ABSTRACT:Recently proposed extension of the empirical model (BELL) of Bell et al. (J Phys Chem Ref Data 1983, 12, 891) with incorporation of the quantum mechanical form of orbital radius from the DM model and a nonlinear feature in addition to the ionic and relativistic corrections is examined for electron-impact single ionization in the K-, L-, and M-shells of ionic and neutral atoms. This leads to the generalization of the parameters of the nonlinear form of the modified BELL (NMBELL) model in terms of the quantum numbers nl of the ionizing orbits. The generalization shows that only three species-independent fitting parameters, dependent only on the orbitals, in the NMBELL model satisfactorily reproduce the electron-impact single ionization cross sections of 42 ionic targets belonging to the He, Li, Be, B, C, O, F, Ne, Mg, Al, P, Ca, and Sc isoelectronic sequences over a wide range of energies up to 200 MeV. The NMBELL model is also found to well account for the L-and M-shell ionization of six neutral atoms up to 1 GeV.