A simple approximation for calculating the small-angle X-ray and neutron scattering from polydisperse samples of independently scattering uniform spheres

A convenient approximation has been obtained for the intensity of the small-angle X-ray or neutron scattering from an assembly of independently scattering spherical particles with constant density when the radius-distribution function is a Gaussian with a full width at half maximum which is not greater than 1.7 times the most probable radius. The approximation expresses the intensity in terms of elementary functions. Criteria are given for setting a bound on the error in the approximation.