@article{Watson:he5605, author = "Watson, Max C. and Curtis, Joseph E.", title = "{Rapid and accurate calculation of small-angle scattering profiles using the golden ratio}", journal = "Journal of Applied Crystallography", year = "2013", volume = "46", number = "4", pages = "1171--1177", month = "Aug", doi = {10.1107/S002188981301666X}, url = {http://dx.doi.org/10.1107/S002188981301666X}, abstract = {Calculating the scattering intensity of an {\it N}-atom system is a numerically exhausting {\it O}({\it N}${\sp 2}$) task. A simple approximation technique that scales linearly with the number of atoms is presented. Using an exact expression for the scattering intensity {\it I}({\bf q}) at a given wavevector {\bf q}, the rotationally averaged intensity {\it I}({\it q}) is computed by evaluating {\it I}({\bf q}) in several scattering directions. The orientations of the {\bf q} vectors are taken from a quasi-uniform spherical grid generated by the golden ratio. Using various biomolecules as examples, this technique is compared with an established multipole expansion method. For a given level of speed, the technique is more accurate than the multipole expansion for anisotropically shaped molecules, while comparable in accuracy for globular shapes. The processing time scales sub-linearly in {\it N} when the atoms are identical and lie on a lattice. The procedure is easily implemented and should accelerate the analysis of small-angle scattering data.}, keywords = {small-angle scattering, data analysis}, }