Nonlocal resonance model for two nuclear degrees of freedom

A nonlocal resonance model (NRM) [W. Domcke, Phys. Rep. 208, 97 (1991)] is a commonly used method of calculating cross sections for elastic and inelastic processes in resonant electron-molecule collisions. Up to now, there has been a great number of studies devoted to implement this approach for molecules with only one nuclear degree of freedom (e.g. N$_2$, H$_2$, HCl etc) In the present work we developed a generalization of the NRM for two degrees of freedom. For testing purposes we have constructed two dimensional model, which captures essential features of resonant collisions of electrons with the CO2 molecule. Final cross sections for few chosen vibrational excitations are being compared with results obtained via a local complex potential approximation, which is so far the only approach dealing with multidimensional phenomena [C.W. McCurdy et al, Phys. Rev. A 67, 042708 (2003)]. We also discuss difficulties arising, when one chooses to work in a time dependent or a time independent formalism.