Evaluation of incoherent scattering intensity by transmission and sample thickness

The H atom has a large incoherent scattering cross section and is a major source of incoherent scattering intensity, (dΣ/dΩ)_inc, in small-angle neutron scattering. By taking account of multiple scattering from H atoms, a useful method (the transmission method or T method) is proposed for the estimation of (dΣ/dΩ)_inc for various types of hydrogen-containing systems. The incoherent scattering intensity is calculated simply from the transmission, T, and the thickness of the sample, t, i.e. (dΣ/dΩ)_inc ≅ [exp(Σ_tott) − 1]/(4πt) = (1 − T)/(4πtT), where Σ_tot ≡ −(lnT)/t is the macroscopic total cross section per unit volume. This method provides a reasonably accurate value of incoherent scattering intensity for various systems. The validity and the extent of applicability of the T method are examined for several samples, including light/heavy water mixtures, polymer gels and surfactant aqueous dispersions.