Modified binary encounter Bethe model for electron-impact ionization

Abstract

Theoretical expressions for ionization cross sections by electron impact based on the binary encounter Bethe (BEB) model, valid from ionization threshold up to relativistic energies, are proposed. The new modified BEB (MBEB) and its relativistic counterpart (MRBEB) expressions are simpler than the BEB (nonrelativistic and relativistic) expressions because they require only one atomic parameter, namely the binding energy of the electrons to be ionized, and use only one scaling term for the ionization of all sub-shells. The new models are used to calculate the K-, L- and M-shell ionization cross sections by electron impact for several atoms with Z from 6 to 83. Comparisons with all, to the best of our knowledge, available experimental data show that this model is as good or better than other models, with less complexity

Copper fine-structure K-shell electron impact ionization cross sections for fast-electron diagnostic in laser-solid experiments

“…From threshold to the dip, our cross section is closed to the ab initio models presented, i.e. the modified relativistic binary encounter Bethe (MRBEB) model of Guerra et al [11] and the combination of distorted-wave-Born and plane-wave-Born (DWB/PWB) models of Bote et al [20]. A good agreement is also observed for the empirical models of Haque et al [21] and Hombourger [22].…”

“…The fitted cross sections of Davies et al [1] are systematically ∼10%-∼20% higher than our calculations. A comparison of our (summed) DW + extrapol cross section in Cu 0 with other models [1,11,[20][21][22] is given in Fig. 2.…”

“…[10]) will therefore not be taken into account by our FAC calculations. This relativistic rise starts at incident electron kinetic energy ε ∼ 100 keV [11]. In order to consider this effect but also the density effect, the empirical trend proposed by Davies et al [1] (Eq.…”

Vanadium fine-structure K-shell electron impact ionization cross sections for fast-electron diagnostic in laser–solid experiments

“…[29]) will therefore not be taken into account by our FAC calculations. This relativistic rise starts at incident electron kinetic energy ε ∼ 100 keV [30]. In order to consider this effect but also the density effect, the modified relativistic binary encounter Bethe (MRBEB) trend of Guerra et al [30] (see Eqs.…”

“…The relativistic distorted-wave (DW) approximation implemented in the FAC atomic code has been used for the incident electron kinetic energies up to 20 times the K-shell threshold energies. Moreover, the resulting DW cross sections have been extrapolated at higher energies using the asymptotic behavior of the modified relativistic binary encounter Bethe model (MRBEB) of Guerra et al (2012) with the density-effect correction proposed by Davies et al (2013). …”