This work is focused on the possibility of using the $R$ -matrix Floquet theory and codes and its extension to laser induced degenerate state to describe dielectronic recombination of Li-like into Be-like ions. The uncertainty concerning the best way to include radiative damping effect is no longer a problem when the full electron collision and radiative processes are treated simultaneously and radiation field is treated to all orders. The method accounts for the reverse process corresponding to single-photon ionization. Following this approach, the $1s^{2}2snl\left({}^{1}S^{\mathrm{e}}\right)$ and $1s^{2}2pnl\left({}^{1}P^0\right)$ Rydberg states, embedded in the electric dipole field of the $2s\text{-}2p$ core, are dressed by a laser field, assumed to be monochromatic, monomode, linearly polarized, and spatially homogeneous. As in the $R$ -matrix Floquet theory, in the external region, since the coupling field potential vanishes, the calculation yields the complete information on the autoionizing rate and field-free positions. Comparisons with available data are presented.

The primary purpose of the present work is to provide new refined results from nonperturbative treatment of the radiative damping effect in dielectronic recombination. The present results are used to test and confirm previously reported method [V. Stancalie, Phys. Plasmas 12, 043301 (2005)] taking full account of the electron collision and radiative processes in a consistent way, when radiation field is considered to all orders. This work refers to the $1s^{2}2s5s\left({}^{1}S\right)$ and $1s^{2}2p7s\left({}^{1}P^0\right)$ configurations, embedded in the electric dipole field of the $2s–2p$ core transition in Li-like C ion. Comparisons with previously reported results are shown. This data are believed to be the first demonstration of $\Delta n=2$ channel in dielectronic recombination of Li-like into Be-like C and are important in plasma diagnostics.