Applications of the method of impact parameter in collisions

Abstract

In the application of quantum mechanics to collisions the method of impact parameter has been largely neglected in favour of the more statistical method put forward by Born in 1926. This is mainly because the method of impact parameter is not applicable to all kinds of collisions. It affords, however, a valid treatment of light collisions in which the momentum transfer is small compared with the momentum of the primary particle, and its application in these cases proves very fruitful. We shall deal, in this paper, mostly with the problems which eminently lend themselves to treatment by this method and which have not been previously considered. One of these is the spatial distribution with respect to the path of the particle of the atoms ionised and excited by it. The results obtained in this respect show the existence of a radius of action characteristic of the velocity of the particle. Another problem field of a moving particle and the perturbation of distant atoms by the field of a moving particle and the perturbation of atoms by radiation—one which bears intimately on the theory of the loss of energy by electric particles put forward by Fermi in 1924. The problem of the relativity effect in light collisions is also fully discussed, the quantum-mechanical relativity corrections to the primary ionisation and loss of energy in light collisions being deduced. These corrections were put forward by the writer some time ago, and compared with experiment. Very recently, however, the problem was considered by Bethe, and M ϕ ller, on the basis of Born's theory, and they arrive at the same results. A feature of the use of the method of impact parameter in this problem, as indeed in others, is that the general physical reasons for the results obtained are readily apparent.