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 f Ps and corresponding deep minima in the Ps-formation differential cross section, and we determine their positions accurately. Due to azimuthal symmetry, each zero in f Ps is part of separate circular rings of zeros for an azimuthal angle range of zero to 2π. We study the velocity field associated with f Ps 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 f Ps , and that it rotates in opposite directions around the two zeros in f Ps . Previously, vortices in the velocity field associated with the transition matrix element have provided an explanation for deep minima in differential cross sections for direct ionization. With the introduction of the extended velocity field, our work shows that vortices can occur also for charge exchange.

Differential positronium-formation cross sections for Ne, Ar, Kr, and Xe

“…Whether the low energy features in Fig. 3 for targets with much greater nuclear charges are related to these phenomena is an open question; however we note that recent elaborate variational calculations for positronium formation in e + + H collisions have established that vortices can indeed occur also for charge exchange [36].…”

Deep Minimum and a Vortex for Positronium Formation in Low-Energy Positron-Helium Collisions

“…The absolute near-forward direction Ps-formation DCS has recently been measured for positron collisions from helium for an incident positron energy E i of 24.7 eV to 138 eV [4,6]. In this paper, we report a zero in f Ps for positron-helium collisions just above the Ps-formation threshold, a corresponding deep minimum in the logarithm of the Ps-formation DCS, a vortex in v ext that is associated with f Ps , and also a minimum in the forward direction Ps-formation DCS [8,9]. We use the complex Kohn variational method to compute two-channel K-matrices for s-, p-, dand f -wave positron-helium collisions in the Ore gap for a fine grid in k, where k is the magnitude of the momentum of the incoming positron k. We optimize the non-linear parameters in the short-range part of the trial wave function in the vicinity of the zero in f Ps to obtain accurate K-matrices in this region.…”

“…Positronium (Ps) formation, a rearrangement process for positron collisions, is of interest in both theoretical and experimental studies [1][2][3][4][5][6]. Recently, we obtained two zeros in the Ps-formation scattering amplitude, f Ps , for positron-hydrogen collisions in the Ore gap [7]. We used the Kohn and inverse Kohn variational methods to compute the two-channel K-matrices, and from these we computed f Ps , the Ps-formation differential cross section (DCS) and the extended velocity field v ext that is associated with f Ps .…”

“…We used the Kohn and inverse Kohn variational methods to compute the two-channel K-matrices, and from these we computed f Ps , the Ps-formation differential cross section (DCS) and the extended velocity field v ext that is associated with f Ps . (The extended velocity field is defined in reference [7].) Corresponding to the zeros in f Ps , there are deep minima in the logarithm of the Ps-formation DCS and vortices in v ext that are associated with f Ps [7].…”

“…(The extended velocity field is defined in reference [7].) Corresponding to the zeros in f Ps , there are deep minima in the logarithm of the Ps-formation DCS and vortices in v ext that are associated with f Ps [7].…”