Aims. Determination of K- and L-shell cross sections of the carbon atom and ions using the modified relativistic binary encounter Bethe (MRBEB) method, a simple analytical scheme based on one atomic parameter that allows determining electron-impact ionization cross sections. The quality of the cross sections calculated with the MRBEB method is shown through: (i) comparison with those obtained with the general ionization processes in the presence of electrons and radiation (GIPPER) code and the flexible atomic code (FAC), and (ii) determination of their effects on the ionic structure and cooling of an optically thin plasma. Results. The three sets of cross sections show deviations among each other in different energy regions. The largest deviations occur near and in the peak maximum. Ion fractions and plasma emissivities of an optically thin plasma that evolves under collisional ionization equilibrium, derived using each set of cross sections, show deviations that decrease with increase in temperature and ionization degree. In spite of these differences, the calculations using the three sets of cross sections agree overall. Conclusions. A simple model like the MRBEB is capable of providing cross sections similar to those calculated with more sophisticated quantum mechanical methods in the GIPPER and FAC codes.
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