Scattering cross section isotropic phase

Quantum theory of scattering. The differential scattering cross section for isotropic potentials is given by the scattering phase shifts r e as... 

Two contributions to Eq. (8) can be identified, the first of these is b > — ) and represents the mean square deviation of individual scattering lengths from the average value. As such it is called the incoherent scattering cross section and constitutes a uniform, isotropic background scattering since it retains no information on the phase of the scattered neutrons. Incoherent scattering cross sections are tabulated as values of a. where ... 

The reason for the large difference between the values of A for positrons and electrons at an energy of 2 eV is that for positrons the s-wave phase shift passes through zero at the Ramsauer minimum and the dominant contribution to the cross section therefore comes from the p-wave, which is quite strongly peaked in the forward and backward directions. In contrast, there is no Ramsauer minimum in electron-helium scattering, and the isotropic s-wave contribution to aT is dominant at this energy. 

WKB-phase shifts are used for the isotropic part of the potential and phase shifts in the sudden limit for the anisotropic part (Cross, 1967) produced cross sections which are also in quantitative agreement with the experimental results (Buck et al., 1975). It proved necessary to introduce a large P,-contribution to the potential in order to get this agreement for the scattering of symmetrical top molecules on atoms. Thus this type of measurements seems to provide a reliable method for the determination of the anisotropic part of the potential. 

Due to the fact that the order parameter Q is related to macroscopic observable quantities such as the susceptibility tensor % (Eq. [32]) and the dielectric tensor f, fluctuations in the components of Q are directly manifested as fluctuations in c and in % and are therefore experimentally measurable. In Section 5 we will show how the fluctuation amplitude, < Qiy( ) >, can be used to calculate cross section of light scattering by fluctuations in the isotropic phase of liquid crystals. 

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