Multiple scattering of scalar waves by point scatterers in one dimension. II

In the first paper of this series, we studied the problem of scattering in one dimension of a wave interacting with n randomly distributed pointlike scatterers by delta-function potentials. Averaging the wave function for a constant amplitude transmitted wave over an ensemble of configurations allowed us to obtain an analytic expression for the optical potential which, in certain limits, took the form of the scatterer density ρ times the scattering strength Γ. We examine the domain in parameter space where ρΓ can be regarded as a good approximation to the optical potential for both this problem and the problem in which the amplitude of the incident wave is constant. The conditions on the parameters are found to be the same in both the preceding problems. We then supplement ρΓ by an appropriate imaginary part. The wave function predicted from this effective potential approximation to the optical potential is in good agreement with that from the exact solution. NUCLEAR REACTIONS Multiple scattering, n randomly distributed point scatterers, one dimension; determination of parameter domain where optical potential is ρ Γ; parameters are ρ (number density), Γ (scattering strength); transmitted and reflected waves.