A theory of radiative-collisional transitions between the ground and metastable ¹S states of a colliding atom is proposed. The theory uses the uniform quasi-classical approximation generalized to the case of spherically asymmetric interactions. The theory takes into account the angular momentum of an emitted (absorbed) photon and allows one to calculate the total and differential scattering cross sections in a wide range of radiation frequencies including both wings and the center of the line of a forbidden atomic transition. The range of admissible collision energies and intensities of an external radiation field is restricted by the use of the adiabatic approximation, as well as the approximation of a weak coupling between the ground and excited states of a quasi-molecule, the potentials of which are assumed to be monotonically repulsive.