Threshold Vibrational Excitation of ${\mathrm{C}\mathrm{O}}_2$ by Slow Electrons

Threshold structures, reminiscent of those seen in the polar hydrogen halides, have recently been observed in the cross sections for electron impact excitation of certain vibrational levels of the nonpolar ${\mathrm{C}\mathrm{O}}_2$ molecule. These structures occur at energies outside the range where shape resonances dominate the dynamics. We propose a virtual state model that describes the multidimensional nuclear dynamics during the collision and explains quantitatively the selectivity observed in the excitation of the Fermi dyad, as well as the pattern of threshold peaks and oscillations seen in the upper levels of the higher polyads.

Figure 1

Cuts through the potential surfaces of ${\mathrm{C}\mathrm{O}}_2$ and ${\mathrm{C}\mathrm{O}}_2^{-}$ where the O-C-O angle $\Theta$, in degrees, is varied and the C-O bond distance is fixed at 2.2 bohrs. In the crossing region, around ${\Theta }_o$, the difference between the curves follows a threshold law predicted by the dipole moment of ${\mathrm{C}\mathrm{O}}_2$. This law allows us to analytically continue the ${\mathrm{C}\mathrm{O}}_2^{-}$ potential into configurations where it is unbound, denoted by dashed curves, and construct a complete surface for the ${\mathrm{C}\mathrm{O}}_2^{-}$ virtual state.

Figure 2

Excitation cross sections for the Fermi polyads in ${\mathrm{C}\mathrm{O}}_2$. Solid lines: theory; dashed lines: experiment (Refs. 5, 6). Top panel: dyad; bottom panel: triad, tetrad, and pentad.

Figure 3

Contour plots of the wave functions for the two components of the Fermi dyad in O-C-O angle, in degrees, and C-O bond distance, in bohrs. The thick line marks the seam where the anion and neutral surfaces cross. The imaginary part of the anion surface is zero above the seam and increases proportionately in regions indicated by the shading. Top panel: upper member of dyad; bottom panel: lower member of dyad.