Principles of Other Mobility Measurements Comparison with NMR Data

Principles of Other Mobility Measurements (Comparison with NMR Data) 

Molecular Translations and Rotations by Quasi-elastic Neutron Scattering (Qens) 

For hydrocarbons in zeolites, only incoherent scattering has to be considered because of the large incoherent cross section of hydrogen. The neutron intensity scattered follows the incoherent scattering law 5i c(Q, (o), which is related to the self-motion of protons, where AQ and Aw denote the neutron momentum transfer and the neutron energy transfer, respectively. 

Assuming for a molecular system the vibrational, rotational, and translational motions as uncoupled, the incoherent scattering law can be expressed as a convolution product of the individual scattering laws for each motion, which can be examined separately  

For the quasi-elastic region ( 2 meV) that is of concern here, the vibrational motions affect only the elastic intensity through a Debye-Waller factor, exp(-Q (M )), where (u ) is the mean square hydrogen amplitude in the vibrational modes. The scattering law for rotations can be written as a sum of an elastic peak intensity and a quasi-elastic component  

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