Collision cross section elastic

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... 

This distance is often called the mean free path. As we can see, it is inversely proportional to the number of particles per unit volume, or the density, and inversely proportional to the collision cross section. The mean free path is most commonly discussed for the ordinary elastic collisions of two molecules in a gas. For such collisions, the collision cross sections come out of the order of magnitude of the actual cross sectional areas of the molecules that is, of the order of magnitude of... 

With respect to the elastic collisions and the excitation or dissociation by electron collisions considered in Eq. (8) the collision cross sections... 

Using two different scales for the cross-section values, the important inelastic collision cross sections of Ne and N2 are shown in Fig. 1 together with the respective cross section Qf U) for momentum transfer in elastic collisions, denoted by d. With respect to Ne, the individual collision cross sections have been taken from Hayashi (1996). The relevant total cross sections Q U),... 

A major obstacle to accurate numerical modeling of plasma chemistry has been the lack of reliable electron collision cross-section data. Electron collisions drive the entire processing plasma chemistry and, hence, are among the most important and critical processes that we need to consider. In addition to cross sections for elastic scattering and momentum transfer, to which the electrical and thermal conductivities are directly related, it is necessary to consider all important... 

The Greek letter a is used here to denote electrical conductivity. It is also used with the subscripts m, e, or i to denote momentum-transfer and elastic and inelastic electron collision cross sections. 

In this section, we look at several methods in current use for calculating electron-molecule collision cross sections relevant to low-temperature plasmas. For the most part, we will avoid technical details, which in any case can readily be found elsewhere (Huo and Gianturco, 1995 Winstead and McKoy, 1996), although we will attempt to describe enough of the implementation to bring out the advantages, disadvantages, and limitations of each method. We will conclude with illustrative examples in which different methods are applied to the same elastic and inelastic electron-molecule collision problems. 

For elastic hard spheres with weak central attractive forces, the collision cross section is enhanced by the attractive force, since two particles can... 

In order to ensure that the target species thermalizes before impinging on the wall of the cell, it is necessary that the density of the buffer gas be large enough to allow for thermalization on a path smaller than the size of the cell. Cells are typically of order 1 cm in diameter. Assuming an elastic collision cross-section of about 10 cm between the target species and helium (an assumption accurately borne out by numerous experiments [3-6]), the minimum density required is typically 3 X 10 cm . This requirement puts a lower limit on the temperature of the buffer gas. Figure 13.3 shows the dependence of number density on temperature for He [7] and He [8] at about 1K. One can see that He can be used at temperatures as low as 180 mK and He as low as 500 mK. 

In both equations [3] and [4], the collisions of ions with neutrals are considered to be a completely elastic process. Thus, the collision cross section obtained is termed the hard-sphere collision cross section. When compared to molecular simulations, these collision cross section measurements can provide detailed structural information about the analyte (31-34). 

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