Strong Coupling in Inelastic Collisions of Electrons with Atoms

The various approximations which have been used to calculate the probability of excitation of an atom by impact with an electron whose energy is not greatly in excess of the threshold are known to fail under certain conditions This is especially true in the important cases in which the excitation proceeds mainly through electron exchange. In these cases the exchange coupling is too strong for approximate methods, which assume weak coupling, to be valid By using a schematic model exact solutions for strong exchange coupling are obtained and compared with the results of different weak coupling approximations It is found that the Born-Oppenheimer approximation is never reliable at low electron energies but if distortion of the incident and scattered waves by the atomic field is allowed for correctly much better results may be obtained.