Many-body forces between ions

The dynamics of ion surface scattering at energies exceeding several hundred electronvolts can be described by a series of binary collision approximations (BCAs) in which only the interaction of one energetic particle with a solid atom is considered at a time [25]. This model is reasonable because the interaction time for the collision is short compared witii the period of phonon frequencies in solids, and the interaction distance is shorter tlian the interatomic distances in solids. The BCA simplifies the many-body interactions between a projectile and solid atoms to a series of two-body collisions of the projectile and individual solid atoms. This can be described with results from the well known two-body central force problem [26]. 

Sodium chloride is a white, crystalline substance held together by the electrostatic forces between its two constituents, sodium ions and chloride ions. Salt is essential for human life. An average person has almost a quarter pound of it distributed throughout his or her body. Many of the sodium ions are found in the blood, where, among other things, they regulate blood pressure. Because salt is lost in sweat and urine, a normal diet requires us to consume it regularly. 

The study of the topology and dynamics of "host and guest systems is one of the ways to evaluate interaction forces. In condensed matter, the interactions between particles (i.e. atoms, molecules, ions) determine their relative equilibrium positions and orientations, and their dynamical behaviour. The calculation of interaction forces is a difficult problem it is a many-body problem, each particle being surrounded by many others. However the host-guest interaction can be reduced to a two-body system, therefore making the problem more easily tractable even if each body is itself a complicated system. 

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