Abstract
Nuclear-spin-symmetry conservation makes the observation of transitions between quantum states of ortho- and para-H$_2$ extremely challenging. Consequently, the energy-level structure of H$_2$ derived from experiment consists of two disjoint sets of level energies, one for para-H$_2$ and the other for ortho-H$_2$. We use a new measurement of the ionization energy of para-H$_2$ [$E_I$(H$_2$)$/hc = 124417.491098(31)$ cm$^{-1}$ to determine the energy separation [118.486770(50) cm$^{-1}$] between the ground states of para- and ortho-H$_2$ and thus link the energy-level structure of the two nuclear-spin isomers of this fundamental molecule. Comparison with recent theoretical results [M. Puchalski et al., Phys. Rev. Lett. 122, 103003 (2019)] enables the derivation of an upper bound of 1.5 MHz for a hypothetical global shift of the energy-level structure of ortho-H$_2$ with respect to that of para-H$_2$.