Variational ab initio $R$-matrix theory is combined with generalized multichannel quantum defect theory, implemented in spheroidal coordinates, to calculate clamped-nuclei ${}^1\Sigma _g^{+}$, ${}^1\prod _g$, and ${}^1\Delta _g^{+}$ electron-ion scattering phase shift matrices for ${\mathrm{H}}_2$. The calculations cover the bound state region below $\mathrm{H}_2{}^{+}1{\sigma }_g$, the resonance region between $\mathrm{H}_2{}^{+}1{\sigma }_g$ and $\mathrm{H}_2{}^{+}1{\sigma }_u$, and they extend beyond the $\mathrm{H}_2{}^{+}1{\sigma }_u$ threshold. They span the range of internuclear distances $1⩽R⩽5\mathrm{a.u.}$ The use of spheroidal instead of spherical coordinates allows a restricted partial wave expansion to be used, thus yielding a compact set of interaction parameters pertaining to the electron-ion scattering dynamics in ${\mathrm{H}}_2$. The accuracy of our fixed-nuclei quantum defects is generally of the order of about 0.02. At the same time the quantum defect matrices obtained here exhibit a smooth behavior across the ionization thresholds and their elements also vary rather smoothly with internuclear distance. These results represent a step toward the goal of constructing a unfied theoretical description of ionization and dissociation fragmentation dynamics of ${\mathrm{H}}_2$.

• Received 12 January 2004

DOI:https://doi.org/10.1103/PhysRevA.70.012713