The total DR rate coefficient averaged over a Maxwell-Boltzmann electron energy distribution at temperature T is given by

where*g*_{i} and *g*_{j} are the statistical weights of the states *i* and *j*, *E*_{ij} is the resonance energy, A_{jia} is the autoionization rate from the states *j* to *i*, *R*_{y} is the Rydberg energy, *k*_{B} is the Boltzman constant, and *a*_{0} is the Bohr radius.
*B*_{j} denotes the radiative stabilizing branching ratio and can be expressed as

where the final states*t* and *t'* are below and above the ionization threshold, respectively.
*B*_{t'} is the branching ratio for radiative stabilization of *t* and can be determined by evaluation *B*_{j} iteratively.

For convenience in plasma modeling we have fitted our total DR rate coefficients by the formula

where*T* is in units of eV.

where

where the final states

For convenience in plasma modeling we have fitted our total DR rate coefficients by the formula

where

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