Abstract
We find a zero in the positronium formation scattering amplitude and a deep minimum in the logarithm of the corresponding differential cross section for positron–helium collisions for an energy just above the positronium formation threshold. Corresponding to the zero, there is a vortex in the extended velocity field that is associated with this amplitude when one treats both the magnitude of the momentum of the incident positron and the angle of the scattered positronium as independent variables. Using the complex Kohn variational method, we determine accurately two-channel K-matrices for positron–helium collisions in the Ore gap. We fit these K-matrices using both polynomials and the Watanabe and Greene’s multichannel effective range theory taking into account explicitly the polarization potential in the Ps-He+ channel. Using the fitted K-matrices we determine the extended velocity field and show that it rotates anticlockwise around the zero in the positronium formation scattering amplitude. We find that there is a valley in the logarithm of the positronium formation differential cross section that includes the deep minimum and also a minimum in the forward direction.
Highlights
Positronium (Ps) formation, a rearrangement process for positron collisions, is of interest in both theoretical and experimental studies [1,2,3,4,5,6]
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 vext 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 vext that are associated with f Ps [7]
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 vext that is associated with f Ps, and a minimum in the forward direction Ps-formation DCS [8,9]
Summary
Positronium (Ps) formation, a rearrangement process for positron collisions, is of interest in both theoretical and experimental studies [1,2,3,4,5,6]. We use the complex Kohn variational method to compute two-channel K-matrices for s-, p-, d- and 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. Ps-formation angular distribution as a function of the angle of the outgoing Ps for three different incident energies of Ps. The paper by Shipman et al [4] shows experimental data of the Ps-formation DCS for positron–helium collisions as a function of Ei with results from theoretical calculations for the forward direction, including those from using the (inverse) Kohn variational method. In Appendix B, we discuss some numerical investigations that we performed and the WG MERT and polynomial fits
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