Electron-ion interactions may be depicted by the following diagram:
|
Figure 1. Inter-related radiative and collisional atomic processes: EIE - electron impact excitation, AI - autoionization, DR - dielectronic recombination, PI - photoionization, RR - radiative recombination. |
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
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.
i is the target
ion wave function in a specific state Si
Li and
i is the wave
function for the free electron in a channel labeled as
SiLiki2
li(SL
);
ki2
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.