The collision between two electrons

Abstract

It is well-known that the problem of the collision between two particles interacting according to the inverse square law is exactly soluble on the wave mechanics, and that the solution yields the same scattering laws as the classical theory. If, however, the two particles are identical, e.g. , two electrons or two α-particles, this is not necessarily the case; for the wave functions used must be antisymmetrical or symmetrical in the co-ordinates of the two particles; and this may affect the scattering laws. In this paper we shall discuss the collision between two particles possessing spin, such as electrons, and also between two particles without spin, such as α-particles. Assuming an inverse square law force between the particles, and neglecting the actual spin forces, we shall deduce from the symmetry properties of the wave functions a scatter­ing law differing considerably from the classical. We shall also mention the various methods by which the effect could be observed, and give some experi­mental evidence in its favour. The application of the exclusion principle to collision problems has been discussed by the author in a previous paper. Suppose we wish to describe the motion of two particles interacting in any field of force. We obtain a solution w (r 1 r 2 ) of the wave equation, where r 1 refers to the position of the first particle, and r 2 to that of the second. If we did not use antisymmetrical wave functions, we should argue that the probability that the first particle should be at r 1 and the second at r 2 would be | w (r 1 r 2 )| 2 , and therefore the probability that one particle should be at r 1 and the other at r 2 would be | w (r 1 r 2 )| 2 + | w (r 2 r 1 )|