Inelastic scattering cross section

Chemi-ionization of Noble Gas Atoms. The form of the A + A potentials, V, has been studied by elastic scattering, - as discussed in Section 3, and well depths and equilibrium separations are listed in TaUe 11. hi the studies of differential scattering cross-sections, inelastic scattering due to energy transfer or ionization <> > was clearly observable at large angles, the... 

The ratio of elastically to inelastically scattered electrons and, thus, their importance for imaging or analytical work, can be calculated from basic physical principles consider the differential elastic scattering cross section... 

If the displacements of the atoms are given in terms of the harmonic normal modes of vibration for the crystal, the coherent one-phonon inelastic neutron scattering cross section can be analytically expressed in terms of the eigenvectors and eigenvalues of the hannonic analysis, as described in Ref. 1. 

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. 

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

Fig. 12. Inelastic one-phonon He scattering cross-section (He beam energy 20 meV and 100 meV) as a function of phonon frequency. (After Ibach )...

SF radiation may be accompanied with inelastic nonlinear scattering, although the scattering cross section is extremely small, typically in the order of 10 cm" per molecule. Such an inelastic scattering effect in the second-order nonlinear optical... 

Incoherent inelastic neutron scattering is efficient in detecting M—H vibrations because the intensity of scattering is proportional to the square of the atomic vibrational amplitude (oc 1/atomic mass) and the scattering cross section (moderately high for H). HCo(CO)4 and H3M3(CO)12 (M = Mn and Re) have been studied, for example.93... 

Eq. (11.30) is strictly applicable only to elastic collisions, in which a = a, and is thus of limited utility. However, it is physically appealing to assume that the cross section o(a, a, / ,/ ) for an inelastic process a = a and ft (i can be written as the integral of the electron scattering cross section oe(J3, f, q) over the velocity distribution of the Rydberg electron in the initial state a. Making this notion explicit, we write19... 

Fig. 2.1. Schematic illustration of the behaviour of the positron-helium and electron-helium total scattering cross sections. Notable are the large differences in magnitude of the cross sections at low energies, their merging at approximately 200 eV and the onset of inelastic processes at the positronium formation threshold EPS in the positron curve.

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. 

This is the optical theorem, and it expresses the conservation of the number of particles in the scattering process. As already mentioned in section 2.2, it is valid even when inelastic processes can occur, although dei is then replaced by the total scattering cross section [Pg.96]

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