  A simple model is presented for the appearance of attraction between two like
charged polyions inside a polyelectrolyte solution. The polyions are modeled as
rigid cylinders in a continuum dielectric solvent. The strong electrostatic
interactions between the polyions and the counterions results in counterion
condensation. If the two polyions are sufficiently close to each other their
layers of condensed counterions can become correlated resulting in attraction
between the macromolecules. To explore the counterion induced attraction we
calculate the correlation functions for the condensed counterions. It is found
that the correlations are of very short range. For the parameters specific to
the double stranded DNA, the correlations and the attraction appear only when
the surface-to-surface separation is less than 7 /AA.
