Transformation cycle between the spherically symmetric correlation function, projected correlation function and differential cross section as implemented inSASfit

Abstract

Edited by E. P. Gilbert, ANSTO, Kirrawee DC, Australia Keywords: spin-echo small-angle neutron scattering; small-angle neutron scattering; data analysis.Transformation cycle between the spherically symmetric correlation function, projected correlation function and differential cross section as implemented in SASfit 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 toG GðÞ, which is the projection of the scattering length density autocorrelation function ðrÞ. Here, a simplified transformation cycle relating the spherically symmetric correlation functioñ ðrÞ, the projected correlation functionG GðÞ and the macroscopic small-angle scattering cross section dAE/d 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 calculateG Gð0Þ 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.research papers

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