Polar systems, elastic scattering

The absence of slow dynamics in this system can be attributed to the fact that the penta-alanine peptide does not have any polar side-chain atom which can form a strong HB with water. With a higher level of hydration, the rotational dynamics of water approached that of bulk water, again as expected. A QENS study of protein dynamics was also carried out on the picosecond timescale of a protein, lysozyme solvated in glycerol at different water contents, h (g water/g lysozyme). For all h, a well-visible low-frequeney vibrational bump was observed. The quasi-elastic scattering can be decomposed into two Lorentzian components, corresponding to motions with charaeteristic time constants of 15 ps and 0.8 ps. The 15 ps component is the slow component, which is in the same range observed in many other experimental studies. 

The mean square variation in Rj is represented by the Debye-Waller factor, aj] X is the elastic mean-free path of the photoelectron and it is the damping term [exp(-2Rj/X)] that invariably limits back-scattering contributions to <4 A from a metal atom in a biological system. The jth. neighbor makes an angle d, with the polarization vector of the incident X ray and the term 3 cos dj averages to 1 for solutions and polycrystalline samples. 

To understand the scattering of electromagnetic radiation from a single electron, it can be assumed that a monochromatic plane wave linearly polarized along the x-axis with electric field E(t) = Eo( is scattered elastically by an electron placed at the origin of the Cartesian coordinate system. For an observer located at distance r from the origin, the electric field of the resultant wave is given by ... 

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