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The total cross sections of electron-impact single-K-shell ionization of 14 atomic targets ranging from H to U ͑1 ഛ Z ഛ 92͒ are calculated using a modified version of the BELI formula ͓Bell et al., J. Phys. Chem. Ref. Data 12, 891 ͑1983͔͒ by incorporating both ionic and relativistic corrections in it. The proposed modified Bell model with a single set of parameters is found to provide an excellent description of the experimental data in the reduced energy range 1 ഛ E / I K ഛ 10 6 ͑E and I K are, respectively, the incident energy and ionization poten-tial͒ with a performance level at least as good as any of the existing methods and models.

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.

An extension of the analytical model of Campos et al (2007 J. Phys. B: At. Mol. Opt. Phys. 40 3835) is proposed to evaluate electron impact single inner-shell ionization cross sections up to the M-shell. The new model includes ionic and relativistic factors in its structure and describes neatly the K-shell ionization cross section data up to 2 GeV, and L- and M-shell ionization data up to 300 MeV. Comparison is also made with other theoretical calculations.

The experimental differential cross-sections of 16 O + 16 O elastic scattering in the energy range 75 MeV E lab 1120 MeV are analysed using families of non-monotonic (NM) shallow nucleus-nucleus potential in the framework of the optical model. The experimental data is reproduced successfully using six families of NM potentials. It is found that all families converge at 350 MeV. The clear indication of the convergence of the potential families at 350 MeV conforms to the Goldberg criterion concerning the removal of discrete ambiguities even for the shallow NM potential. The study further suggests that the energy of convergence heralds the occurrence of the primary rainbow at that incident energy.