Inelasticity corrections for time-of-flight and fixed wavelength neutron diffraction experiments

Time-of-flight neutron diffraction methods are widely used to study the structure of liquids and glasses. The scattering nuclei in these experiments suffer nuclear recoil in the course of the neutron scattering process, which gives rise to distortions to both the self and distinct structure factors extracted from the data. These distortions are in general difficult to evaluate quantitatively, especially when the mass of the nucleus is similar to that of the neutron, such as when hydrogen is present in the material being studied. Traditional treatments of this effect generally assume the neutron energy is lower than the excitation energy of an atom, but for time-of-flight diffraction this is never the case, and the experiments typically sample a wide range of energy transfers from sub-meV to tens of eV. In addition, by attempting to produce an analytical correction, such methods invariably make a long list of approximations which can be difficult to justify in particular cases. Here, a model for the scattering kernal is developed based on the well known harmonic oscillator model A.C. Zemach and R.J. Glauber, Phys. Rev. 101, 118 (1956)]. This is shown to have the correct first and second moments of the scattering kernal for both the self and distinct scattering, and is used to estimate the self and distinct scattering from a diatomic ‘dumbell’ molecule. The model gives a realistic account of the single atom scattering from light and heavy water over a wide range of incident neutron energies, but is not yet accurate enough to perform quantitative corrections. In lieu of a quantitative approach, a ‘top hat’ convolution method is developed to perform the subtraction of self scattering from real data, and to allow data from multiple detector banks to be merged into a single structure factor. The harmonic oscillator model is also used to address the question of inelasticity effects on the interference scattering. For the intramolecular correlations at least at low scattering angles up to ～40° it is found that the effect of inelasticity is rather small – around 0.6% on the estimated OH bond length for H₂O. Although the emphasis here is on time-of-flight diffraction, the model is quite general and can just as easily be applied to the case of fixed wavelength neutron diffraction where it also gives accurate results.