Slow-neutron multiple scattering

Abstract

Abstract Slow-neutron scattering is perhaps the most powerful method presently available for investigating the structure and dynamics of materials on the atomic level. With relatively few exceptions it can be used to advantage for any material whether it be in the solid, liquid or gaseous state. In the past few years the importance of applying multiple-scattering corrections has come to be recognized, particularly in the case of liquids and gases for which one is interested in mapping the complete scattering function. The present article presents a review and extension of the theoretical basis for such corrections from the point of view of the Vineyard theory of multiple scattering. The theory is formulated for a sample of arbitrary size and shape and a general expression is obtained for the effective scattering function as an expansion in terms of orders of scattering (single, double, etc.). The general properties of this expansion are investigated with particular emphasis on the question of convergence and on ways of improving the rate of convergence by, e.g., the use of absorbing spacers. Exact results are obtained for the multiple scattering in an infinite plane slab. An approximate, semianalytic theory of multiple scattering is developed as an alternative to the Monte Carlo approach. The theory is applied to plane slab, spherical and cylindrical geometries. Finally, a detailed discussion is given of the multiple-scattering correction for recent experiments on liquid neon.