Electron impact ionization cross-section

Fig. 2.18. Electron-impact ionization cross-section for the Ni K shell, as a function of reduced electron energy U [2.128] U = Ep/Ek, where Ep is the primary electron energy and E

Fig. 3.31. Distributions (i)/(Ee) dEe of electron energy (E ) for a low-pressure HF-plasma (suffix pi, Maxwellian with temperature = 80000 K) and an electron beam (suffix eb, simplified to Gaussian shape with 40 eV half-width) (ii) rTx (Ej) ofthe Ej dependent electron impact ionization cross-section for X=Ti...

The mass spectrum of 1-torr ethylene in 20-torr He is also shown in in Figure 14. Remembering that the (electron impact) ionization cross-section for ethylene is 20 times higher than that for He, we expect almost... 

POSITIVE ION-ELECTRON IMPACT IONIZATION CROSS SECTIONS ... 

Quantum mechanical and selected semiclassical and semiempirical methods for the calculation of electron impact ionization cross sections are described and their successes and limitations noted. Experimental methods for the measurement of absolute and relative ionization cross sections are also described in some detail. Four theoretical methods, one quantum mechanical and three semiclassical, have been used to calculate cross sections for the total ionization of the inert gases and small molecules and the results compared with experimental measurements reported in the literature. Two of the theoretical methods, one quantum mechanical and one semiclassical, have been applied to the calculation of orientation-dependent electron impact ionization cross sections and the results compared with recent experiments. 

The EM method has been tested on the inert gases and a range of small molecules and gives good agreement with experimental results in almost all cases.17 This method will be discussed further in relation to the orientation dependence of the electron impact ionization cross section in a later section. The semiempirical polarizability method described below was developed to calculate and to use it with the amax values obtained from this method in order to calculate the energy dependence of the cross section. 

A multitude of semiempirical and semiclassical theories have been developed to calculate electron impact ionization cross sections of atoms and atomic ions, with relatively few for the more complicated case of molecular electron impact ionization cross sections. One of the earlier treatments of molecular targets was that of Jain and Khare.38 Two of the more successful recent approaches are the method proposed by Deutsch and Mark and coworkers12-14 and the binary-encounter Bethe method developed by Kim and Rudd.15,16 The observation of a strong correlation between the maximum in the ionization efficiency curve and the polarizability of the target resulted in the semiempirical polarizability model which depends only on the polarizability, ionization potential, and maximum electron impact ionization cross section of the target molecule.39,40 These and other methods will be considered in detail below. 

This formalism was originally devised for single ionization of ground-state atoms, but has now been successfully applied to the calculation of electron impact ionization cross sections for a range of molecules, radicals, clusters, and excited state atoms. Like many of the semiempirical and semiclassical methods used to describe the electron impact process, the theory has its roots in work carried out by J.J. Thomson, who used classical mechanics to derive an expression for the atomic electron impact ionization cross section,2... 

This expression reproduces the experimentally measured ionization efficiency curves surprisingly well, considering the simplicity of the model on which it is based. There is a discontinuity in the function at the maximum (when X = Xmax) but this affects only a small region of the ionization efficiency curve, and satisfactory values of the cross section are still obtained over this region. A great advantage of this method is that it is very simple to apply, depending on only three parameters the molecular polarizability volume, the ionization potential, and the maximum electron impact ionization cross section. These can be measured or calculated values (from the ab initio EM method described above, for example). 

The experimental determination of a total electron impact ionization cross section requires the measurement of four quantities19 ... 

There are several other methods which have been used in the experimental determination of electron impact ionization cross sections. Nottingham and Bell76,77 developed a method specifically for the purpose of accurately determining the absolute electron impact ionization cross section of mercury. A semicircular electron velocity analyzer included in their design ensured that very high energy resolution was possible since only electrons of the required velocity emerged from the analyzer into the ionization chamber. Other aspects of the experiment are similar to the condenser plate method. 

Figure 6. Comparison of electron impact ionization cross sections calculated by the...

Figure 7. Correlation of atomic maximum electron impact ionization cross sections with (a/ 0)1/2/ where E0 is the atomic ionization potential.

None of the three theories used to calculate electron impact ionization cross sections could be considered to render the others obsolete. The BEB method gives the best fit to the functional form of the ionization efficiency curve for small molecules, it provides a better fit to the experimental data closer to the ionization threshold than the other methods, but it underestimates the maximum ionization cross sections for heavier molecules. The DM method provides a better fit to the ionization efficiency curves for the heavier molecules, especially for electron energies greater than max, but it tends to overestimate the cross sections for heavier molecules and it underestimates E for lighter molecules. The EM method performs as well as the other methods for the value of amax for the light molecules but underestimates the cross sections for heavy molecules by a factor similar to the overestimation of the DM method. The polarizability method outperforms the BEB and the DM methods for the calculation of and when combined with the value from the EM calculation reproduces the ionization efficiency curve as well as the BEB method. 

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