The positron-hydrogen system at low energies

Abstract

Calculations of lowenergy positron-hydrogen and positroniumproton scattering using the close coupling method are reported at eErgkk belowthe ionization threshold. The chanAelspace ir&uded six hydrogen (Is. 2s. 2p, 3s. 3p and 3d) and six positronium (Is, 2s. 2p, 3s. 4s and 3p) states. Comparisons with more accurate calculations demonstrate that this model should give integrated cross sections accurate to 10%. Cross sections are computed with a fine energy mesh and a total of 11 resonances associated with the H(n = 2) and Ps(n = 2) thresholds have been identified and the resonance positions and widths determined.Calculalions of the total cross section and the positronium formation cross section for positronhydrogen scattering are consistent with the available experimental data. Cross sections for elastic scattering in the Ps(ls)-p entrance channel are dominated by a strong polaridion potential and vary from 1000 ro; at threshold to 15 at 1.0 Ryd. Cross sections for the Ps(ls) + p + e+ + H(nl) rean'angement collision are also reporred since these provide baseline data relevant to exp"ments aimed at making antihydrogen atoms. Differential ccoss sections for elastic Ps(ls)-p and e+-H(ls) scattering and for electron transfer to the hydrogen atom ground state are also reported at selected energies.

Positron-Hydrogen Scattering, Annihilation, and Positronium Formation

“…We also compare the present phase shifts with those obtained by Schwartz (1961) [14] obtained by using the Kohn variational principle, Houston and Drachman (1971) [18], by using the Harris method, Kohn variational calculation of Humberston and Wallace (1972) [19], and Gien (1997) [20], by using the Harris-Nesbet method in Table 2. The 21-state close-coupling approximation phase shifts obtained by Mitroy and Ratnavelu (1995) [21][22][23] are lower than the present results. [21][22][23] has reported a large basis close-coupling calculation of scattering at low energies.…”

“…The 21-state close-coupling approximation phase shifts obtained by Mitroy and Ratnavelu (1995) [21][22][23] are lower than the present results. [21][22][23] has reported a large basis close-coupling calculation of scattering at low energies. The phase shifts of these calculations are lower than the present results given in Table 2.…”

Formation of antihydrogen by the charge-transfer reaction

“…One of the most promising methods that has been suggested for producing antihydrogen [5 -7] is to use the charge-exchange process computing the integral cross section from the positronium ground state, differential cross sections were also computed [11]so that the recoil conditions appropriate to the collision could also be determined. Another very recent calculation was the hyperspherical close-coupling calculation of Igarashi, Toshima, and Shirai [12].The cross sections from this model are expected to be of similar accuracy to those of Mitroy and Ratnavelu [11]for the ground state.…”

“…It was found that the charge-transfer cross section should peak around 14~ao for incident positronium energies of 5 -10 eV. A more accurate calculation using a mixed physical and pseudostate basis was recently carried out [11] in the energy region below the ionization threshold. Besides is larger than the cross section from the positronium ground state.…”

“…The relative size of this correction was largest for Ps(m =4) initial states and smallest for the Ps(ls) initial state. The actual procedure used to estimate the cross section for these higher Rydberg levels was obtained from the cross section to the [9] and twelve-state (4) [11]close-coupling calculations, and the hyperspherical calculation (~) [12]. [18,19], and with the hyperspherical cross sections [12], would indicate that the cross section at the maximum is probably accurate to about 50%.…”