Elastic cross section

The elastic cross sections for scattering and recoil in the Lab-frame are related to the cross section in the CM-frame by... 

Third, a further simplification of the Boltzmann equation is the use of the two-term spherical harmonic expansion [231 ] for the EEDF (also known as the Lorentz approximation), both in the calculations and in the analysis in the literature of experimental data. This two-term approximation has also been used by Kurachi and Nakamura [212] to determine the cross section for vibrational excitation of SiHj (see Table II). Due to the magnitude of the vibrational cross section at certain electron energies relative to the elastic cross sections and the steep dependence of the vibrational cross section, the use of this two-term approximation is of variable accuracy [240]. A Monte Carlo calculation is in principle more accurate, because in such a model the spatial and temporal behavior of the EEDF can be included. However, a Monte Carlo calculation has its own problems, such as the large computational effort needed to reduce statistical fluctuations. 

Hayashi s (1989) compilation highly overestimates the total inelastic cross section below 100 eV. These are inconsistent with measured W values. Although the total cross section is reasonably well determined, uncertainties in the elastic cross section might have led Hayashi to overestimate the inelastic cross section. Figure 4.5 shows these cross sections. It is seen, however, that one theoretical calculation is consistent with W value measurement (Pimblott et al., 1990). In any case, Hayashi s values for total inelastic cross section are much greater than all major calculations, and the discrepancy is directly traceable to overestimates of excitation cross sections. 

Figure 3 Inelastic and elastic cross sections for electron impact excitation of the water molecule the data are from the review by Mark et al. [19]. The total interaction cross section ctt was determined from the sum of cross sections for all elastic and inelastic processes. Inelastic channels include the vibrational modes Cvi (the bending mode with threshold 0.198 eV), cTv2 (the sum of two stretching modes with thresholds 0.453 and 0.466 eV), and CvS (a lump sum of other vibrational excitation modes including higher hormonics and combinational modes with an assigned threshold of 1 eV). The electronic excitations and <7 2 have threshold energies of 7.5 and 13.3 eV. Ionization cross sections are those of Djuric et al. (O), and Bolarizadah and Rudd ( ). (From Ref 19.)...

Elastic collision cross sections are important for track simulation and diiferential cross sections are needed to calculate angular deviation in the track trajectory. Pimblott et al. [9] have given an elaborate analysis for gaseous water and compared the results with the experiments of Katase et al. [12]. In brief, the total elastic cross section... 

To get accurate results from this approach, it is necessary that the collisional changes in the internal energy be small compared to the translational energy. Then one can accurately assume a common translation path for all coupled internal states. In the usual applications of this method, one does not include interference effects between different classical paths, so that translational quantum effects, including total elastic cross sections, are not predicted. If the perturbation approximation is also used, accuracy can be guaranteed only when the sum of the transition probabilities remains small throughout the collision. 

The complex phase shift can be obtained from exact numerical solution of the radial Schrodinger equation.2 The following quantities can immediately be given in terms of 8r The differential elastic cross section in the center-of-mass system... 

Figure 2. Central part of apparatus used for measurement of differential elastic cross sections for scattering of helium metastables from ground-state atoms (reproduced from Brutschy et al.30)... 

The calculated total elastic cross section for He(2 S) + Ar is given elsewhere.102 There are currently no data for comparison. Trujillo has also measured cross sections for He(23S ) + Ne,Kr.136 Using essentially the same apparatus Harper and Smith138 have extended the cross section measurements to He(23S,) + H2,CO,02,N2 and Ne + He,Ne,Ar,Kr,H2,C0,N2,02. 

For the elastic scattering of a beam of unpolarized projectiles by an unpolarized target, the cross section has axial symmetry about the incident beam direction and therefore no dependence upon the azimuthal angle 4>, so that the differential elastic cross section is related to its integral counterpart by... 

Rescigno, T.N., McCurdy, C.W. and McKoy, V. (1975). Low energy e —H2 elastic cross sections using discrete basis functions, Phys. Rev. A 11, 825-829. 

The total elastic cross section [Pg.96]

The total elastic cross section and the forward (9 = 0) differential cross section are infinite. 

In the DSMC technique, the probability that a chemical reaction occurs is the ratio of the reaction cross section to the elastic cross section. The most commonly applied chemistry model is the Total Collision Energy (TCE) form employed by Boyd based on a general model proposed by Bird. In this model, the probability of reaction, P, is obtained by integrating the microscopic equilibrium distribution function for the total collision energy, and equating it to a chemical rate coefficient, Kf. Specifically, the mathematical form of the probability is obtained from the following integral ... 

For a comparison, we cite the expression for the elastic cross section, 0 (A), written in the same approximation ... 

In the e + M case, a very sensitive Indicator of shape resonance behavior Is the vibrational excitation channel. Vibrational excitation Is enhanced by shape resonances (3,17), and Is typically very weak for non-resonant scattering. Hence, a shape resonance, particularly at Intermediate energy (10-40 eV) (41,50), may be barely visible In the vlbratlonally and electronically elastic scattering cross section, and yet be displayed prominently In the vlbratlonally Inelastic, electronically elastic cross section. 

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