calculated directly from a single aggregate simulation. It
is shown that increasing polydispersity shifts the location of the cross-over
between the fractal and Porod regimes towards low $q$-value.
