Nuclear dynamics in resonant electron-molecule scattering beyond the local approximation: Vibrational excitation and dissociative attachment inH2andD2

Vibrational excitation and dissociative electron attachment via the ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{+}{}_{}{}^{}$ shape resonance in ${\mathrm{H}}_2$ is treated within the framework of Feshbach’s projection-operator formalism. The problem of nuclear motion in the complex, energy-dependent, and nonlocal potential of the ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{+}{}_{}{}^{}$ resonance is solved with the use of a separable expansion of the nonlocal potential. The resonance energy, width function, and level-shift function, which characterize the resonance in the fixed-nuclei limit, are taken from recent ab initio calculations based on the many-body optical-potential approach [M. Berman, C. Mündel, and W. Domcke, Phys. Rev. A 31, 641 (1985)]. Integral cross sections for vibrational excitation of ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ up to v=4 and for dissociative electron attachment to ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ molecules in the vibrational levels v=0, 1, and 2 have been calculated. The calculations provide a good overall description of the experimental data for both ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$. Pronounced isotope effects and a strong dependence of the attachment cross section on the vibrational state of the target molecule are found, in qualitative agreement with experimental observations. The accuracy of two widely used approximations, the adiabatic-nuclei approximation and the local-complex-potential model, is quantitatively assessed for this prototype resonance. While the off-shell adiabatic-nuclei approximation provides a qualitatively satisfactory description of vibrational excitation, we observe a stunning failure of the local-complex-potential model. Empirical local complex potentials, fitted to reproduce experimental vibrational excitation and dissociative attachment data in ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ within the local-potential model, lack any physical meaning.