Publisher Summary This chapter highlights the nonlocality in interactomic potentials. Interatomic potentials are usually taken to be purely local. With this assumption, the potential is obtained through the use of Born–Oppenheimer approximation. This usually leads to a long range attractive van der Waals' potential and a short range steep repulsion. When such potentials are used in the study of many-body systems, the results are not very satisfactory. The low density and poor binding resulting from these calculations is a result of the large radius of the repulsive core. Within the framework of local potentials, it is not possible to reduce the core radius. It is possible that higher order corrections in Brueckner theory might improve the results, and it is worth studying the consequences of replacing part of the local repulsion by a momentum dependent repulsion. The set of phase shifts determines the potential uniquely only if the potential is assumed to be local. The uncertainty in the potential when the phase shifts are specified is referred to as the off shell uncertainty.