Quantum-Defect Theory of ExcitedΠu1−Levels ofH2

Quantum-defect methods are used to calculate, by a single unified procedure, the full spectrum of $J=1\mathrm{}$ ${{}_{}{}^1{}_{}{}^{}\Pi _{\mathrm{u}}^{}{}_{}{}^{}}^{-}$ Rydberg levels of ${\mathrm{H}}_2$, extending from the lowest levels of the $2p{\pi }^{-}$ $C{{}_{}{}^1{}_{}{}^{}\Pi _{\mathrm{u}}^{}{}_{}{}^{}}^{-}$ state to the high members of the $\mathrm{np}{\pi }^{-}$ series between the ${{\mathrm{H}}_2}^{+}\mathrm{}(v=0\mathrm{})\mathrm{}$ and ${{\mathrm{H}}_2}^{+}\mathrm{}(v=1\mathrm{})\mathrm{}$ ionization thresholds. Results for the $C$ state are substantially improved over previous calculations based on direct integration of the vibrational Schrödinger equation, while results at higher energies reproduce with high accuracy the recently observed spectrum, including local perturbations.