Energy difference between the (ν=0,R=1) and the (ν=0,R=3) states ofH2, measured with interseries microwave spectroscopy ofH2Rydberg states

We measure several transitions between specific Rydberg levels in the nearly degenerate (ν=0, R=1) n=28 and (ν=0, R=3) n=16 Rydberg manifolds of ${\mathrm{H}}_2$ with microwave spectroscopy. These measurements can be combined with calculations of the Rydberg fine structure to deduce the energy difference between the two states of the free ${\mathrm{H}}_2$ core. The result, E(ν=0, R=3)-E(ν=0, R=1)=288.859 00(8) ${\mathrm{cm}}^{\mathrm{-}1}$, represents the most precise determination to date of any spectral property of the hydrogen molecular ion, to our knowledge.