H, He-like recombination spectra II: $l$-changing collisions for He Rydberg states

TL;DR

This paper improves the accuracy of helium spectral predictions by refining $l$-changing collision rate calculations, which are crucial for precise primordial helium abundance measurements in cosmology.

Contribution

It introduces a criterion for applying energy-degenerate collisional theories to He atoms and proposes a modified Bethe approximation that aligns well with quantum calculations.

Findings

Different theoretical approaches cause ~10% variation in He I emissivities.

The modified Bethe approximation improves rate coefficient accuracy.

Differences in $l$-changing rates impact primordial helium abundance estimates.

Abstract

Cosmological models can be constrained by determining primordial abundances. Accurate predictions of the He I spectrum are needed to determine the primordial helium abundance to a precision of $< 1$% in order to constrain Big Bang Nucleosynthesis models. Theoretical line emissivities at least this accurate are needed if this precision is to be achieved. In the first paper of this series, which focused on H I, we showed that differences in $l$-changing collisional rate coefficients predicted by three different theories can translate into 10% changes in predictions for H I spectra. Here we consider the more complicated case of He atoms, where low-$l$ subshells are not energy degenerate. A criterion for deciding when the energy separation between $l$ subshells is small enough to apply energy-degenerate collisional theories is given. Moreover, for certain conditions, the Bethe approximation originally proposed by Pengelly & Seaton (1964) is not sufficiently accurate. We introduce a simple modification of this theory which leads to rate coefficients which agree well with those obtained from pure quantal calculations using the approach of Vrinceanu et al. (2012). We show that the $l$-changing rate coefficients from the different theoretical approaches lead to differences of $\sim 10$% in He I emissivities in simulations of H II regions using spectral code Cloudy.