Binary-encounter Bethe theory

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. 

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. 

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