The creation, destruction, and transfer of multipole moments in electron–ion three-body recombination using the Gell-Mann–Goldberger–Watson method

We use the Gell-Mann–Goldberger–Watson (GGW) method to further develop and elaborate on our earlier investigation of electron–ion three-body scattering. The GGW method is used to obtain multipole moment creation, destruction, and transfer rate formulae by the three-body recombination of electrons with ions assuming short-range interaction potentials. This approach leads to the derivation of the rate coefficient formula obtained previously via the alternative wave-packet propagation method. We show how to include exchange effects into the formalism, allowing extension of its validity to lower incident electron energies, and also introduce the Liouville-space formulation. Furthermore, we indicate that this method makes the relevance of the formulae to relativistic systems more transparent, demonstrating its validity for high incident electron energies and heavy ions. The Liouville-space formulation is used to facilitate the derivation of a selection rule for the rate coefficients for cylindrically symmetric plasmas, which is of practical importance for the proper formulation of population-alignment collisional-radiative modeling. (paper)