Reduction of small-angle scattering profiles to finite sets of structural invariants

This paper shows how small-angle scattering (SAS) curves can be decomposed in a simple sum using a set of invariant parameters called K_n which are related to the shape of the object of study. These K_n, together with a radius R, give a complete theoretical description of the SAS curve. Adding an overall constant, these parameters are easily fitted against experimental data giving a concise comprehensive description of the data. The pair distance distribution function is also entirely described by this invariant set and the D_max parameter can be measured. In addition to the understanding they bring, these invariants can be used to reliably estimate structural moments beyond the radius of gyration, thereby rigorously expanding the actual set of model-free quantities one can extract from experimental SAS data, and possibly paving the way to designing new shape reconstruction strategies.