A benchmark calculation for resonant electron - hydrogen elastic scattering at low energies

Abstract

Two independent calculations have been carried out to obtain accurate differential cross sections (DCS) and spin asymmetries for the elastic scattering of electrons from ground-state hydrogen over the energies of the lowest and resonances. They use the IERM method and the direct numerical approach of Wang and Callaway. The effects of the ionization continuum on DCS, resonant positions, and spin asymmetries are re-examined in light of the present calculations. The calculated elastic DCS are compared with the experiments of Williams and the calculation of McCarthy and Shang. A benchmark calculation for the phaseshifts has been tabulated to assist future experimental normalization procedures.

Potential splitting approach to e–H and e–He+scattering

“…We have numerically demonstrated that terms corresponding to non-factorisable part Ψ R 1 of the distorted incoming wave (15) decrease with increase in R. While these terms do not vanish as fast as for the Temkin-Poet model, they still can be neglected for moderate values of R and Q. When comparing our numerical results with previously published results [19,[21][22][23] we find that the relative differences are less than 10 −3 . We can thus state that our potential splitting method allows us to obtain numerically exact solutions for the threebody scattering problem with a Coulomb interaction.…”

“…The oscillation character of this cross section at small energies is also the Coulomb effect. We compared our calculated values with other results [19,21,22], and with the accurate data for electron-hydrogen elastic scattering in the vicinity of resonance states [23]. The relative difference is found to be less than -10 3 .…”

“…Due to this interaction the cross section also exhibits oscillating behaviour at small energies. The calculated values were compared to other results [19,21,22], and to the accurate data for electron-hydrogen elastic scattering in the vicinity of resonance states [23]. The relative difference is found to be less than 10 −3 .…”

“…Furthermore, the scattering amplitudes are calculated from the non-rotated spatial part of the solutions, i.e. r 1 , r 2 ≤ Q, with representations (23,25). This means that the asymptotic behavior ( 24) is used so Q should be chosen large enough for this behavior to be valid.…”

Differential cross sections in electron - hydrogen scattering at energies lying between then= 3 andn= 4 thresholds

“…As we did not include the ionization continuum, the 15-state R-matrix calculation is not expected to give accurate quantitative results. However, we have enough evidence to show that the 15-state R-matrix calculation will give qualitatively correct resonance profiles for the differential cross section (DCS) (see Fon et al 1994, 1995a, Odgers et al 1995, Wang et al 1996, Williams 1988 at energies up to the n = 5 threshold (13.06 eV). We are guided by the empirical convergence rule (Burke et al 1966(Burke et al , 1967 which states that close-coupling calculations for e − -atom scattering at electron energies below the ionization threshold in which physical states with increasing principal quantum number n are used, yield correct qualitative excitation cross sections in the energy up to the highest threshold explicitly included.…”