Theory of laser-assisted spontaneous radiative recombination

We study the process of laser-assisted radiative recombination of electron with proton by using a semiclassical approach involving calculation of classical trajectories in combined laser and Coulomb fields. Due to chaotic scattering in the combined fields$^1$, the radiation probability as a function of the impact parameter and the constant phase of the laser field exhibits fractal structures similar to those observed in bremsstrahlung$^2$. We obtain a strong enhancement of the recombination cross section as compared to the laser-free case due to the Coulomb focusing effect$^3$. For sufficiently low incident electron velocities the cross section becomes infinite, and we limit it by assuming a finite laser pulse duration of about 1 ps. With this assumption we obtain the gain factor for capture into the ground state of the hydrogen atom of about 74 for a terawatt field, and about 49 for a gigawatt field. $^1$L. Wiesenfeld, Phys. Lett. A {\bf 144}, 467 (1990). $^2$H. B. Ambalampitiya and I. I. Fabrikant, Phys. Rev. A {\bf 99}, 063404 (2019). $^3$Th. Brabec, M. Yu. Ivanov, and P. B. Corkum, Phys. Rev. A {\bf 54} R2551 (1996).