Comparison of positronium, positron and electron collisions with hydrogen at low velocities

Abstract

Recent experimental findings indicate that at equal velocity electron and ortho-positronium scattering cross sections are similar over a wide range of velocities and targets where both elastic and inelastic processes can take place. We present a comparative study of positronium, positron and electron elastic scattering from atomic hydrogen in order to investigate if a similar behaviour occurs for this target at low velocities where inelastic channels are closed. We calculate elastic cross sections for the three projectiles using Kohn-type variational methods which allows us to make a detailed study of the differences and similarities. We find a qualitative similarity in the spin-weighted elastic integrated cross sections for positronium and electron scattering and a good agreement between the singlet integrated cross sections. However, this agreement does extend to the low velocity region and where the agreement is found in the integrated cross sections we show that it is not present in the individual partial waves cross sections. Interestingly, given the agreement we find in the singlet integrated cross section for electron and positronium scattering, when comparing the overall shapes of the corresponding singlet differential cross sections we find different angular and velocity dependencies.

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

“…The present calculations for the K-matrices extend the variational calculations of Humberston et al [30] for the s-, p-and d−waves to higher partial waves. An error in the d-wave calculation of [30] had recently been corrected as reported in Woods et al [38] and Van Reeth et al [42]. We calculate the f -wave K-matrix elements using sets of short-range terms in the trial wave function with the three units of angular momentum on either the positron or the electron and a set in which one unit is associated with the electron and two with the positron [29,30,37,43].…”

Special issue on antihydrogen and positronium

“…The exchange interaction between the ein Ps and those in the atoms and molecules it collides with have been found [73,74] to be at the root of observed similarities between eand Ps scattering cross sections [75,76], and Van Reeth et al [77] and Gribakin et al [78] both address this topic here. Van Reeth and coworkers use a Kohn variational technique to study at low energies (equivalent to speeds below 1 a.u.)…”

Confined variational calculation of positronium-hydrogen scattering below the positronium excitation threshold

“…The effect of the short-range mixed-symmetry terms has been investigated by Van Reeth and Humberston in their study of e − -H scattering, and it has been found to be more important for the singlet than for the triplet D-wave phase shifts [25,50]. On the other hand, through a comparison between the CVM and cKohn results in Table III, one can see that the short-range mixed-symmetry terms are more important for the triplet than for the singlet.…”