  Rydberg states of atoms are of great current interest for quantum
manipulation of mesoscopic samples of atoms. Long-range Rydberg-Rydberg
interactions can inhibit multiple excitations of atoms under the appropriate
conditions. These interactions are strongest when resonant collisional
processes give rise to long-range C_3/R^3 interactions. We show in this paper
that even under resonant conditions C_3 often vanishes so that care is required
to realize full dipole blockade in micron-sized atom samples.
