Intramolecular particle scattering

The normalized scattering intensity is a complex function of both the intermolecular structure factor S(q), which describes the distribution on the polyelectrolyte molecules in solution, and the intramolecular particle scattering factor P(q) which is the Fourier transform of the segment distribution (probability density) within one macromolecule. Only for rigid spheres the simple relation... 

Pseudo ID crystals are often described by a tight binding Hubbard type model with matrix elements t j and tj. (t >>tj, ), an intramolecular Coulomb interaction, U, and an electron-phonon interaction parameter, X. The quasiparticle states of the electrons can be described by the usual Bloch model with wave vector, k, provided that U is sufficiently small compared with the band width, At. However, because of phase space considerations, particle-particle scattering is much more important in ID than in 3D systems. 

This energy exchange is dependent on the kinetic energy of the gas particles scattered from the solid surface, which can be experimentally measured. In the most simple model when the surface is rigid and the intramolecular vibrations do not affect the collision, only mixing of the normal and parallel E components of the... 

The first term on the right-hand side of Eq. (Al) contains the intramolecular interference function, or particle scattering factor, defined by (4,5)... 

Meyerhoff have found it necessary to use a special extrapolation method to eliminate the effects of particle interactions and intramolecular interferences. They point out that neglect of these aspects may introduce errors in the direct evaluation of the polydispersity using these scattering techniques. 

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