Elastic scattering cross section of photons by water: limits for the free atom approximation

Several papers can be found in the literature in which elastic and inelastic experimental scattering cross sections of photons by water with energies in the keV range are measured. Usually, the authors use some kind of normalization with theoretical values, because of the difficulties in obtaining some parameters necessary to obtain absolute cross sections from the measurements. A reasonable range of momentum transfer has been covered, but nevertheless, inconsistencies and gaps still remain. In this work, we address the problem performing absolute cross section measurements in the high momentum transfer region (0.33 angstrom(-1) <= x <= 4.5 angstrom(-1)), where no structure effects can be observed. We compare the results with theory to validate it in an intermediary region (0.33 angstrom(-1) <= x <= 1.72 angstrom(-1)) and then use the experimental values to normalize data in the low-energy region (0.078 angstrom(-1) <= x <= 1.72 angstrom(-1)) to obtain the experimental cross section in that region. From the comparison, we concluded that for momentum transfers, x between 0.7 and 4.5 angstrom(-1) the scattering can be considered as being due to free atoms in freemolecules. Therefore, the scattering cross sections may be considered as a sum of those from free atoms. Theoretically, the scattering cross sections can be obtained from the form factors as well as from the second-order perturbation theory (S-matrix) because there is no significant difference between both. On the other hand, for x <= 0.7 angstrom(-1), interference between the photon-scattered amplitudes due to liquid structure generates oscillations in the cross section values. Copyright (C) 2014 John Wiley & Sons, Ltd.