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Transformation cycle between the spherically symmetric correlation function, projected correlation function and differential cross section as implemented in SASfit
Author(s) -
Kohlbrecher J.,
Studer A.
Publication year - 2017
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s1600576717011979
Subject(s) - physics , correlation function (quantum field theory) , autocorrelation , scattering , small angle scattering , function (biology) , scattering length , neutron spin echo , projection (relational algebra) , neutron scattering , range (aeronautics) , cross section (physics) , mathematical analysis , computational physics , small angle neutron scattering , quantum mechanics , mathematics , algorithm , materials science , statistics , evolutionary biology , dielectric , composite material , biology
Spin‐echo‐based small‐angle neutron scattering techniques like spin‐echo SANS (SESANS) or spin‐echo modulated SANS (SEMSANS) as well as dark‐field (DF) imaging are directly sensitive to , which is the projection of the scattering length density autocorrelation function . Here, a simplified transformation cycle relating the spherically symmetric correlation function , the projected correlation function and the macroscopic small‐angle scattering cross section dΣ/dΩ is introduced. The suggested changes to the cycle make it easier to include size distribution on an absolute scale if the data from the different techniques are fitted simultaneously. As up to now only very few analytical expressions for the projected correlation function are known, a numerical transformation of known scattering functions into the projected correlation function in the SASfit software package is supplied. Furthermore, a new analytical expression for the projected correlation function for polymers that can be described by the generalized Gaussian coil model is provided. For this polymer model, the Hankel transform used to calculate from the SANS signal is divergent for a certain parameter range describing a polymer in a good solvent and finite in the case of a poor solvent. It is therefore a suitable example of how the experimentally available q range can strongly influence the obtained results.