Radiative recombination of bare ions with low-energy free electrons

Radiative recombination of bare ions with electrons is discussed as a time-reversed photoionization process in the nonrelativistic dipole approximation. Analytical expressions for the radiative-recombination cross section and the angular distribution of the emitted photons are derived for an arbitrary (n,l) state in the low-energy limit. In this approximation, the anisotropy of the emitted photons is described by an energy-independent parameter ${\mathrm{\beta }}_{\mathit{n}\mathit{l}}$. The radiative-recombination rate coefficients, both differential and angle integrated, for any (n,l) state can, in this limit, be expressed in analytical form. This result holds also for an anisotropic electron-velocity distribution characterized by a longitudinal ${\mathit{kT}}_{\mathrm{\parallel }}$ and transverse ${\mathit{kT}}_{\mathrm{\perp }}$ electron-beam temperatures. The results are discussed in context of the state-selective radiative-recombination experiments planned to be studied in electron coolers of heavy-ion storage rings.