The scattering of electrons by atoms

The scattering of a stream of charged particles by a spherically symmetrical electrostatic field was first investigated, from the point of view of the wave mechanics, by Born. Various authors have developed his ideas and have applied them to the scattering of electrons by atoms, which for the purpose have been treated simply as fields of force. The purpose of the present note is to obtain formulæ for the scattered intensity by methods similar to those used in calculating the scattering of X-rays by an atom. The formulæ obtained have all been published elsewhere, either by the present author, or by others; it has, however, appeared worth while to publish the present method of obtaining them, partly because the analysis is particularly simple, secondly because the results are expressed in a form easy to compare with those for X-rays, and thirdly because the method makes it clear under what conditions the approximations used will lead to a sufficiently accurate result. Experiments on the scattering of streams of charged particles measure the “scattered intensity”; we shall first define just what we mean by this. Suppose we have a beam of particles of such intensity that one particle crosses unit area in unit time. Suppose that the beam fall on one scattering centre—that is to say, on one atom, at a point O. Suppose that a disc, of area R2 d ω be placed at a point P, distant R from O, and such that OP makes an angle θ with the original direction of motion of the particles. The disc is to be normal to OP, so that it subtends a solid angled ω at O. Then if Iθ d ω be the number of particles striking the disc per unit time, Iθ is what we call the scattered intensity.