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Abstract We study the process of laser-assisted radiative recombination of an electron with a proton in a cold hydrogen plasma employing the semiclassical Kramers’ approach which involves calculation of classical trajectories in combined laser and Coulomb fields and the use of the correspondence principle. Due to the Coulomb focusing effect, recombination is the most effective when the initial electron momentum is parallel to the laser polarization. Orders of magnitude enhancement of the cross section, as compared to the laser-free case, is observed in this case. With increasing angle between the electron momentum and polarization, the recombination cross section drops. However, even after averaging over Maxwellian velocity distribution we obtain a substantial enhancement of the recombination rate constant, as compared to the zero-field case. For the field intensities in the range 30–350 MW cm⁻², the enhancement occurs in the region of the radiation wavelength from 5 to 20µm and for the plasma temperature from 20 to 300 K.