At low ion energies, the approximation of independent collisions between atoms starts to break down. This issue can be to some extent augmented by solving the collision integral for multiple simultaneous collisions. However, at very low energies (below ~1 keV, for a more accurate estimate see ) the BCA approximation always breaks down, and one should use molecular dynamics ion irradiation simulation approaches because these can, per design, handle many-body collisions of arbitrarily many atoms. The MD simulations can either follow only the incoming ion (recoil interaction approximation or RIA ) or simulate all atoms involved in a collision cascade .