Cold and thermal neutron scattering in liquid water: cross-section model and dynamics of water molecules

A cross-section model for incoherent inelastic scattering of slow neutrons in liquid water is developed. The model is expressed basically in terms of a width function (a mean squared displacement of a water molecule) and, equivalently, a generalized frequency distribution (a vibrational density of states). The microscopic dynamics of water molecules is fully described from very general considerations connected with jump diffusion, intermolecular vibration, hindered rotation and intramolecular vibration. The model covers a wide time range of the order of 0.1 fs to 1 μ s . Hence a full set of double-differential and total cross sections for neutron incident energies from 0.1 μ eV to 10 eV is calculable. Satisfactory agreement with neutron-scattering and molecular-dynamics results is found at many different temperatures between 0 °C and 100 °C. This indicates the usefulness of the present model for generation of an advanced cross-section library for practical purposes.