Bethe logarithm for the H2+ and HD+ molecular ions

摘要

The Bethe logarithm is calculated for the lowest rotational-vibrational states of H2n+ and HD+ hydrogennmolecular ions in awide range of vibrational (v = 0–4) and total orbital momentum (L = 0–4) quantum numbers.nNumerical results with eight to nine significant digits are obtained for all the states within this range. This allows usnto reduce an error in the leading-order radiative contribution, which results eventually in the relative uncertainty ofnrovibrational frequency intervals at a level lower than 10−11. This high precision is important for the rovibrationalnspectroscopy experiments of hydrogen molecular ions aiming to determine the electron-to-proton mass ratio.