我们已经发展了有关包含原子水平逐行治疗的早期宇宙H, He i和He ii的改进复合计算。与以前的计算相比，我们发现两个主要区别。首先，由于H激发态下的非平衡过程，氙电离分级比<=800的红移约低10％。第二，He i重组比原先预料慢得多且被延迟至H再结合。我们描述了新成果基本物理原理并提出了一个重现计算的简单方法。这使得对于任意宇宙观，电离历史（和电离量，比如宇宙微波背景异向性所依赖的功率光谱）的快速计算成为可能，而不需要考虑在我们完整模型中所使用的数以百计的原子水平。
We have developed an improved recombination calculation of H, He i, and He ii in the early universe that involves a line-by-line treatment of each atomic level. We find two major differences compared with previous calculations. First, the ionization fraction Xe is approximately 10% smaller for redshifts <=800 because of non- equilibrium processes in the excited states of H. Second, He i recombination is much slower than previously thought, and it is delayed until just before H recombines. We describe the basic physics behind the new results and present a simple way to reproduce our calculation. This should enable a fast computation of the ionization history (and of the quantities such as the power spectrum of cosmic microwave background anisotropies that depend on it) for arbitrary cosmologies, without the need to consider the hundreds of atomic levels used in our complete model.