High-precision spectroscopy of hydrogen molecular ions

In this paper, we overview recent advances in high-precision structure calculations of the hydrogen molecular ions (H₂⁺ and HD⁺), including nonrelativistic energy eigenvalues and relativistic and quantum electrodynamic corrections. In combination with high-precision measurements, it is feasible to precisely determine a molecular-based value of the proton-to-electron mass ratio. An experimental scheme is presented for measuring the rovibrational transition frequency (v,L):(0,0)→(6,1) in HD⁺, which is currently underway at the Wuhan Institute of Physics and Mathematics.