Potential scattering theory

The mobility of quasi-free electrons has recently been explained by the deformation potential theory. Originally from solid-state physics, this theory was applied by Basak and Cohen [68] to liquid argon. The theory assumes that scattering occurs when the electron encounters a change or fluctuation in the local density which results in a potential change. The potential is assumed to be given in terms of dFo/dfV, d Fo/dfV, etc. The formula they derived for the mobility is ... 

Byron Jr., F.W. and Joachain, C.J. (1981). A third order optical potential theory for elastic scattering of electrons and positrons by atomic hydrogen. J. Phys. B At. Mol. Phys. 14 2429-2448. 

Figure 1 displays the experimental characteristic curve obtained and the p values employed to generate it. The existence of very little scatter in the data demonstrates that the isotherms of the various adsorbates were successfully correlated as a single temperature-independent characteristic curve. This fact corroborates the applicability of the Potential theory to the carbon under study. 

It was Fermi who realized that it was possible to invoke an equivalent potential, which can be used to calculate the changes in the wavefunction outside the interaction by perturbation theory [13]. The unknown form of the strong nuclear interaction can be replaced by a new potential, which gives the same scattered wavefunction as the square well potential. In the derivation of Fermi s equivalent or pseudo potential [14] it is seen that the magnitude of the scattering potential depends on the scattering length of the nucleus and the mass of the neutron, m ... 

In scattering theory, it can be proven that the scattered wave function, outside the effective radius from the scattering potential, should look like [39] ... 

For the case of time-independent scattering theory based on a scattering potential, the deflection function is given by [22]... 

P.C. Waterman Matrix Methods in Potential Theory and Electromagnetic Scattering (to be published)... 

In region (1), the electron can be considered as quasifree. (An electron is regarded as completely free only in the vacuum.) The structure of the fluid is unperturbed by the presence of the excess electron. The wave function is extended. The basic electron/liquid interaction may be treated as single scattering of an electron on a molecule or atom modified by the structure factor of the liquid, S(q) (Lekner, 1967), or it is considered as multiple scattering off density fluctuations in the framework of the deformation potential theory (Basak and Cohen, 1979). 

Townsend minimum exists in dense and liquefied rare gases at lower energies than in the low density gas as predicted by the earlier analyses (Christophorou, 1975 Christophorou and McCorkle, 1976). The failure of the theory (e.g., Lekner, 1967) to clearly identify such a minimum may be due to an overcorrection for the screening of the electron scattering potential. Clearly further theoretical work is indicated. 

Another statistical mechanical approach makes use of the radial distribution function g(r), which gives the probability of finding a molecule at a distance r from a given one. This function may be obtained experimentally from x-ray or neutron scattering on a liquid or from computer simulation or statistical mechanical theories for model potential energies [56]. Kirkwood and Buff [38] showed that for a given potential function, U(r)... 

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