Recombination Spectra: I. Calculations for Hydrogenic Ions in the Limit of Low Densities

The capture–cascade equations are solved for a hydrogenic system with an infinite number of energy levels. It is assumed that radiative processes alone determine the populations of the states nl . The rate of populating nl due to the processes of capture and cascade is $$N_eN_+\alpha^{(c)}_{nl}$$ and the quantum emission rate in a line n → n ′ is $$N_eN_+\alpha_{nn^\prime}$$ . The coefficient $$\alpha^{(c)}_{nl}(T)$$ is tabulated for Cases A and B (nebulae optically thin or optically thick in Lyman lines) and for T in the range T = 10 ⁴t °K, log ₂t = −3(1)3. The intensities of the Balmer, I_{n →2} , and Paschen I_{n →3} lines in the recombination spectra of H I , and the Pickering, I_{n →4} , and Pfund, I_{n →5} , lines in the spectra of He II are tabulated relative to I_{4, 2} (H Iλ 4861) = 100 and to I_{4, 3} (He IIλ 4686) = 100 respectively. The tables are for $$n\leqslant20$$ and T in the range given above. Values are also given for the absolute intensities of I_{4, 2} (H I ) and I_{4, 3} (He II ). Calculated relative intensities in the spectra of H I and of He II are compared with observed intensities in the planetary nebula NGC 7662. The agreement is not altogether satisfactory. To obtain better agreement it appears to be necessary to take account of collisional transitions nl → nl ± 1 for the higher levels.