Near-threshold vibrational excitation ofH2by positron impact: A projection-operator approach

Abstract

We report vibrational excitation $({\ensuremath{\nu}}_{i}=0\ensuremath{\rightarrow}{\ensuremath{\nu}}_{f}=1)$ and total cross sections for positron scattering by ${\mathrm{H}}_{2}$. 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 the vibrational excitation cross section is in good agreement with available experimental data [Sullivan et al., Phys. Rev. Lett. 86, 1494 (2001)]. Though our fixed-nuclei calculations do not indicate the existence of a ${e}^{+}$-${\mathrm{H}}_{2}$ virtual state, a proper description of the $T$ matrix threshold behavior is essential (the adiabatic approximation is inadequate). The projection operator approach has long been a powerful tool for studies of nuclear dynamics in electron-molecule collisions, and its application to positron scattering is timely since couplings to nuclear degrees of freedom are known to be very important at low impact energies.