Leading-order relativistic and radiative corrections to the rovibrational spectrum ofH2+andHD+molecular ions

Abstract

High-precision variational calculations for the rovibrational states in the range of the total orbital momentum $L=0--4$ and vibrational quantum number $v=0--4$ for the $\mathrm{H}_{2}{}^{+}$ and $\mathrm{H}{\mathrm{D}}^{+}$ molecular ions are presented. Relativistic and radiative corrections of orders ${R}_{\ensuremath{\infty}}{\ensuremath{\alpha}}^{2}$, ${R}_{\ensuremath{\infty}}{\ensuremath{\alpha}}^{2}(m∕M)$, ${R}_{\ensuremath{\infty}}{\ensuremath{\alpha}}^{3}$, ${R}_{\ensuremath{\infty}}{\ensuremath{\alpha}}^{3}(m∕M)$, and, partially, ${R}_{\ensuremath{\infty}}{\ensuremath{\alpha}}^{4}$ are taken into consideration as well as the finite size structure of proton and deuteron. It is found that the relative theoretical uncertainty due to uncalculated contributions of orders ${R}_{\ensuremath{\infty}}{\ensuremath{\alpha}}^{4}$ and higher to the reference transition frequency interval $(L=0,v=0)\ensuremath{\rightarrow}(0,1)$ is about $1\phantom{\rule{0.3em}{0ex}}\mathrm{ppb}$.