Recombination Spectra: II. Collisional Transitions Between States of Degenerate Energy Levels

Previous work has shown that calculated recombination spectra may be sensitive to collisional transitions of the type nl → nl ′ ( l ′ = l ± 1). With equal energies for nl , nl ′, the usual collision theory expressions give infinite cross-sections, but finite results are obtained on introducing a cut-off at large impact parameters. At very low densities the cut-off is determined by the radiative lifetimes of the excited states and at higher densities it is determined by the Debye radius. For conditions in planetary nebulae ( N e ∼ 10 4 cm −3 , Te ∼ 10 4 °K), collisional transitions, nl → nl ′, are faster than radiative transitions, nl → n ′ l ′ ( n ′ < n ), for n ≳ 15 for H I and for n ≳ 22 for He II .