An accurate treatment of the radiative-cascade problem requires detailed
calculations of recombination into excited states. Few detailed
photoionization calculations had been performed for *n* > 2 states, before
the work of the OP. It has been noted (Storey [1982]) that,
in C ^{+}, the dominant contribution to the recombination coefficient
of the 2s2p^{2} ^{2}D
state comes from the
2s2p(^{3}P^{o})3d ^{2}F^{o} resonance. It is not only
an important source of recombination for this state, but for the whole ion,
particularly at low temperatures when the average free electron energy lies
close to threshold. The 2s2p(^{3}P^{o})3d ^{2}P^{o}
resonance, although higher in energy is also a significant source of
recombination.

In general, the theoretically calculated energies of states are higher than the experimental values. For low temperature recombination work, the placement of resonances is critical. A change in the position of the resonances can lead to a large change in the the value of the total recombination coefficient if the average free electron energy is lower than the resonance energy.

The experimentally determined positions of the ^{2}F^{o}
and ^{2}P^{o} resonances (Moore [1970]) are 3301 cm^{-1}
and 5523 cm^{-1} above the 2s^{2} (^{1}S)
threshold. This compares
with the theoretically calculated values of 3778 cm^{-1} and
6172 cm^{-1}. We evaluate the resonance contributions to the total
recombination coefficient using their experimental rather than the
theoretical energies by, in effect, moving these two resonances.

This is done by fitting the photoionization cross-section in the energy
region around the resonances using a Fano profile (Fano [1961]). For a
resonance superimposed on a constant background the profile is given by

The value of can be estimated from the minimum point,

This form does not allow for any energy dependence in the background, and
therefore can only be used to fit a narrow energy range. The theoretical
position and width of the resonance are used to start an iterative procedure
to determine the quantities *q*,
and .
A new profile is then
generated, differing only in the energy of the peak of the profile, and
integrated to give a new value of the contribution to the recombination
coefficient from the resonance and the adjacent energy region. Using the new
profile gives a modified recombination coefficient for the state with the
resonance contributions evaluated at their experimental positions. This method
was applied to all cross-sections in which the two resonances appeared, for
all states .
In Fig. 3, we compare the recombination coefficients
for the 2s2p^{2} ^{2}D
term computed with the two lowest lying resonances
in their calculated and experimentally determined positions. There are
significant changes to the recombination coefficients as a result,
particularly at low electron temperatures. For example, the placement of the
2s2p(^{3}P^{o})3d ^{2}F^{o}, ^{2}P^{o}resonances at their experimental positions brings about a
increase in
the recombination coefficient of the 2s2p^{2} ^{2}D
state at 1000 K.

The total recombination coefficient of a state depends,
in general, on the relative populations of the C ^{2+}
2s^{2}(^{1}S) and 2s2p(^{3}P^{o}) states.
For the temperature and density range under consideration here,
the fraction of the population in the 2s2p(^{3}P^{o})
state is always less than 0.01% and so we ignore recombination
from this state in the present calculation.

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