Close-coupling approach to a model problem for resonant collisions of electrons with diatomic molecules

In the theoretical study of electron-molecule collisions, resonant processes such as vibrational excitation and dissociative electron attachment and recombination are difficult to model due to the breakdown of common techniques such as the adiabatic-nuclei approximation. For this reason, it is useful to have an exactly solvable model so that the validity of different theories can be tested, such as the two-dimensional model introduced by Houfek et al. [Phys. Rev. A 73, 032721 (2006)] and extended to charged targets by Hvizdo\ifmmode \check{s}\else \v{s}\fi{} et al. [Phys. Rev. A 97, 022704 (2018)]. We have applied the convergent close-coupling method, a well-established approach for solving a variety of scattering problems, to this two-dimensional model problem. Dissociative attachment and recombination are treated within the same formalism, and the direct and resonant contributions to vibrational excitation are both fully accounted for as a result of solving the close-coupling equations. To accurately model these processes at all energies, the two-center approach is used, in which the states of the dissociated fragments are explicitly included in the expansion of the wave function of the scattering system. Cross sections for vibrational excitation, dissociative attachment, and direct dissociation are calculated for NO-like and ${\mathrm{F}}_{2}$-like targets, and excellent agreement is found with existing results. Cross sections for vibrational excitation and dissociative recombination are calculated for a ${\mathrm{H}}_{2}^{+}$-like target, and despite challenges with modeling the many resonances of the cross section, we find reasonably good agreement with existing results.