  We report on a novel approach to the Deam-Edwards model for interacting
polymeric networks without using replicas. Our approach utilizes the fact that
a network modelled from a single non-interacting Gaussian chain of macroscopic
size can be solved exactly, even for randomly distributed crosslinking
junctions. We derive an {\it exact} expression for the partition function of
such a generalized Gaussian structure in the presence of random external fields
and for its scattering function $S_0$. We show that $S_0$ of a randomly
crosslinked Gaussian network (RCGN) is a self-averaging quantity and depends
only on crosslink concentration $M/N$, where $M$ and $N$ are the total numbers
of crosslinks and monomers. From our derivation we find that the radius of
gyration $R_{\mbox{\tiny g}}$ of a RCGN is of the universal form
$R_{\mbox{\tiny g}}^2=(0.26 \pm 0.01)a^2 N/M$, with $a$ being the Kuhn length.
To treat the excluded volume effect in a systematic, perturbative manner, we
expand the Deam-Edwards partition function in terms of density fluctuations
analogous to the theory of linear polymers. For a highly crosslinked
interacting network we derive an expression for the free energy of the system
in terms of $S_0$ which has the same role in our model as the Debye function
for linear polymers. Our ideas are easily generalized to crosslinked polymer
blends which are treated within a modified version of Leibler's mean field
theory for block copolymers.
