Deep minima and vortices for positronium formation in low-energy positron-hydrogen collisions

Abstract

Using the two-channel Kohn and inverse Kohn variational methods, we investigate ground-state positronium (Ps) formation in positron-hydrogen collisions in the Ore gap. We find two zeros in the Ps-formation scattering amplitude fPs and corresponding deep minima in the Ps-formation differential cross section (DCS), and we determine their positions accurately. Due to azimuthal symmetry, each zero in fPs is part of separate circular rings of zeros for an azimuthal angle range of zero to 2π. We study the velocity field associated with fPs in which we treat the magnitude of the momentum of the incident positron and the angle of the outgoing positronium as variables, and we refer to this velocity field as the extended velocity field. We show that it has two vortices that are connected with the zeros in fPs, and that it rotates in opposite directions around the two zeros in fPs. Previously, vortices in the velocity field associated with the transition matrix element have provided an explanation for deep minima in DCSs for direct ionization. With the introduction of the extended velocity field, our work shows that vortices can occur also for charge exchange.