  We present a theory for the equilibrium structure of polyelectrolyte
solutions. The main element is a simple, new optimization scheme that allows
theories such as the random phase approximation (RPA) to handle the harsh
repulsive forces present in such systems. Comparison is made with data from
recent neutron scattering experiments of randomly charged, hydrophilic polymers
in salt-free, semi-dilute solution at various charge densities. Models with
varying degrees of realism are examined. The usual explanation of the
invariance observed at high charge density has been counterion condensation.
However, when polymer-polymer correlations are treated properly, we find that
modeling polymer-counterion correlations at the level of Debye-Huckel theory is
sufficient.
