Tests of a Hankel transform method of determining electron densities of long cylinders from small-angle X-ray scattering data

The Hankel transform method proposed by Fedorov & Aleshin (1966; Vysokomol. Soed. 8, 1506; English translation, 1967: Polymer Science USSR 8, 1657) for calculating the electron density of long cylindrical particles with circular cross section is tested with theoretical intensity functions for which the density can be found both by an exact calculation and by numerical integration. (In this method, the density is assumed to depend only on the distance from the cylinder axis.) The tests show how the degree of resolution obtained in the density curve is related to the largest scattering angle at which data are available. For the step function density corresponding to a cylinder with uniform electron density, the requirements are more severe than for continuously decreasing density functions. The possibility of obtaining useful results with the available scattering data from two biological macromolecules is discussed.