J-resolved He I emission predictions in the low-density limit

Determinations of the primordial helium abundance are used in precision cosmological tests. These require highly accurate He I recombination rate coefficients. Here we reconsider the formation of He I recombination lines in the low-density limit. This is the simplest case and it forms the basis for the more complex situation where collisions are important. The formation of a recombination line is a two-step process, beginning with the capture of a continuum electron into a bound state and followed by radiative cascade to ground. The rate coefficient for capture from the continuum is obtained from photoionization cross sections and detailed balancing, while radiative transition probabilities determine the cascades. We have made every effort to use today's best atomic data. Radiative decay rates are from Drake's variational calculations, which include QED, fine structure, and singlet-triplet mixing. Certain high-$L$ fine-structure levels do not have a singlet-triplet distinction and the singlets and triplets are free to mix in dipole-allowed radiative decays. We use quantum defect or hydrogenic approximations to include levels higher than those treated in the variational calculations. [Abstract clipped]