We study the repulsive van der Waals interaction of cold rubidium $70S_{1/2}$ Rydberg atoms by analysis of time-delayed pair correlation functions. After excitation, Rydberg atoms are allowed to accelerate under the influence of the van der Waals force. Their positions are then measured using a single-atom imaging technique. From the average pair correlation function of the atom positions we obtain the initial atom-pair separation and the terminal velocity, which yield the van der Waals interaction coefficient $C_{6}$. The measured $C_{6}$ value agrees well with calculations. The experimental method has been validated by simulations. The data hint at anisotropy in the overall expansion, caused by the shape of the excitation volume. Our measurement implies that the interacting entities are individual Rydberg atoms, not groups of atoms that coherently share a Rydberg excitation.
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