Optical thickness in the He I singlet spectrum of nebulae

An integral equation expressing the transfer of resonance line radiation in the He I singlets has been solved for nebular models consisting of differentially expanding uniform spheres. Solutions have been obtained numerically for a variety of temperatures, optical depths, expansion velocities, and scattering functions appropriate to nebulae. Comparison of the transfer solutions to observed helium-singlet line intensities gives optical depths for various nebulae in the resonance lines in the ground-state bound-free continuum. There is considerable variation seen in the He0 optical thicknesses: at the bound-free continuum limit A504, the optical depth ranges from 0.064 to 0.72 in a group of 14 observed nebulae. The He0 abundance does not appear sufficiently high in any of these objects to modify existing He/H ratios for nebulae derived on the basis of negligible neutral helium. Further discussion of the results demonstrates that transfer solutions of this type provide a sensitive observational test of computed ionization-stratification models for nebulae. Subject headings: nebulae - radiative transfer