Zeros of Rydberg-Rydberg Foster interactions

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.