Polarization horizontal scattering-angle

From simple geometrical consideration (cf. Fig. 2.1) it follows that at a synchrotron the ideal polarization factor is only a function of the horizontal component of the scattering angle. Thus we conveniently express the polarization factor in terms of the horizontal scattering-angle... 

Here I0 is the intensity of the x-ray beam, r0 = e2/mc2 is the classical electron radius (2.82 x 10 15 m)., P(9,) is the polarization of the x-rays it depends on the angle between the polarization and the scattering vector. For horizontally polarized x-rays, it takes the form P(0, < >) = 1 - sin220 sin2t)>, where 20 is the scattering angle and < > the azimuthal angle with respect to the vertical direction. The formfactor ) is the Fourier transform of the atomic electron density ... 

Figure 7. Polarization pattern, given as a polar plot of the HRS intensity as a function of the angle of polarization of the fundamental wave, for an aqueous suspension of 20 nm diameter gold, (a) Vertically polarized SH scattered light and (b) horizontally polarized SH scattered light (Reprinted from 44 with permission from the American Physical Society)...

The polarization factor, Pol, takes into account the variation in scattering intensity caused by the beam polarization, as can be anticipated because elastic scattering is forbidden along the polarization direction of the incident beam. Synchrotron sources typically produce X-ray beams that are linearly polarized in the horizontal plane. Most synchrotron-based scattering measurements are performed with the scattering angle measured in the vertical plane, so that P= 1. For horizontal scattering spectrometers with a horizontally-polarized beam, the polarization factor is P = cos(2 ). A number of spectrometers scan the detector in both the vertical and horizontal planes. 

As discussed in section, R J q,c) and R (q,c) are expressed in terms of R.Jq,c), / ,( , ), andR Jq,c) by Equations 8.2 and 8.3, respectively, with R (0,c)=0. The vertical and horizontal components of light scattered with vertically polarized light from a dilute solution extrapolated to zero scattering angle, Ry (0,c) and R (0,c), respectively, for a monodisperse solute with identical anisotropic scattering elements are given by [13, 28, 84-86] ... 

Figure 9-4. The scattering profile of small particles with vertically (v) and horizontally h) polarized incident light. Upper row the oscillating dipole position and definition of the angles dv and h. Lower row polar plot of the light-scattering intensity (indicated by arrows) in the xy plane.

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