The total two-photon decay rate of hydrogen-like ions is studied using relativistic quantum electrodynamics. In particular, we analyse how finite nuclear size and QED vacuum polarization corrections affect the decay rate. To calculate these corrections, a finite basis set method based on $B$-splines is used for the generation of quasi-complete atomic spectra and, hence, of the relativistic Green’s function. By making use of this $B$-spline approach, high precision calculations have been performed for the $2s_{1/2}\to 1s_{1/2}+2\gamma$ and $2p_{1/2}\to 1s_{1/2}+2\gamma$ decay of hydrogen-like ions along the entire isoelectronic sequence. The results of these calculations show that both, QED and finite nuclear size effects, are comparatively weak for the $2s_{1/2}\to 1s_{1/2}+2\gamma$ transition. In contrast, they are much more pronounced for the $2p_{1/2}\to 1s_{1/2}+2\gamma$ decay, where, for hydrogen-like Uranium, the decay rate is reduced by 0.484% due to the finite nuclear size and enhanced by 0.239% if the vacuum polarization is taken into account.

中文翻译：

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类氢离子双光子衰变中的真空极化和有限核尺寸效应

使用相对论量子电动力学研究了类氢离子的总双光子衰变率。特别是，我们分析了有限的核尺寸和QED真空极化校正如何影响衰减率。为了计算这些校正，基于$乙$-样条线用于生成准完全原子光谱，并因此用于相对论格林函数。通过利用这个$乙$-样条方法，已针对 $2s_{\mathrm{1个}/2}\to \mathrm{1个}{s}_{\mathrm{1个}/2}+2\gamma$ 和 $2p_{\mathrm{1个}/2}\to \mathrm{1个}{s}_{\mathrm{1个}/2}+2\gamma$类氢离子沿整个等电子序列的衰变。这些计算的结果表明，QED和有限的核尺寸效应对于$2s_{\mathrm{1个}/2}\to \mathrm{1个}{s}_{\mathrm{1个}/2}+2\gamma$过渡。相比之下，对于$2p_{\mathrm{1个}/2}\to \mathrm{1个}{s}_{\mathrm{1个}/2}+2\gamma$ 衰变，对于类似氢的铀，由于有限的核尺寸，衰变率降低了0.484％，如果考虑到真空极化，则衰变率提高了0.239％。