Binary-encounter-Bethe

Theoretical models of the electron impact ionization process have focused on the calculation of the ionization cross section and its energy dependence they are divided into quantum, semiclassical and semiempirical. Methods for the calculation of the ionization cross section and experimental techniques developed for the measurement of absolute ionization cross sections will be described in more detail below. Cross sections calculated using the semiempirical additivity method developed by Deutsch and Mark (DM) and their coworkers,12-14 the binary-encounter-Bethe (BEB) method of Kim and Rudd,15 16 and the electrostatic model (EM) developed by Vallance, Harland, and Maclagan17,18 are compared to each other and to experimental data. 

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. 

The binary-encounter-dipole (BED) model of Kim and Rudd [31] couples the modified form of Mott cross section [32] with the Bom-Bethe theory [27]. BED requires the differential continuum oscillator strength (DOS) which is rather difficult to obtain. The simplest approximate version of BED is the binary-encounter-Bethe (BEB) [31] model, which does not need the knowledge of DOS for calculating the EISICS. 

Hydrocarbon molecules are abundant constituents of planetary atmospheres and major compounds in combustible gas mixtures and in fusion edge plasmas [7-11]. Methane is the simplest of these hydrocarbon molecules. Acetylene, C2H2, is the simplest hydrocarbon molecule that contains 2 carbon atoms. Thus absolute total and partial photon [24-27] and electron [15,28-34] ionization cross-sections and nascent fragment ion energy distributions [19,20,28,36-40] have been studied extensively for these molecules. For the deuterated methane molecule electron impact ionization and dissociative ionization cross-sections were determined for the CD (x=l—4) molecule and radicals applying a fast neutral beam technique [41]. Electron impact total ionization cross-sections have been determined also theoretically applying the BEB (Binary-Encounter-Bethe) model [42], the DM (Deutsch-Mark) method [43] and the JK (Jain-Khare) method [44], Partial electron impact ionization cross-sections were calculated for methane [45,46] as well as total electron impact cross-sections for various CH radicals [47]. The dissocia-... 

Figure 10 Experimental (solid symbols) and theoretical (dashed line, distorted-wave Born approximation full line, Deutsch-Maerk formula and BEB (Binary-Encounter-Bethe) approximation) electron ionization cross section for helium.

The relative success of the binary encounter and Bethe theories, and the relatively well established systematic trends observed in the measured differential cross sections for ionization by fast protons, has stimulated the development of models that can extend the range of data for use in various applications. It is clear that the low-energy portion of the secondary electron spectra are related to the optical oscillator strength and that the ejection of fast electrons can be predicted reasonable well by the binary encounter theory. The question is how to merge these two concepts to predict the full spectrum. 

It is notable that the photoionization cross sections does not appear in the BEB expression, although it is required in the Bethe model instead, a simple functional form has been assiuned (Kim and Rudd, 1994). A more elaborate model that does incorporate the photoionization cross section, referred to as the binary-encounter-dipole (BED) model, was also proposed by Kim and Rudd (1994). The BED model is suitable for calculation not only of the total ionization cross section but of the singly differential cross section, i.e., the eross section for a... 

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