Experimental total scattering functions

Experimentally, the EISF is the fraction of the total quasielastic intensity contained in the purely elastic peak. For an exact experimental determination of the EISF the neutron spectra have to be fitted with the correct scattering function which consists of the elastic and a series of quasielastic terms (see [14, 28, 29]). Approximately, however, the EISF can be determined in a kind of model-indepen-dent data evaluation by fitting the neutron spectrum with a single Lorentzian plus an elastic term. Although in this way the line shape is not correct (except for N = 2 and 3), the EISF thus obtained allows statements to be made about the geometry for the localized motion. For the present chapter two EISFs, both spatially averaged (for powder samples), are of particular relevance ... 

Figure 11 Total cross sections due to proton (left) and alpha particle (right) impact on water vapor. Total ionization cross sections were obtained by fitting polynomial functions to the experimental data [198-200]. The curve for excitation was assumed to be the same between protons and alpha particles. Elastic scattering was evaluated by the classical mechanics trajectory calculations [Eqs. (16) and (17)].

These equations provide useful checks on the consistency of the experimentally measured values of aT with the calculated values of the real part of the forward scattering amplitude, or the scattering length they have been used as such by Bransden and Hutt (1975). For helium, these authors took the measured total cross sections of Coleman et al. (1976b) in the energy range 2-800 eV below 2 eV they used an extrapolation based on a least-squares fit of the functional form... 

It is instructive to make a quantitative comparison between the experimental and theoretical curves. The light scattering intensity, expressed as the Rayleigh ratio, is a function of the size and number of particles. If all three reactions shown in Figure 7 polymerize at the same rate, Rp, then at a given time, say 10 seconds, the total volume of polymer formed, VT, will be the same in all three. Under these conditions, the scattering intensity becomes a direct measure of the relative number of particles ... 

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