Two-Particle Collisions. I. General Relations for Collisions in the Laboratory System

The relations between the energies and angles for two-particle collisions are given for the case of conservative central forces. They have been derived in the laboratory system of coordinates, since this system is of prime importance for the interpretation of the experimental results. The dependence on the law of interaction enters the obtained relations through the function for the c.m.-system scattering angle. Some remarks on the statistics of encounters are given, and the cross sections for collisions in which the colliding particles experience given changes in energy and direction are derived. These cross sections can be used to determine the cross sections describing various physical processes. On the basis of the cross sections derived for the scattering problem, one can suggest that the "diffraction" pattern of scattered particles is due to quantized states of the scattering particles, rather than to the law of interaction.