Electron-ion interactions may be depicted by the following diagram:

Quantum mechanically *all* of the atomic processes shown may be treated
by a wavefunction expansion that represents the total e+ion system in
terms of the coupled eigenfunctions of the ``target'' or the ``core'' states
of the ion, i.e.

where _{i} is the target
ion wave function in a specific state *S*_{i}
*L*_{i} and
_{i} is the wave
function for the free electron in a channel labeled as
*S*_{i}*L*_{i}*k*_{i}^{2}
*l*_{i}(*SL*);
*k*_{i}^{2}
being its
incident kinetic energy. While the close coupling approximation (e.g.
the R-matrix method) includes coupling between the
target states of the ion, simpler approximations such as the distorted
wave or the central field approximations neglect the coupling effects
which may be important at low energies.

One particularly important coupling effect manifests itself as autoionizing resonances, from doubly-excited states of the e+ion system (the center of the Fig. 1), that can substantially enhance the cross sections and rates for excitation, photoionization and recombination. The near threshold region of the cross sections, that dominates the rate of electron excitation and line formation for forbidden and intercombination transitions, may be particularly affected by broad and extensive resonance structures. Dipole allowed transitions are less affected. In general therefore it is necessary to employ the accurate close coupling approximation for the forbidden and the intercombination lines, but for the dipole allowed transitions the distorted wave approximation often suffices to obtain rates to 10-30% uncertainty.

A brief discussion of a few points related to the atomic processes is given next.