Multiple-Scattering corrections in ‘spherical’ and ‘ring’ geometry

A method is given for making a correction for multiple scattering in experiments to measure the angular distribution of elastically scattered neutrons, when the average path length of the neutron in the specimen is comparable with, but not substantially greater than, the scattering mean free path. In the case of isotropic nuclear scattering the probabilities of multiple scattering are evaluated for a sphere and for ring specimens of circular and rectangular cross-section; double scattering by direct reduction of the appropriate integrals and higher order processes by approximate methods. The anisotropic.scattering of neutrons of several MeV is dealt with by representing the cross-section σ(θ) = σ₁(θ) + σ₂(θ) as the sum of σ₁(θ), a forward peak, and σ₂(θ) a more or less isotropic remainder term. Nuclear scattering events are then divided into two types according as to which partial cross-section is involved, and double-scattering processes correspondingly divided into four classes. The probabilities of all the four last-mentioned classes are calculated from the results of the theory for isotropic scattering. Higher multiplicities of scattering are treated in the same way.