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The modified BELL (MBELL) formula (Haque et al 2006 Phys. Rev. A 73 012708) has been applied to the M-shell ionization of neutral and ionic atoms to deduce the `generalized' parameters of the 3s, 3p and 3d orbits. A single set of parameters for each of these orbits and that previously determined for each of 1s, 2s and 2p orbits can reproduce satisfactorily the features of the total electron impact ionization cross-sections (EIICS) of 21 M-shell targets in the Na, Mg, Al, Si, P, S, Cl, Ar and Ca isoelectronic sequences. The generalized parameters are also found to provide an excellent account of the M-shell EIICS data of Pb, Bi and U atoms at relativistic energies in the range from 20 to 250 MeV.

A simple modification of the empirical model of Hombourger (HEMP) [1998 J. Phys. B 31 3693] is proposed with ionic and relativistic corrections in it. The modified HEMP (MHEMP) model has been applied to 11 H- and He-like ionic targets with a wide range of atomic numbers Z = 5–92 to calculate the electron impact single ionization (EISI) cross sections. MHEMP with a single set of parameter values is found to describe excellently the experimental EISI cross sections of B4+, C4+, N6+, O7+, Ne8+, Mo41+, Dy65+, Au78+, Bi82+, U90+ and U91+ up to an incident energy of about 460 keV.

The total cross-sections of electron impact single K-shell ionization of C, N, O, Cr, Mn, Fe, Cu, Ga, Ge and Zr atoms are computed using the previously propounded relativistic and non-relativistic BED, relativistic DM and Gryzinski models. We also propose a hybrid RDM model combining the relativistic component of the Gryzinski model with the non-relativistic DM model. The calculated cross-sections are compared to the available experimental data as well as some predictions, made by Khare et al, from the plane wave Born approximation theory.

Previously developed BEB, RBEB, DM and recently developed RDM models are employed for the computation of cross-sections of electron impact single K-shell ionization of atoms with atomic numbers from Z = 19 to 103 to augment the work recently done involving atoms with Z = 6 to 40. The calculated cross-sections are compared with the available experimental data over a wide energy range up to 1000 MeV. The RDM model with simple relativistic factor is found to be at least as good as the DM model with a more complex factor up to about 60 MeV. However, the latter one is found to work satisfactorily up to about 1000 MeV.