We study static-field ionization of He-like ions with nuclear charge number in the range of $2\le Z\le 36$. Both the tunneling and over-the-barrier regimes are considered. We calculate the ionization rates by three approximate methods: a fitting formula based on the Perelemov-Popov-Terent’ev (PPT) formula, a perturbative expansion in powers of $1/Z$, and a single-active electron approximation, and compare them with reference ionization rates computed by the multiconfiguration time-dependent Hartree-Fock (MCTDHF) approach. The relative deviation of the rates computed by the PPT-based fitting formula and the third-order perturbation theory from the rates computed by the MCTDHF approach is found to be around 10%. We discuss quantitatively the contribution from the exchange interaction during the ionization by comparing the single-active electron rates and the reference rates in which multielectron effects are included. We find that a single-active electron approximation, where the exchange interaction is neglected, results in the overestimation of the ionization rates by 30% for He and 2% for He-like Kr, showing that the magnitude of the effect of the exchange interaction scales approximately as $1/Z$.

中文翻译：

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类氦离子的静态场电离模型，用于诊断光场强度

我们研究He离子的静态场电离，其核电荷数在 $2\le ž\le 36$。同时考虑了隧道和越过障碍的制度。我们通过三种近似方法计算电离速率：基于Perelemov-Popov-Terent'ev（PPT）公式的拟合公式，$\mathrm{1个}/ž$，以及单活性电子近似，并将其与通过多配置时变哈特里-福克（MCTDHF）方法计算出的参考电离率进行比较。发现基于PPT的拟合公式和三阶微扰理论计算出的速率与MCTDHF方法计算出的速率的相对偏差约为10％。我们通过比较单活性电子速率和包含多电子效应的参考速率来定量讨论电离过程中交换相互作用的作用。我们发现，忽略交换相互作用的单活性电子近似值会导致He的电离率高估30％，He样Kr的电离率高估2％，$\mathrm{1个}/ž$。