Coherent and incoherent neutron scattering in disordered alloys

Abstract

The problem of neutron scattering in a disordered alloy with mass- and force-constant disorder in combination with different atomic scattering lengths is considered. By diagrammatic analysis it is shown that the total intensity can be decomposed into an incoherent, i.e., dispersion-free, part consisting of the sum of all connected diagrams and into a coherent part which can be represented as the product of the usual average Green's function times the square of an effective scattering length which itself also contains only connected diagrams. Sum rules for the coherent and incoherent intensities are derived. Especially we represent the results for both intensities in the weak scattering limit, in the average-$t$ matrix and the coherent-potential approximation.