Nuclear dynamics in resonant electron-molecule scattering beyond the local approximation: The 2.3-eV shape resonance inN2

Resonant electron scattering from the ${\mathrm{N}}_2$ molecule is treated within the framework of Feshbach's projection-operator formalism. The problem of nuclear motion in the complex, nonlocal, and energy-dependent potential of the resonance state is solved with the use of basis-set expansion methods. The width function $\Gamma \mathrm{}(E,R)\mathrm{}$ of the 2.3-eV shape resonance is taken from previous ab initio calculations A. U. Hazi, T. N. Rescigno, and M. Kurilla, [Phys. Rev. A 23, 1089 (1981)]. The potential-energy curve $V_1\mathrm{}\left(R\right)\mathrm{}$ of the discrete electronic state giving rise to the resonance is adjusted to obtain quantitative agreement with experiment for the $v=0\mathrm{}\to 1$ vibrational excitation channel. Calculated cross sections are reported for many vibrational excitation channels including scattering from vibrationally excited target molecules and are compared with experiment. The results are in good agreement with experiment as far as experimental data are available. The information on the 2.3-eV shape resonance in ${\mathrm{N}}_2$ obtained in this way (potential-energy curve, width function, complex pole of the $S$ matrix, phase shift, etc.) is discussed and compared to the results of other ab initio and empirical calculations. Particular emphasis is laid on the assessment of the accuracy of the local complex potential approximation (boomerang model). It is shown that the local approximation is excellent for the 2.3-eV resonance in ${\mathrm{N}}_2$ as far as the calculation of vibrationally inelastic cross sections is concerned. The local complex potential emerging from the present study differs significantly from the potential obtained empirically by Dubé and Herzenberg [Phys. Rev. A 20 194 (1979)], although the calculated cross sections are virtually identical for a large number of channels. We discuss the precision with which a local complex potential can be defined.