  We investigate dispersive optical nonlinearities that arise from Rydberg
excitation blockade in cold Rydberg gases. We consider a two-photon transition
scheme and study the non-linear response to a weak optical probe in presence of
a strong control beam. For very low probe fields, the dominant nonlinearities
are of the third order and they can be exactly evaluated in a steady state
regime. In a more general case, the change in average atomic populations and
coherences due to Rydberg interactions can be characterized by properly defined
scaling parameters, which are generally complex numbers but in certain
situations take the usual meaning of the number of atoms in a blockade sphere.
They can be used in a simple "universal scaling" formula to determine the
dispersive optical nonlinearity of the medium. We also develop a novel
technique to account for the Rydberg interaction effects, by simplifying the
treatment of nonlocal interaction terms, the so-called collisional integrals.
We find algebraic relations that only involve two-body correlations, which can
be solved numerically. All average populations and coherences are then obtained
straightforwardly.
