Projection-operator calculations for molecular shape resonances: TheΣu+2resonance in electron-hydrogen scattering

A complete scattering-theoretic description of the ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{+}{}_{}{}^{}$ shape resonance in fixed-nuclei electron-${\mathrm{H}}_2$ scattering is given within the framework of the projection-operator formalism of Feshbach. Polarization and correlation effects are included via the many-body optical-potential approach using the two-particle-hole Tamm-Dancoff approximation. The calculations result in a well-defined and physically meaningful separation of the T matrix and the eigenphase sum into a smooth background term and a resonant term, which varies rapidly with energy and internuclear distance. T matrices, eigenphase sums, and Feshbach resonance parameters ${\epsilon }_d$, Γ(E), and Δ(E) are obtained for a range of internuclear distances extending from the equilibrium distance of ${\mathrm{H}}_2$ to 2.75 a.u. These fixed-nuclei data provide the basis for the ab initio calculation of cross sections for vibrational excitation and dissociative attachment in ${\mathrm{H}}_2$ beyond the local-complex-potential approximation, to be reported in a forthcoming paper.