Quantum theory of inelastic multiple scattering in phase space

Abstract

We propose a general framework in which inclusive inelastic scattering of medium- or high-energy hadrons on nuclei can be discussed, without resorting either to the fixed scatterer approximation, or to a frankly classical description. A combination of Watson's multiple scattering theory and the Wigner representation—which had to be extended for this purpose—enables us to visualize the reaction in phase space as a series of inelastic two-body collisions, separated by propagations in an optical potential. The inclusive multiple scattering series can be summed up in principle by solving a one-body integral equation in phase space. This “cascade equation” is derived in a simple nuclear model, and shown to be equivalent to a transport equation for the Wigner density matrix of the projectile. Quantum-mechanical interference and wave effects can be treated systematically within this scheme. In the static, eikonal approximation, we recover the results of Glauber theory, and in the classical limit a particular form of the Boltzmann equation.