Solution of the proton-hydrogen scattering problem using a quantum-mechanical two-center convergent close-coupling method

Abstract

Details of the recently developed quantum-mechanical two-center convergent close-coupling approach (Abdurakhmanov et al 2016 J. Phys. B: At. Mol. Phys. 49 03LT01) to proton-hydrogen scattering are presented. The formulation is based on the exact (fully quantum-mechanical) three-body Schrödinger equation. The total scattering wavefunction is expanded using a two-center pseudostate basis. This allows one to include all underlying processes, namely, direct scattering and ionization, electron capture into bound and continuum states of the projectile. The off-shell integration in the coupled-channel Lippmann–Schwinger integral equations emerging from the three-body Schrödinger equation for the scattering wavefunction is taken analytically which greatly reduces computational effort. While the calculated electron capture cross sections are in a good agreement with experiment, some discrepancy exists for the ionization cross sections.

Proton impact on ground and excited states of atomic hydrogen

“…Theoretical results from the aforementioned studies [2,4,8,9] are shown alongside the present results. For H(1s) collisions the included results from [17] are from calculations based on the quantum-mechanical convergent close-coupling (QM-CCC) method, which is viewed as an exact treatment of the quantum-mechanical threebody Schrödinger equation. It is noteworthy that the AOCC-GTO calculation in [10] considered all 2p m initial states, but the reported cross sections are averaged over the m substates, and thus, not appropriate to compare with the results shown in the present figure. Comparisons of the present TC-BGM capture cross sections for H(2p) collisions, when averaged across the m states, agree with the AOCC-GTO calculation within 2% or better.…”

“…Experiment: Shah1981 [18]; Shah1987 [19]; and Shah1998 [20]. Theory: QM-CCC [17]; WP-CCC [9]; AOCC-GTO [10]; and present TC-BGM.…”

“…In figure 4, several sets of ionization cross sections for H(n = 1) and H(n = 2) collisions are compared with the present TC-BGM results. The sets include experimental measurements by Shah and co-workers [18][19][20] along with theoretical data from QM-CCC [17], WP-CCC [9], and AOCC-GTO [10] approaches. Additional results based on a scaling model are also presented for comparison in order to help understand some of the discrepancies shown in the present results.…”

“…Among all the cross sections that were compared, discrepancies with those approaches are mainly evident in the ionization results. Considering that these discrepancies are of some concern, the results produced by the TC-BGM should be viewed as a notable achievement since fewer pseudostates are needed to reach a similar level of accuracy compared to the convergent close-coupling approaches [5,9,17] which uses a significantly larger basis.…”

Recent progress in the description of positron scattering from atoms using the convergent close-coupling theory

“…A proper formulation of Ps-formation processes requires a combined basis consisting of two independent basis sets for each of the centres which makes theoretical studies considerably more challenging than for electronscattering. Furthermore, the positron-atom system is an ideal prototype of the ubiquitous collision systems such as proton-atom scattering, where charge-exchange processes also require a two-centre treatment, see Abdurakhmanov et al [41] for example.…”