A semi-empirical method for the calculation of cross sections for the electron-impact ionization of negatively charged fullerenes

We extended our previously developed semi-empirical method for the calculation of cross section functions (absolute value and energy dependence) for the electron-impact ionization of the neutral fullerenes C₆₀ and C₇₀ and of the ionized fullerenes C₆₀^q+ (q=1-3) to the calculation of multiple ionization processes of the negatively charged fullerenes C_m^- (m=60, 70, and 84). Systematic trends and tendencies are highlighted and a detailed comparison with available experimental data is made. Predictions are also made for cross sections for the ionization of the neutral fullerene C₈₄ up to charge state z=6. An attempt is made to elucidate the origin of an experimentally observed scaling law that relates the ratio of the measured ionization cross sections of different fullerenes m and m′, σ_-1,z(m)/σ_-1,z(m′), where the subscript "-1" refers to the fact that the initial target is negatively charged and "z" denotes the charge state of the final ion, to the corresponding ratio of the geometric cross sections σ_geom(m)/σ_geom(m′) to the power "z".