Near threshold vibrational excitation of molecules by positron impact: A projection operator approach

We report vibrational excitation (ν_i=0→ν_f=1) cross-sections for positron scattering by H₂ and model calculations for the (ν_i=0→ν_f=1) excitation of the C-C symmetric stretch mode of C₂H₂. The Feshbach projection operator formalism was employed to vibrationally resolve the fixed-nuclei phase shifts obtained with the Schwinger multichannel method. The near threshold behavior of H₂ and C₂H₂ significantly differ in the sense that no low lying singularity (either virtual or bound state) was found for the former, while a e⁺-acetylene virtual state was found at the equilibrium geometry (this virtual state becomes a bound state upon stretching the molecule). For C₂H₂, we also performed model calculations comparing excitation cross-sections arising from virtual (-iκ₀) and bound (+iκ₀) states symmetrically located around the origin of the complex momentum plane (i.e. having the same κ₀). The virtual state is seen to significantly couple to vibrations, and similar cross-sections were obtained for shallow bound and virtual states.