A method of reducing termination errors in radial distribution functions

The radial distribution function [g(r)] of a liquid can be obtained from an integral transform of its X-ray scattering intensity I(μ). Experimentally, I(μ) can be measured over only a limited range, leading to termination errors in g(r). Using the strict positivity of g(r), an iterative method is proposed to reduce these errors. The negative portions of each successive distorted approximation of g(r) are replaced by the value zero and this function is used to generate I(μ) in the non-measured range. Computer calculations on a model function yield encouraging results. The method appears to have an advantage over current approaches as it does not require a knowledge of the hard-core diameter of the atoms. It is also expected to work in the case of molecular liquids where there are some difficulties in applying the current methods.