Quasi-classical scattering theory and bound state production processes

Abstract

We develop a theoretical approach to collisions involving complex systems with special emphasis to applications involving a short wavelength approximation. Use of the Wigner representation casts the quantum mechanical scattering problem in the form of a stochastic process. Useful analogies to classical transport theory may then be drawn. Monte Carlo calculations of production processes are then discussed in this framework. One immediate result is the derivation of the correct formula for bound state production via the Monte Carlo method. Further development of our general formalism yields a diagrammatic procedure useful for the calculation of various inclusive cross-sections. This is then applied to the problem of fast deuteron production in high energy proton-nucleus collisions. A lowest order calculation is made involving no free parameters. The resulting formulae are physically transparent. Experimental data are reproduced with an accuracy consistent with the first-order, parameter-free nature of the calculation.