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Reduction of small‐angle scattering profiles to finite sets of structural invariants
Author(s) -
Houdayer Jérôme,
Poitevin Frédéric
Publication year - 2017
Publication title -
acta crystallographica section a
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.742
H-Index - 83
ISSN - 2053-2733
DOI - 10.1107/s205327331700451x
Subject(s) - radius of gyration , invariant (physics) , scattering , radius , function (biology) , small angle scattering , mathematics , set (abstract data type) , geometry , mathematical analysis , algorithm , physics , computer science , optics , mathematical physics , computer security , nuclear magnetic resonance , evolutionary biology , biology , programming language , polymer
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.