Impact parameter model

Figure 13. Comparison between the experimentally derived anisotropy parameters P(N") for the various H + NH CX), V2 = 0, N" = K" product channels arising in the photolysis of jet-cooled NH3 molecules at 216.38 nm (triangles) and those calculated using a qualitative impact parameter model (squares).

In the impact parameter model (IPM), it is assumed that the position of beam-2 remains fixed while beam-1 moves in a straight line with a constant velocity v [18,19]. 

The orbiting and the classical and semiclassical impact parameter models have been used to interpret inelastic scattering data in chemiionization, the dependence of ionization cross-section on collision energy and electron energy spectra, in order to gain information about the potential curves, V and V, and the autoionization width, (/ ). 

Bloch employed what chemists call the semiclassical model, where the motions of the projectile and the target nucleus are treated classically while target electrons obey quantum mechanics. In this model the impact parameter p refers to the target nucleus rather than an electron. In genuine quantum mechanics, angular momentum takes over the role of an impact parameter [9]. 

Figure 19 The upper portion of the figure shows the effective charge of the He" projectile as a function of the ejected electron energy that is obtained from the experiment [68], Born theory [70], and the model of Toburen et al. [71]. The lower portion of the figure is the same data, but plotted in terms of the impact parameter. The impact parameter is obtained using the relationship between projectile velocity, energy loss, and impact parameter defined by the Massey criterion. (See the text and Ref 71 for details.)...

In the line-of-centers model, the collision s effectiveness depends on the impact parameter, b. In general, the reaction probability is a function of energy and impact parameter, P (b, e). An integral over all possible impact parameters... 

In the classical version of the optical model, as developed mainly by Ross and co-workers,35-46-47 each impact parameter b manifests a certain reaction probability P(b), the classical opacity. Although a complex potential as in (11.12) is probably meaningless in a purely classical context, if we use the (rigorous) rate interpretation of T(r), we may derive24... 

As mentioned, the erosion of a solid surface depends on the collisional force, angle of incidence, and material properties of both surface and particles. Although abrasive erosion rates cannot be precisely predicted at this stage, some quantitative account of erosion modes which relates various impact parameters and properties is useful. In the following, a simple model for the ductile and brittle modes of erosion by dust or granular materials suspended in a gas medium moving at a moderate speed is discussed in light of the Hertzian contact theory [Soo, 1977]. 

Berend and Benson s classical treatment of V-V transfer [81] employs a two-dimensional collision model of a pair of diatomics with identical Morse interaction potentials between each pair of atoms. The Morse range parameter a was determined from experimental data for the N2-N2 T-V process. In-all, six functions are employed, one between each pair of atoms (Figure 3.5). Molecule CD, oriented at an angle / relative to its velocity vector, collides with molecule AB, with impact parameter b. Molecule AB is taken to be oriented parallel to the velocity vector of CD. The instantaneous angle between the molecular axis of AB and the line joining the centers of mass is denoted t). Cross sections for the reactions... 

As mentioned above, the processes (19.24)-(19.29) have not been studied for electronically excited states of H2. An estimate of the cross-sections for processes (19.24), (19.27)-(19.29) for N > 2 can be made by the SSH model. The available and relatively simple theoretical methods (such as the Born, Born-Rudge and impact-parameter method) can be used to calculate also the cross-section for reactions (19.26), but the difficulties of determining the higher resonant states of prevent easy estimates of cross-sections for reactions (19.25) when N > 2. 

Some of the gaps in the database can be filled by routine (but tedious and time-consuming) calculations using simplified theoretical models (e.g., BGG-model for electron-impact excitation and ionization of H2(NA v) states, the more involved impact-parameter method for excitation, etc.) For some of above listed processes (such as those mentioned under (d) and (e)), however, it is necessary to develop appropriate theoretical models for description of their dynamics. 

Remember 19.2 The presence of noise in data can have a direct impact on model identification and on the confidence interval for the regressed parameters. The correctness of the model alone does not determine the number of parameters that can be obtained. 

We have used trajectory calculations to calculate this quantity [26]. Our method distinguishes between effective trajectories that contribute to P(E ,E) and those with very large impact parameter which do not. The P(E ,E) thus found, obeys conservation of probability and detailed balance and is independent of the impact parameter. The method is demonstrated for benzene-Ar collisions at various temperatures and internal energies. With this method, it is possible to combine ab initio inter and intramolecular potentials with trajectory calculations, obtain P(E ,E) and use that in master equation calculations to obtain rate coefficients and population distributions without resorting to any a priori assumptions and energy transfer models. 

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