The Relativistic Linear Boltzmann Transport Equation.

In this thesis the relativistic linear Boltzmann transport equation is applied to an experiment in pion production by 740 MeV protons incident on a variety of nuclei. This equation is solved by the Monte Carlo method of generating a single particle intranuclear cascade. The transport equation is derived starting with the N-body equation of motion for quantum mechanics in phase in order to determine under what conditions it is a valid approximation. It is shown that it should be a valid semi-classical approximation provided that: (1) The kinetic energy of the transport particle is much greater than its energy of interaction with the mean nuclear potential field. (2) The two-body collision interactions which make up the single particle intranuclear cascade take place over space and time intervals which are small relative to the internucleon space and time intervals for interactions within the nucleus and also compared to the space and time scales over which the probability distribution undergoes variation. In the pion production calculation condition (2) is only approximately met but reasonable agreement with the experimental data is obtained similar to that obtained in other theoretical calculations compared to this experiment.