Elastic incoherent neutron scattering on systems of biophysical interest:: Mean square displacement evaluation from self-distribution function

In the present work an operational recipe for the mean square displacement (MSD) determination, highlighting the connection between the self-distribution function and average statistical values, is presented. The determination of the MSD and of its contributions associated with different mechanisms, together with their thermal behavior, is performed by evaluating the self-distribution function derived by elastic incoherent neutron scattering (EINS). The approach is tested on EINS data collected by the backscattering spectrometer IN13 (ILL, Grenoble, France) on two model systems such as dry myoglobin in trehalose and poly(ethylene glycol) with mean molecular weight M(w) = 400 (PEG 400).