Elastic experiment, wave vector

Let us consider a small-angle scattering experiment. The radiation falls on molecules in a container at fixed pressure. Let us study the scattering in a volume V which is small with respect to the volume of the container but not microscopic (see Fig. 7.1). An elastic transfer wave vector q corresponds to each scattering angle 0 with q — 2k0 sin 0/2, (k0 being the incident wave vector) and the scattering is characterized by the differential cross-section... 

Despite the great incoherent cross-section of the H-atom, elastic coherent neutron scattering experiments may be used at a lower resolution to detect the presence of clusters of H2O molecules. The method used is that of small-angle neutron scattering, often labeled by its acronym SANS . In such an experiment, the scattered intensity of a sample is recorded as a fnnction of the angle 6 between the wave vectors of the scattered and initial waves or, equivalently, as a function of the amplitude Q of the wave vector difference Q = k -ic2 0f the scattered beam defined by and incident beam defined by ki (the wave vector defines the direction of propagation of a wave, as seen in eq. (3.6)). As can be seen in Figure 11.1, these quantities are related by the equation ... 

The basic features of any scattering experiment, whether it uses light, x-rays, or neutrons, are schematically represented in Figure 10.7. They consist of (1) a radiation source, (2) a system of collimation and/or monochromation, (3) the sample, and (4) a detection system. The incident radiation is characterized in terms of its wavelength, Xq, wave vector kg with magnitude and energy Eq. In the case of elastic... 

In a scattering experiment [20, 21], a monochromatic X-ray beam with the wave vector kj hits a material and is scattered elastically on the electrodes of the atoms at the angle 20diff. (Fig. 4.10a). As the scattering is elastic, the absolute values of the wave vector ki of the initial beam and the wave vector ks of the scattered beam are equal ... 

Here 71 and K22 are the twist viscosity and elastic constant, g is a wave vector of the distortion mode under investigation (it depends on the geometry of the experiment, in particular, on the light scattering angle), the signs (+) and (—) in (6.34) are related to the cases q > Qq, and < 0 where qo = 2ttIPq is the equilibrium pitch. 

The neutron ray with the wave vector Ko is scattered through an angle of 6 into a solid angle AQ. The scattered ray has a wave vector Ki and the position of the scattering center is described by the vector R. In elastic scattering experiments the absolute values of Kq and Xi are both equal to In/X. The scattering vector Q can be defined as... 

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