Multielectron ionization of atoms by fast ions: an approximation by normalized exponentials

Multielectron ionization of neutral atoms by fast positive ions is considered in terms of the independent particle model. A relatively simple technique for calculating the multielectron ionization probabilities and cross sections through the impact parameter is suggested in which one-electron ionization probabilities are represented as normalized exponentials p nl(b) = p nl(b) = p nl(0)exp(−αnl b), where b is the impact parameter and n and l are quantum numbers of the target atomic shell. Exponent αnl is determined from the Born one-electron ionization cross section for target atoms, and preexponential p nl(0) (the ionization probability at a zero impact parameter) is found from a geometrical model. This technique provides the normalization condition p nl(b) ≤ 1 irrespective of the velocity and charge of striking ions and makes it possible to calculate the one-, two-, and three-electron ionization cross sections, which, when added up, make a major contribution to the total cross section, up to a factor of 2. The results of our computations are compared with experimental data and analytical results of other authors