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The application of the quantum theory to the collision of electrons with atoms has now been worked out in some detail. For fast collisions the calculations present no difficulty, since Born's method may be applied and the probability of excitation of a given level of a simple atom can be worked out quite accurately. The corresponding problem for the case of slow collisions is much more difficult and requires a knowledge of the exact solution of the equation representing the motion of electrons in the static field of the atom considered. Using such solutions obtained by Faxén and Holtsmark's method, and allowing also for electron exchange, Massey and Mohr have been able to calculate excitation probabilities for low voltage impact in hydrogen and helium.
H. S. W. Massey (Fri,) studied this question.