On the radiative collision between fast charged particles

Abstract
The radiation emitted in the collision of a fast charged particle with a nucleus has been treated in quantum mechanics by Heitler, Bethe, and various other authors. In all cases the nucleus has been considered infinitely heavy, the field of the nucleus being then an external field so that the problem reduces to a one-body problem. It may be of some interest to consider the more general case, where the two colliding particles have masses comparable with each other. When a fast particle traverses matter many different elementary processes are possible. Some of these are: (1) collisions with the atomic electron; (2) collisions with the atomic nucleus in both cases without emission of radiation; we further have (3) radiative collisions with the atomic electrons; and (4) radiative collisions with the nucleus. If the colliding particle is an electron the third process is of the type we wish to consider where the masses of the particles are comparable. For not too large velocities of the incident particle the stopping of the particle is mainly due to the first process, which has been treated in quantum mechanics by various authors. For very large velocities and large atomic number the fourth process is the most important. If, however, the velocity is very large and the atomic number small the third process will presumably give a contribution to the stopping which is large compared with that of the first and comparable with that of the fourth process. Further, when one has treated the radiative collision of two electrons, one can immediately answer two other questions. If one of the electrons after the collision is in a negative state the collision process is the converse of the photo-production of a pair of positive and negative electrons in the presence of an electron. And if both electrons are in a negative state after the collision we have the converse process of the simultaneous production of two pairs by a photon. (The last process is only possible if the particles are not free.)

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