Many-body theory of positron binding in polyatomic molecules.

Positrons bind to molecules leading to vibrational excitation and spectacularly enhanced annihilation. Whilst positron binding energies have been measured via resonant annihilation spectra for $\sim$ 80 molecules in the past two decades, an accurate \emph{ab initio} theoretical description has remained elusive. Of the molecules studied experimentally, calculations exist for only 6, and for these, standard quantum chemistry approaches have proved severely deficient, agreeing with experiment to at best 25\% accuracy for polar molecules, and failing to predict binding in non-polar molecules. The theoretical difficulty lies in the need to accurately account for positron-molecule correlations including polarisation of the electron cloud, screening of the positron-molecule Coulomb interaction by molecular electrons, and the unique non-perturbative process of virtual-Ps formation (where a molecular electron temporarily tunnels to the positron). Their roles in positron-molecule binding have yet to be elucidated. Here, we develop a diagrammatic many-body description of positron-molecule interactions that takes account of the correlations, applying it to calculate positron binding energies for the molecules for which both theory and experimental results exist. Delineating the effects of the correlations, we find that, in particular, virtual-Ps formation dramatically enhances binding in organic polar molecules, and can be essential to support binding in non-polar molecules. Overall, we find the best agreement with experiment to date (in some cases to within $\sim$5-10\% percent). The approach can be extended to provide predictive calculations of positron scattering and annihilation $\gamma$ spectra in molecules and condensed matter. Such capability is required to, e.g., develop antimatter-based technologies including positron traps, beams and ...