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At nonrelativistic energies, for arbitrarily complicated collisions of distinguishable or indistinguishable particles, with or without rearrangement, correct formal expressions for the cross sections are known and well established. Nonetheless, all inelastic collision cross sections must be estimated, rather than predicted accurately, because even with present high spread computers there is no three‐or‐more particle collision for which it is practical to solve the Schroedinger equation exactly. The validity of the customary Born approximation, and of other more elaborate approximate calculations, are discussed, mainly with reference to electron excitation cross sections. The evidence suggests that a ``compound ion model'' of excitation, which is contrasted with the more usual ``direct interaction model,'' may prove helpful in understanding the sharp peaks and other anomalous features in some excitation cross sections near threshold. It is argued briefly that (i) there are reasons to think that at high energies Born approximation is not valid for exchange amplitudes, which are the only amplitudes appearing in excitation involving change of spin multiplicity; (ii) there are circumstances when Born approximation becomes increasingly valid as the incident electron energy is decreased.