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HyRec: A fast and highly accurate primordial hydrogen and helium recombination code by Yacine Ali-Haïmoud and Christopher M. Hirata (2011 journal publication; 2010 preprint, 10.1103/PhysRevD.83.043513)

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Tags: Work by Christopher M. Hirata, Work by Yacine Ali-Haïmoud
Physical Review D 83, 043513. Section VI.B, equation (97), explicitly gives the factor four from neutral-helium spin degeneracy; the following section treats departure from Saha equilibrium.
arxiv.org/abs/1011.3758
arxiv.org/html/1011.3758v2
doi.org/10.1103/PhysRevD.83.043513

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