The collision of slow electrons with atoms. II.—General theory and inelastic collisions

Although a satisfactory theory of the collisions of fast electrons with atoms is provided by the method of Born-Dirac, a complete theory of slow collisions has not yet been developed. This is due to the large number of complicating factors which cannot be neglected when the time of interaction between atoms and the incident wave is considerable. These complications include the distortion of the incident and scattered waves by the atomic field, the exchange of electrons between atom and colliding beam, and the disturbance of the atomic wave functions by the incident wave. The effect of the second of these phenomena was considered in detail to a first approximation by us and found to be of considerable importance. In this paper, the accuracy of the calculation could not be regarded as high inasmuch as the other disturbing effects were neglected. It was then shown in a later paper how the effect of the disturbance of the incident wave could be included in the calculation, and it was found that for the elastic scattering the agreement with experiment was considerably improved. On applying the method to the calculation of inelastic collision probabilities, the effect of the distortion of the incident wave was found to be small in comparison with, say, the effect of exchange. However, when one considers physically the excitation of an atom by electron impact, it is clear that the distortion of the outgoing wave by the field of the excited atom will be of greater importance than that of the incident wave by the normal atom. This is due to the greater spread of the field of the excited atom and also to the increased wave-length of the outgoing wave. In the same way, the distortion of the outgoing wave may be important in the case of elastic exchange.