Scattering potentials, electron

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. 

The atomic scattering factor for electrons is somewhat more complicated. It is again a Fourier transfonn of a density of scattering matter, but, because the electron is a charged particle, it interacts with the nucleus as well as with the electron cloud. Thus p(r) in equation (B1.8.2h) is replaced by (p(r), the electrostatic potential of an electron situated at radius r from the nucleus. Under a range of conditions the electron scattering factor, y (0, can be represented in temis... 

The scattering cross-section is considerably different from the Rutherford cross-section, because the distance of closest approach, Ri i , is rather large at low energies. Thus, electronic screening of the interaction between the nuclei is important. The screened scattering potential V(r) reads ... 

Friedel used the local perturbation f/—as a model for the scattering potential, reduced it even to one spherically symmetric scatterer and calculated the scattering by free electrons. By that, for the scatterer at the origin labeled by j = 0,... 

When experimental results are later introduced, it will be seen that the significance of the final-state scattering in PECO measurements is confirmed by the observation that for C li core ionizations, which must therefore proceed from an initial orbital that is achiral by virtue of its localized spherical symmetry, there is no suggestion that the dichroism is attenuated. The sense of the chirality of the molecular frame in these cases can only come from final-state continuum electron scattering off the chiral potential. Generally then, the induced continuum phase shifts are expected to be of paramount importance in quantifying the observed dichroism. 

Parity violating electron scattering. Recently it has been proposed to use the (parity violating) weak interaction to probe the neutron distribution. This is probably the least model dependent approach [31]. The weak potential between electron and a nucleus... 

The potential is related to the charge density, Fourier transform of electron charge density is commonly known as the X-ray scattering factor. To relate electron scattering factor to the X-ray, which gives... 

A small problem arises when the crystal thickness and temperature factors are refined simultaneously, because these parameters are highly correlated. Raising both the thickness and the temperature factors results in almost the same least-squares sum. This is not an artifact of the calculation method but lies in the behavior of nature. Increasing the Debye-Waller factor of an atom means a less peaked scattering potential, which in turn results in a less sharply peaked interaction with the ncident electron wave. It can be shown that a thickness of 5 nm anc B=2 will give about the same results as a thickness of 10 nm and B=6 A. ... 

The dynamic calculations include all beams with interplanar distances dhki larger than 0.75 A at 120 kV acceleration voltage and thickness between 100 A and 300 A for the different zones. The structure factors have been calculated on the basis of the relativistic Hartree - Fock electron scattering factors [14]. The thermal difiuse scattering is calculated with the Debye temperature of a-PbO 481 K [15] at 293 K with mean-square vibrational amplitude

= 0.0013 A following the techniques of Radi [16]. The inelastic scattering due to single-electron excitation (SEE) is introduced on the base of real space SEE atomic absorption potentials [17]. All calculations are carried out in zero order Laue zone approximation (ZOLZ). 

Some of these quantities are experimentally measurable from scattering experiments [1,2] or relate to physically interesting quantities which appear in different problems. For example p ) gives the kinetic energy of any nonrelativistic system, (r ) is related to the diamagnetic susceptibility, (r ) relates to the electron-nucleus potential energy,... 

Based on the first-principles study of helium adsorption on metals (Zaremba and Kohn, 1977), Esbjerg and Nprskov (1980) made an important observation. Because the He atom is very tight (with a radius about 1 A), the surface electron density of the sample does not vary much within the volume of the He atom. Therefore, the interaction energy should be determined by the electron density of the sample at the location of the He nucleus. A calculation of the interaction of a He atom with a homogeneous electron distribution results in an explicit relation between the He scattering potential V r) and the local electron density p(r). For He atoms with kinetic energy smaller than 0.1 eV, Esbjerg and Nprskov (1980) obtained... 

Esbjerg, N., and Nprskov, J. K. (1980). Dependence of the He-scattering potential at surfaces on the surface-electron-density profile. Phys. Rev. Lett. 45, 807-810. 



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