Vibrational excitation in N2 O via the 2.3-eV shape resonance

The vibrational excitation of ${\mathrm{N}}_{2}$O by electrons in the energy range 1-4 eV has been studied with a crossed-beam apparatus using an energy resolution of 22 meV and an observation angle of 40\ifmmode^\circ\else\textdegree\fi{}. The scattering in the middle of this energy range is dominated by the $^{2}\ensuremath{\Sigma}^{+}$ shape resonance which contributes to the excitation of about 20 vibrational modes. The vibrational modes belong to four series, namely, the $n00$, $n10$, $n01$, and $n02$ series with the quantum number $n$ ranging from 0 to 7. The energy dependence of the differential vibrational cross sections is bell shaped and exhibits no fine structure. At the center of the $^{2}\ensuremath{\Sigma}^{+}$ resonance (2.3 eV), the $n00$ series is most intensely excited and has a cross section of (9.6 \ifmmode\pm\else\textpm\fi{} 3.5) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}18}$ ${\mathrm{cm}}^{2}$/sr for $n=1$ and an exponentially decreasing magnitude for successively higher $n$. A similar trend of the branching ratio has also been observed in the $n01$ series. The present experiment combined with a calculation of Dub\'e and Herzenberg demonstrates that the impulse picture which was originally proposed for the case of vibrational and rotational excitation in ${\mathrm{H}}_{2}$, is applicable to this triatomic molecule as well. The width $\ensuremath{\Gamma}$ for the $^{2}\ensuremath{\Sigma}^{+}$ shape resonance of ${\mathrm{N}}_{2}$O has been found to be 0.7 eV in the center of the Franck-Condon region, and it decreases for larger internuclear separations.