The data file AMJUEL: Additional Atomic and Molecular ... - eirene

we have subtracted the (negative) potential energy contribution from these coefficients before
fitting.
More generally, the fitted coefficients, therefore, read:
⟨σ · v · E⟩fit = ⟨σ · v · E⟩ − ∆Esubtr.⟨σ · v⟩
with ∆Esubtr. specified for each particular rate coefficient below, together with the fitting coefficients.
By default we have chosen ∆Esubtr. = 0. in this expression for all processes in which the
potential energy is enhanced (“sub-elastic” processes, such as ionization, excitation).
For the opposite case (recombination, collisional de-excitation, i.e., “super-elastic” processes,
we have chosen ∆Esubtr. = ∆Epot
One can show with some boring algebra on the matrices which arise in collisional radiative
models that with this particular choice of the subtracted energy loss rate for collisional radiative
electron cooling rates the remaining fitted expression ⟨σ · v · E⟩fit turns out to be exactly the
radiation energy loss rate associated with a particular process.
In other words: the total effective electron cooling rate is the sum of the effective radiation
energy loss rate plus the effective potential energy loss rate, however, with the latter rate being
simply given as
⟨σ · v · ∆Epot⟩effective = ∆Epot · ⟨σ · v⟩effective
In this expression ⟨σ · v⟩effective is just the effective rate coefficient for the process under consideration,
i.e. the coefficient for the same process as given in section H.4.
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