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The dimensionless collision strength ${\Omega }_{ij}(E)$ describes electron-impact transitions between two atomic levels before thermal averaging. It can vary rapidly with collision energy, especially near excitation thresholds. The quantity entering a thermal collision rate coefficient for an atomic transition is its effective collision strength, usually denoted ${{\rm Y}}_{ij}(T_e)$, rather than one value of ${\Omega }_{ij}$.^[ref]

For levels $E_j>E_i$, write $\Delta E=E_j-E_i$ and measure the scattering variable $E\ge 0$ above the upper-level threshold. With a Maxwellian electron population,Let $g_i,g_j$ be the statistical weights of atomic levels, and set $T_K=T_e/(1\mathrm{K})$. The excitation and de-excitation rate coefficients areTheir ratio obeys detailed balance. The numerical coefficient is $8.63\times 10^{-6}$ when the rate coefficient is expressed in $\mathrm{c}{\mathrm{m}}^3{\mathrm{s}}^{-1}$.^[ref]

If ${\Omega }_{ij}(E)$ is constant over the sampled energy range, the normalized integral gives ${{\rm Y}}_{ij}={\Omega }_{ij}$. Otherwise low-energy resonances can strongly alter the thermal result. For a non-Maxwellian velocity distribution, compute the appropriate cross-section–speed average; a tabulated Maxwellian effective collision strength is not automatically transferable. Multiplying $q_{ij}$ by electron number density gives the excitation rate per target chemical atom.

The effective collision strength is the dimensionless thermal average of an electron-impact collision strength. For a Maxwellian electron population, with collision energy $E$ measured above the upper-level threshold,It is a function of temperature, rather than a cross section evaluated at one representative energy.

If $\Omega$ is constant, the normalized exponential weight gives ${\rm Y}=\Omega$. Near-threshold resonances can instead strongly change the average, particularly at low temperature. Atomic excitation and de-excitation rate coefficients use this average together with statistical weights and, for excitation, the appropriate Boltzmann threshold factor.^[ref]

Peter Young documents atomic collision data used by the CHIANTI spectroscopy database. His technical report specifies how effective collision strengths, averaged over a Maxwellian electron distribution, are stored and scaled as functions of temperature.^[ref]

An effective collision strength is not an energy-resolved collision strength evaluated at one representative energy. Documenting the averaging and file conventions lets plasma calculations combine data consistently. This entry identifies the author of the CHIANTI report, rather than inferring an identity from the common name alone.

Sultana N. Nahar co-investigated atomic collision data for four-times-ionized neon. Resolving near-threshold resonances changed the effective collision strengths needed to interpret temperature-sensitive infrared and optical line ratios.^[ref]