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arXiv · 2506.22164

Second-order corrections of orders $m\alpha^6$ and $m\alpha^6(m/M)$ to the spin-averaged energy in the HD$^+$ and H$_2^+$ ions

Vladimir I. Korobov·Jean-Philippe Karr·Zhen-Xiang Zhong
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Abstract

The relativistic second-order corrections at orders $m\alpha^6$ and $m\alpha^6(m/M)$ in hydrogen molecular ions are calculated. Convergence of numerical results is studied, which allows estimating the relative numerical uncertainty to be less then $10^{-5}$. This accuracy is sufficient to enable future improvement of theoretical predictions beyond the 1 ppt (part-per-trillion) precision level for the ro-vibrational transition frequencies.

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Vladimir I. Korobov, Jean-Philippe Karr, Zhen-Xiang Zhong. 2025-06-27. Second-order corrections of orders $m\alpha^6$ and $m\alpha^6(m/M)$ to the spin-averaged energy in the HD$^+$ and H$_2^+$ ions. https://arxiv.org/abs/2506.22164

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