Scattering cross-section, for electron

Electrons of 150 eV and neutrons of 0.1 eV possess a DeBroglie wavelength of about 1 A, which matches the elementary lattice dimensions in crystals. The appreciable scattering cross sections for electrons causes them to be strongly absorbed and thus... 

Since the nuclear and electronic scattering cross sections for alpha particles are well known, the relative concentrations of the elements and their depth profiles can be easily obtained. The relative element concentrations are determined by the relative scattering intensities. The depth profile is obtained from the energy spread of the scattered particles, which lose energy before and after the nuclear collision, by inelastic scattering with electrons. The knowledge of the elements areal density and of the film thickness allows the determination of film density. 

In substitutional metallic solid solutions and in liquid alloys the experimental data have been described by Epstein and Paskin (1967) in terms of a predominant frictional force which leads to the accumulation of one species towards the anode. The relative movement of metallic ion cores in an alloy phase is related to the scattering cross-section for the conduction electrons, which in turn can be correlated with the relative resistance of the pure metals. Thus iron, which has a higher specific resistance than copper, will accumulate towards the anode in a Cu-Fe alloy. Similarly in a germanium-lithium alloy, the solute lithium atoms accumulate towards the cathode. In liquid alloys the same qualitative effect is observed, thus magnesium accumulates near the cathode in solution in bismuth, while uranium, which is in a higher Group of the Periodic Table than bismuth, accumulated near the anode in the same solvent. 

Figure 3 Elastic and inelastic scattering cross sections for scattering into an annular detector of inner collection angle 0i, for lOOkV electrons.

Figure 8.3 The vibrational elastic and inelastic differential cross sections for electron scattering off LiF at = 5.44 eV (Alhassid and Shao, 1992b, where the source of the data is given). Solid lines with an improved dipole interaction [which breaks the 0(4) symmetry]. Long dashed lines the calculations by Bijker and Amado (1986). The short dashed lines are the Bom approximation.

Applications that would benefit from the described achievements are commonly bottlenecked by a lack of general procedures to interpret intensity data. Recently, it was suggested to interpret STEM data by extraction of single atom scattering cross sections For HRTEM, Figure 8 highlights a suitable method for intensity quantification from reconstructed electron exit waves. 

The Compton scattering cross section per electron of the stopping material is independent of Z, and thus the cross section per atom goes as Z. For energies about 0.5 MeV, it varies roughly as 1 /Er... 

In contrast to the case of X-ray scattering, cross sections for low-energy electrons from atoms are large (on the order of 10 A2/atom). 

As the positron energy is raised above the positronium formation threshold, EPs, the total cross section undergoes a conspicuous increase. Subsequent experimentation (see Chapter 4) has confirmed that much of this increase can be attributed to positronium formation via the reaction (1.12). Significant contributions also arise from target excitation and, more importantly, ionization above the respective thresholds (see Chapter 5). In marked contrast to the structure in aT(e+) associated with the opening of inelastic channels, the electron total cross section has a much smoother energy dependence, which can be attributed to the dominance of the elastic scattering cross section for this projectile. 

Fig. 5.5. Inelastic scattering cross sections for positron-02 collisions. Key ,

Fig. 5.23. Ratio of K-shell ionization cross sections for electrons and positrons scattering from silver and copper at various impact energies -----, Born approximation calculation including a Coulomb correction (see text) -, Born...

Charlton, M., Griffith, T.C., Heyland, G.R. and Twomey, T.R. (1980a). Total scattering cross sections for low-energy electrons in helium and argon. J. Phys. B At. Mol. Phys. 13 L239—L244. 

Smart, J.H. and Stein, T.S. (1980). Measurements of total scattering cross sections for low-energy positrons and electrons colliding with krypton and xenon. Phys. Rev. A 22 1872-1877. 

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