The present theoretical work aims at the characterization of argonium, namely, the molecular ions ³⁶ArH⁺ and ³⁸ArH⁺, revealed recently in the Crab Nebula and the PKS 1823-211 galaxy. The intent is to scrutinize the radiative processes of association, Ar+H⁺→ArH⁺, and charge transfer, Ar⁺+H→Ar+H⁺. To accomplish these two tasks, the corresponding potential-energy curves and dipole moments are chosen in order to construct the ground and the two first excited ArH⁺ molecular states. Once all the required ArH⁺ curves are well established and their physical and spectroscopic values contrasted with previous published data, the cross sections, for the formation of the ionic dimer ArH⁺ by radiative association and for the radiative charge transfer in the Ar⁺+H collisions, are computed quantum-mechanically at lower and higher energies. Finally, the temperature-dependent rate coefficients are calculated, and the numerical results are discussed and fitted to a selected analytical expression.