Positron - hydrogen and positronium - proton scattering at intermediate and high energies

Abstract

Abstract. Positron scattering from atomic hydrogen is studied at energies ranging from 4 to 100 Ryd using the close-coupling approach and cross sections from both the e + -H and Psp entrance channels are reported in a basis comprising 1s, 2s and 2p states of the hydrogen and positronium atoms. Comparative studies with widely used approximation methods such as the first Born, unitarized Born and second Born approximations are presented. With the exception of elastic scattering for the Ps(1s)-p entrance channel, it was found that on-shell approximations such as the first Born and the unitarized Born approximations are reasonably accurate for collisions not involving particle transfer provided the energy is sufficiently high. Rearrangement collisions on the other hand are dominated by off-the-energy-shell scattering and the accurate approximation at high energies is the second Born approximation. Further, the effects of positronium channels on the direct reactions are investigated and we conclude that the positronium formation channels can be omitted for energies greater than 20 Ryd. Elastic scattering in the Ps(1s)-p entrance channel is seen to be unique, the high-energy behaviour of the phase shifts is different from any other quantum system.

Continuum effects on positron scattering of atomic hydrogen at intermediate energies

“…These measurements show conflicting trends at E < 100 eV. Mitroy (1996) show better agreement with the UCL data over the whole energy range. Nevertheless, there are some disconcerting differences between the CC(30, 3) and CC(28, 3) models for the energy range between 35 and 80 eV.…”

“…Theoretical studies of positron-hydrogen scattering in the intermediate-energy regime is a challenging endeavour as it would imply a lot of discrete states and the continuum must be incorporated in a practical manner. Ratnavelu et al (1996) had used a simple six-state close-coupling calculation that used three H states (1s, 2s, 2p) and three Ps states (1s, 2s, 2p) to study positron scattering from atomic hydrogen at intermediate energies of 4-100 Ryd. It provided a comprehensive and realistic study of the scattering process but nevertheless incomplete, as higher discrete states and the continuum were neglected.…”

“…It provided a comprehensive and realistic study of the scattering process but nevertheless incomplete, as higher discrete states and the continuum were neglected. Recently, Kernoghan et al (1996) and Mitroy (1996) have used a large L 2 basis of hydrogen states (30 and 28 states, respectively) together with the Ps(1s), Ps(2s) and Ps(2p) states to study positron scattering by atomic H at intermediate energies. Although they have been performed in momentum space (Mitroy 1996) and in coordinate space (Kernoghan et al 1996), both methods should be equivalent.…”

Positron scattering from atomic sodium

“…The splitting of the cross section in this manner has implications about the application of the '1/n 3 rule'. Since the first Born cross sections are known to scale as 1/n 3 (Guha and Mandal 1980), recent positron scattering calculations (Kernoghan 1996b, McAlinden et al 1996, Mitroy 1996 have estimated the positronium cross sections into levels omitted from the channel space by assuming the cross sections scale as 1/n 3 . The validity of this procedure is certainly called into question by the present results.…”

“…Second, procedures have been developed to compute the previously intractable rearrangement matrix element connecting the positronatom channels with the positronium channels. These improvements have resulted in recent calculations that have covered almost all aspects of the positron-hydrogen system (Igarashi and Toshima 1994, Kernoghan et al 1995, 1996b, Mitroy 1995a, b, 1996, Mitroy and Stelbovics 1994, Ratnavelu et al 1996, Kuang and Gien 1997.…”