  The dipole-dipole interaction among ultra-cold Rydberg atoms is simulated. We
examine a general interaction scheme in which two atoms excited to the x and x'
states are converted to y and y' states via a Forster resonance. The atoms are
arranged in two spatially separated groups, each consisting of only one species
of atom. We record the fraction of atoms excited to the y' state as the
distance between the two groups is varied. With zero detuning a many-body
effect that relies on always resonant interactions causes the interaction to
have a finite range. When the detuning is greater than zero, another many-body
effect causes a peak in the interaction when the two groups of atoms are some
distance away from each other. To obtain these results it is necessary to
include multiple atoms and solve the full many-body wave function. These
simulation results are supported by recent experimental evidence. These
many-body effects, combined with appropriate spatial arrangement of the atoms,
could be useful in controlling the energy exchange among the atoms.
