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

We report vibrational excitation (νi=0→νf=1) cross-sections for positron scattering by H2 and model calculations for the (νi=0→νf=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.