QED corrections of orders $m{\alpha }^6$ and $m{\alpha }^6(m/M)$ for HD${}^{+}$ rovibrational transitions beyond Born-Oppenheimer approximation

Abstract

The effective Hamiltonian of $m{\alpha }^6$ and $m{\alpha }^6(m/M)$ order corrections for hydrogen molecular ions has been derived in [ Z.-X. Zhong, \emph{et al.}, Phys. Rev. A {\bf98}, 032502(2018).], in this work we express the energy correction in the form of finite-value effective operators. The cut-off regularization scheme is used to determine finite part of divergent operators of the leading-order recoil corrections. Numerical calculations of first-order contributions are performed in the Hylleraas basis set. Combining the second-order terms calculated in recent work [V. I. Korobov, \emph{et al.}, Mol. Phys. e2563023 (2025).], the $m{\alpha }^6$-order corrections for the fundamental rovibrational transition are obtained with an uncertainty three times smaller than in previous calculations.

arXiv comment14 pages, 0 figures

References in corpus (12)

• Probing QED and fundamental constants through laser spectroscopy of vibrational transitions in HD+
• Proton-Electron Mass Ratio from Laser Spectroscopy of HD${}^{+}$ at the Part-Per-Trillion Level
• Fundamental transitions and ionization energies of the hydrogen molecular ions at the few ppt level
• Relativistic corrections of mα^6 order to the ro-vibrational spectrum of H_2^+ and HD^+ molecular ions
• Proton-electron mass ratio by high-resolution optical spectroscopy of ion ensembles in the resolved-carrier regime
• Theoretical transition frequencies beyond 0.1 ppb accuracy in H${}_2^{+}$, HD${}^{+}$, and antiprotonic helium
• Rotational spectroscopy of cold, trapped molecular ions in the Lamb-Dicke regime
• Calculation of the relativistic Bethe logarithm in the two-center problem
• Calculation of the nonrelativistic Bethe logarithm in the velocity gauge
• Relativistic corrections of order mα^6 to the two-center problem
• Expansion of bound state energies in powers of m/M and (1-m/M)
• Precision spectroscopy of the hydrogen molecular ions HD${}^{+}$