The O III 52 ▪m/88 ▪m emission-line ratio in planetary nebulae

R-matrix calculations of electron impact excitation rates in 0 III are used to derive the electron-density-sensitive emission-line ratioR = 1 (2s ² 2p ²³ P ₂-2s ² 2P ²³ P ₁)/I (2s ²2p ²³ P ₁ - 2s ²2p ²³ P ₀) =I (52μm)/I (88μm) for a range of electron temperatures(Te = 5000-20000 K) and densities(N _e =10–10 ⁵ cm⁻³) applicable to planetary nebulae. Electron densities deduced from the observed values ofR in several planetary nebulae are in excellent agreement with those deduced from C1 I and Ar IV, which provides support for the accuracy of the atomic data adopted in the calculations.