The theory of impact-radiation recombination (ionization) in a low-temperature plasma is based on the representation of this process as a random walk of a recombining (released) electron in the discrete space of the atom's energy levels. Different methods of studying recombination (ionization) are considered. The described modified diffusion approximation, combining the possibilities of the previously developed approaches, takes into account the real energy structure of the atom, the influence of the radiative transitions, and the relationship between the non-equilibrium distributions of the atoms over the levels and of the electrons over the energies. A solution is presented for the Fokker--Planck equation expressed in finite-difference form, and analytic expressions are obtained for the ionization and recombination coefficients. The results are compared with the published experimental data.