Introduction to Relativistic Collisions

The space and time used to describe nonrelativistic collisions are the classical space and absolute time; transitions between different inertial reference frames are mediated by a well known Galilean transformation. The space and time, in which relativistic collisions take place, is the four-dimensional flat space-time of the special theory of relativity.

The dynamics of nonrelativistic ion-atom collisions is fully described by the corresponding Schrödinger equation. This wave equation is of Hamiltonian type and explicitly contains all the interactions between the elementary particles (electrons and nuclei) the ion and atom are composed of, including interactions acting both between and within the colliding atomic particles.

In relativistic collisions such a ‘single-equation’ description is possible only if the fields acting on the colliding particles can be regarded as external perturbations, which themselves are not influenced by the collision. For instance, in collisions between a bare nucleus and an hydrogen-like ion the behavior of the electron can be treated by using the Dirac equation in which the interactions between the electron and the nuclei are taken as independent of the electron motion.

In ion-atom collisions, in which both the ion and atom carry electrons, the fields acting on the colliding particles in general cannot be regarded as external. If the latter is the case, the description of ion-atom collisions cannot be based merely on the Dirac equation. Instead, it has to include self-consistent considerations for charged particles and the electromagnetic field.

In this chapter we shall very briefly consider the special theory of relativity and the Maxwell and Dirac equations.