Double Resonance Spectroscopy of the $D {}^1 \Pi_u^+$ and $B''\bar{B}^1\Sigma^+_u$ States Near the Third Dissociation Threshold of H$_2$

Double-resonance laser spectroscopy via the $E,F {\,}^1 \Sigma_g^+, v'=6, J'$ state was used to probe the energy region below the third dissociation limit of molecular hydrogen. Resonantly-enhanced multi-photon ionization spectra were recorded by detecting ion production as a function of energy using a time of flight mass spectrometer. Energies and line widths for the $v = 14 - 17$ levels of the $D{}^1 \Pi_u^+$ state of H$_2$ are reported and compared to experimental data obtained by using VUV synchrotron light excitation and fully ab initio non-adiabatic calculations of $D {}^1 \Pi_u^+$ state energies and line widths. Several high vibrational levels of the $B''\bar{B\,}^1\Sigma^+_u$ state were also observed in this region. Term energies and rotational constants for the $ v=67-69$ vibrational levels are reported and compared to highly accurate ro-vibrational energy level predictions from fully ab initio non-adiabatic calculations of the first six ${}^1 \Sigma_u^+$ levels of H$_2$. While additional observed transitions can be assigned to other other states, several unassigned features in the spectra highlight the need for a fully integrated theoretical treatment of dissociation and ionization in this energy region.