Ring Vortices for Positronium Formation in Positron-Hydrogen Collisions in the Ore Gap

Using the inverse Kohn variational method, we determine K-matrices, the Ps-formation scattering amplitude $f_{\rm Ps}$, and the corresponding differential cross section (DCS) for positron-hydrogen collisions in the Ore gap (6.8 to 10.2 eV) [1]. We also determine the velocity field associated with $f_{\rm Ps}$ [1]. There are two zeros in $f_{\rm Ps}$ and the Ps-formation DCS for when these quantities are functions of the magnitude of the momentum of the incident positron, ${\bf k}$, and the scattering angle of the outgoing Ps. Associated with each zero in $f_{\rm Ps}$, there is a ring vortex. By making a linear expansion of $f_{\rm Ps}$ about the vicinity of a zero, we determine for each zero the expectation value of the $y$-component of the angular momentum, $\langle L_y \rangle$, over a small area (circle or square) in the vicinity of the zero, where the $z$-axis is the direction of ${\bf k}$ and the $x$-axis is in the plane of ${\bf k}$ and the momentum of the outgoing Ps. \vskip 0.2truecm \noindent [1] A.~W.~Alrowaily, S.~J.~Ward, P.~Van Reeth, in preparation.