= Three-level forbidden-line density diagnostic
{title2=$j_{31}/j_{21}=(A_{31}\nu_{31}/A_{21}\nu_{21})(n_3/n_2)$}
In a three-level ion, <statistical equilibrium> must include collisional coupling between both upper levels as well as excitations from the ground. The upper populations solve a two-by-two linear system when expressed relative to the ground population. Their line ratio is a rational function of <electron density>, interpolating between a collisionally excited low-density limit and a collisional Boltzmann limit. Closely spaced upper energies reduce <temperature> sensitivity, but neglecting upper-level collisional mixing can bias the inferred <density>.
Back to article page
