Inelastic cross sections

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 differential cross section for inelastic collisions exciting the nth state of the target then takes the fomi... 

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... 

This chapter deals with qnantal and semiclassical theory of heavy-particle and electron-atom collisions. Basic and nsefnl fonnnlae for cross sections, rates and associated quantities are presented. A consistent description of the mathematics and vocabnlary of scattering is provided. Topics covered inclnde collisions, rate coefficients, qnantal transition rates and cross sections. Bom cross sections, qnantal potential scattering, collisions between identical particles, qnantal inelastic heavy-particle collisions, electron-atom inelastic collisions, semiclassical inelastic scattering and long-range interactions. 

The cross section for inelastic scattering of beam of particles by potential V(r, R) is... 

For electronic transitions in electron-atom and heavy-particle collisions at high unpact energies, the major contribution to inelastic cross sections arises from scattering in the forward direction. The trajectories implicit in the action phases and set of coupled equations can be taken as rectilinear. The integral representation... 

Parker G A and Pack R T 1978 Rotationally and vibrationally inelastic scattering in the rotational lOS approximation. Ultra-simple calculation of total (differential, integral and transport) cross sections for nonspherical molecules J. Chem. Phys. 68 1585... 

The probability for a particular electron collision process to occur is expressed in tenns of the corresponding electron-impact cross section n which is a function of the energy of the colliding electron. All inelastic electron collision processes have a minimum energy (tlireshold) below which the process cannot occur for reasons of energy conservation. In plasmas, the electrons are not mono-energetic, but have an energy or velocity distribution,/(v). In those cases, it is often convenient to define a rate coefficient /cfor each two-body collision process ... 

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. 

The X-ray spectrum observed in PIXE depends on the occurrence of several processes in the specimen. An ion is slowed by small inelastic scatterings with the electrons of the material, and it s energy is continuously reduced as a frmction of depth (see also the articles on RBS and ERS, where this part of the process is identical). The probability of ionizii an atomic shell of an element at a given depth of the material is proportional to the product of the cross section for subshell ionization by the ion at the reduced energy, the fluorescence yield, and the concentration of the element at the depth. The probability for X-ray emission from the ionized subshell is given by the fluorescence yield. The escape of X rays from the specimen and their detection by the spectrometer are controlled by the photoelectric absorption processes in the material and the energy-dependent efficiency of the spectrometer. 

A type of molecular resonance scattering can also occur from the formation of short-lived negative ions due to electron capture by molecules on surfrices. While this is frequently observed for molecules in the gas phase, it is not so important for chemisorbed molecules on metal surfaces because of extremely rapid quenching (electron transfer to the substrate) of the negative ion. Observations have been made for this scattering mechanism in several chemisorbed systems and in phys-isorbed layers, with the effects usually observed as smaU deviations of the cross section for inelastic scattering from that predicted from dipole scattering theory. 

Values of the total cross-section a a for A1 Ka, radiation, relative to the carbon Is level, have been calculated by Scofield [2.7], and of the asymmetry parameter /Ja by Redman et al. [2.8]. Seah and Dench [2.3] have compiled many measurements of the inelastic mean free path, and for elements the best-fit relationship they found was ... 

It is generally accepted that the centrifugal sudden (CS) approximation is the most reliable approximate method. Its results are usually very close to those obtained by ab initio close coupling (CC) calculations. The integral and differential cross-sections of Ar inelastic scattering on nitrogen were performed for a few low-frequency rotational transitions and four different interaction potentials [205]. Much better agreement of CC with CS results was found than with IOS calculations performed in... 

Fig. 5.2. Computed percentage error (absolute value) for the He-N2 (j, = 0) system using potential function HFD1. The state to state inelastic cross-sections are compared at several collision energies as a function of A j transitions. The B value for N2 is taken to be about 2 [207],...

Connor J. N. L., Sun H., Hutson J. M. Exact and approximate calculations for the effect of potential anisotropy on integral and differential cross-sections Ar-N2 rotationally inelastic scattering, J. 

Pack R. T. Close coupling test of classical cross-sections for rotationally inelastic Ar-N2 collisions, J. Chem. Phys. 62, 3143-8 (1975). 

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