Molecular size effects on diffraction resonances in positronium formation from fullerenes

We previously predicted [P.A. Hervieux et al., Phys. Rev. A \textbf{95}, 020701 (2017)] that owing to predominant electron capture by incoming positrons from the molecular shell, C$_{60}$ acts like a spherical diffractor inducing resonances in the positronium (Ps) formation as a function of the positron impact energy. By extending the study for a larger C$_{240}$ fullerene target, we now demonstrate that the diffraction resonances compactify in energy in analogy with the shrinking fringe separation for larger slit size in classical single-slit experiment. The result brings further impetus for conducting Ps spectroscopic experiments with fullerene targets, including target- and/or captured-level differential measurements. The ground states of the fullerenes are modeled in a spherical jellium frame of the local density approximation (LDA) method with the exchange-correlation functional based on the van Leeuween and Baerends (LB94) model potential, while the positron impact and Ps formation are treated in the continuum distorted-wave final state (CDW-FS) approximation.