High resolution calculation of low energy scattering in $e^-e^+\bar{p}$ and $e^+e^-\mbox{He}^{++}$ systems via Faddeev-Merkuriev equations

Abstract

The potential splitting approach incorporated into the framework of Faddeev-Merkuriev equations in the differential form is used for calculations of multichannel scattering in $e^-e^+\bar{p}$ and $e^+e^-\mbox{He}^{++}$ systems. Detailed calculations of all possible S-wave cross-sections are performed %in systems $e^+e^-\bar{p}$ and $e^+e^-\mbox{He}^{++}$ in the low-energy region which supports up to seven open channels including the rearrangement channels of ground and excited states of antihydrogen, positronium and helium ion formations. All known sharp resonances of the systems obtained and approved by a number of authors are clearly reproduced in the calculated cross sections. In cross sections for energies above the threshold corresponding to $n=2$ state of antihydrogen the prominent oscillations of Gailitis Damburg type have been found.