Cross section, differential inelastic

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

Ion-impact excitation has been widely studied in the rare gases260 270 and for alkali metal ion-atom collisions.271 280 In many cases excitation functions have been measured (i.e., total cross sections as a function of initial relative translational energy), and in some instances the angular dependencies of the differential cross sections for inelastic scattering have been determined. The most striking feature of the results from these experiments is the oscillatory structure that is evident in many of the... 

Quantum-mechanically, the process of energy loss by electrons can be considered as formally equivalent to the absorption of photons, so that we may express the differential cross-section for inelastic scattering (energy loss) under the dipole approximation as ... 

The term 3(— l/e q, co)) is referred to as the dielectric loss function. Structures in this function can be correlated to bulk plasmon excitations. In the vicinity of a surface the differential cross section for inelastic scattering has to be modified to describe the excitation of surface plasmons. The surface energy loss function is proportional to 3(—l/e(, cu) + 1). In general, the dielectric function is not known with respect to energy and momentum transfer. Theoretical approaches to determine the cross section therefore have to rely on model dielectric functions. Experimentally, cross sections are determined by either optical absorption experiments or analysis of reflection energy loss spectra [107,108] (see Section 4.3). 

Fig. 10. Differential cross sections for inelastic scattering of 31 Mev protons by tin the experimental points are those of Eisberg and Igo, the full curves are those calculated by Hayakawa, Kawai, and Kikuchi.

The decrease at larger angles of the differential cross-section for inelastic scattering can be understood qualitatively in terms of a constructive interference from the many high angular momentum components which are present in a collision of a fast nucleon with a nucleus. Even in a nucleus as light as A1 and at an energy as low as 100 Mev kR 10, and 10 phase shifts need to be considered. 

Fig. 12.14a,b> Measurement of differential cross sections for inelastic atom-molecule collisions in crossed beams, (a) Schematic level scheme, (b) experimental arrangement [12.31]... 

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... 

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... 

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... 

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. 

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.

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