Hyperfine structure in the H${}_2^{+}$ and HD${}^{+}$ molecular ions at $m{\alpha }^6$ order

Abstract

A complete effective Hamiltonian for relativistic corrections at orders $m{\alpha }^6$ and $m{\alpha }^6(m/M)$ in a one-electron molecular system is derived from the NRQED Lagrangian. It includes spin-independent corrections to the energy levels and spin-spin scalar interactions contributing to the hyperfine splitting, both of which had been studied previously. In addition, corrections to electron spin-orbit and spin-spin tensor interactions are newly obtained. This allows improving the hyperfine structure theory in the hydrogen molecular ions. Improved values of the spin-orbit hyperfine coefficient are calculated for a few transitions of current experimental interest.

References in corpus (16)

• Radiative Corrections to the Muonium Hyperfine Structure. I. The ${\alpha }^2(Z\alpha )$ Correction
• 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
• Nonrelativistic QED approach to the Lamb shift
• Relativistic corrections of mα^6 order to the ro-vibrational spectrum of H_2^+ and HD^+ molecular ions
• Higher-order effective Hamiltonian for light atomic systems
• The NRQED lagrangian at order 1/M^4
• Hydrogen molecular ions for improved determination of fundamental constants
• Higher-order recoil corrections for triplet states of the helium atom
• Test of the theoretical hyperfine structure of the molecular hydrogen ion at the 1-ppm level
• Vibrational spectroscopy of H2+: hyperfine structure of two-photon transitions
• Relativistic corrections of mα^6(m/M) order to the hyperfine structure of the H_2^+ molecular ion
• Two-photon spectroscopy of trapped HD${}^{+}$ ions in the Lamb-Dicke regime
• Relativistic corrections of order mα^6 to the two-center problem
• NRQED approach to the fine and hyperfine structure corrections of order $m{\alpha }^6$ and $m{\alpha }^6(m/M)$ -- Application to the hydrogen atom
• Spin-orbit corrections of order $m{\alpha }^6$ to the fine structure of $(37,35)$ state in ${}^4{He}^{+}\bar{p}$ atom

Cited by in corpus (6)

• Proton-electron mass ratio by high-resolution optical spectroscopy of ion ensembles in the resolved-carrier regime
• Higher-order corrections to spin-spin scalar interactions in HD${}^{+}$ and H${}_2^{+}$
• Variational versus perturbative relativistic energies for small and light atomic and molecular systems
• Higher-order corrections to spin-orbit and spin-spin tensor interactions in hydrogen molecular ions: theory and application to H${}_2^{+}$
• Higher-order corrections to the spin-orbit and spin-spin tensor interactions in HD${}^{+}$
• Spin-orbit interaction in the HD${}^{+}$ ion