Extensive theoretical and experimental studies have been carried out for the past 20 years on electron-ion recombination processes, as they are applied to the analysis of astrophysical and laboratory plasmas. We review the basic understanding gained through these efforts, with emphasis on some of the more recent progress made in recombination theory as the recombining system is affected by time-dependent electric fields and plasma particles at low temperature. Together with collisional ionization and excitation processes, recombination is important in determining ionization balance and excited-state population in non-equilibrium plasmas. The radiation emitted by plasmas is usually the principal medium with which to study the plasma condition, as it is produced mainly during the recombination and decay of excited states of ions inside the plasma. This is especially true when the plasma under study is not readily accessible by direct probes, as in astrophysical plasmas. Moreover, external probes may sometimes cause undesirable disturbances of the plasma.Electron-ion recombination proceeds in several different modes. The direct modes include three-body recombination (TBR) and one-step radiative recombination (RR), all to the ground-and singly-excited states of the target ions. By contrast, the indirect resonant mode is a two-step dielectronic recombination (DR), which proceeds first with the formation of doubly-excited states by radiationless excitation/capture. The resonant states thus formed may relax by autoionization and/or radiative cascades. For more exotic modes of recombination, we consider off-shell dielectronic recombination (radiative DR = RDR), in which an electron capture is accompanied by simultaneous radiative emission and excitation of the target ion. Some discussion on attachment of electrons to neutral atoms, resulting in the formation of negative ions, is also given.When resonance states involve one or more electrons in high Rydberg states, presence of an external or intrinsic electric field in the vicinity of the target ions can seriously affect the ionic states involved and the resulting reaction rates. Such perturbative fields can be intrinsic, as in the case of the plasma ion field, or externally imposed. A proper theoretical treatment of this difficult problem is crucial in understanding the recombination process which takes place in a field contaminated environment. The simple off-shell dressing procedure of high Rydberg states by a time-dependent field is reviewed, and the possibility of an anomalously large enhancement in the rates, due to the momentum coherence effect (MCE), is discussed.

Approximately orthogonal channel projection operators are constructed for the charge-exchange processes in ion-atom collisions at high energies. The adiabatically perturbed stationary-state wave functions are suitably modified to take into account the motion of the heavy cores to which electrons are bound. By proper adjustment of the phase factors, it is shown that the orthogonality property between states in the modified set can be maintained. The resulting projection operators are mutually orthogonal everywhere in the configuration space, and satisfy the asymptotic requirements to first order in the electron-ion mass ratio. Single asymmetric and symmetric charge exchanges as well as double exchanges are studied in some detail, but no actual applications are given.

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