The Helium Triplet Spectrum in Expanding Nebulae. I. The Capture-Cascade Intensities

The equations of radiative capture and subsequent cascade are formulated and solved for the triplet states of neutral helium. Incorporating recent improvements in fundamental atomic parameters for he- hum, the solution explicitly takes into account all energy levels (n,l) through n = 20 and estimates the contributions of higher levels. Cross-sections specifying the redistribution of electrons within higher levels by collisions are estimated and incorporated into the solution. The populations of the energy levels and relative intensities for spectral series of interest are thus obtained for Te = 100000 and 200000 K and for N6 ranging from 500 to over 1O~ cm~. Density-dependent collisional effects are found to he marginally observable, but a systematic deviation between the theoretical calculations and the observed intensities of the higher n3D-23P transitions still remains Otherwise, the agreement between observations and calcu- lations is within observational error. The intensities computed are used as sources in Paper IT, where the modification of the triplet spectrum due to the metastability of the 23S state is treated