Convergence in the calculation of X-ray scattering intensities from liquids

Abstract By a simple model calculation, the convergence of the summation over lattice points in the calculation of X-ray scattering intensities from liquids has been examined. It is shown that the expression so far used for the contribution of the continuous region in the real-space expansion is inappropriate, and a correct expression is proposed. The convergence is, however, slow in the region of small s -values. For the reciprocal-space expansion, it is shown that addition of the contribution from the continuous region greatly improves the convergence.