The theoretical treatment of low-energy e⁺-H₂scattering using the Kohn variational method

Abstract

We present calculations of et-H2 scattering below the positronium formation threshold at 8.63 eV for the Xi, X : , II, and II s mmetries using the generalized Kohn method. Mixing of the two lowest partial waves IS allowed for in the Xi, X : and IIu symmetries, using a two channel K-matrix. Comparisons with Kohn calculations of the lowest partial waves of these symmetries show that mixing of partial waves has a relatively small effect on the contributions to the total scattering cross section at the energies considered. The IT, calculation includes only the lowest partial wave. As well as separable short-range correlation functions, the trial functions used in these calculations include Hylleraas-type functions containing the positron-electron distance as a linear factor and functions appropriate for taking into account long-range polarization of the hydrogen molecule. The sum of the contributions to the total scattering cross section from these calculations accounts for experimental values up to incident energies of about 5-6 eV, the main contribution coming from the Z: symmetry below -2 eV and the IIu symmetry above -2 eV. This is a major step forward towards our aim of carrying out accurate calculations for e+-H, scattering up to the positronium formation threshold. Inclusion of the Hylleraastype functions, which take into account short-range interactions between the positron and target electrons, is of great importance in achieving the agreement with experiment. Comparisons are made with recent R-matrix calculations.

The lives and deaths of positrons in the interstellar medium

“…Due to the weakness of its cross section, this process cannot be investigated in the laboratory, and again one must rely on theoretical calculations. The work of Bhatia et al (1977) has not been corrected or updated by any later works, so we still use the rate they obtained for direct annihilation with H. For He and H 2 the method is similar, except that we calculated the cross section using estimates of the dependence of Z eff , the effective charge 2 , on the kinetic energy from Campeanu & Humberston (1977) and Armour et al (1990), respectively. The measured Z eff in H 2 at room temperature is ≈45% larger than the theoretical evaluation (CH2001).…”

Scattering of low- to intermediate-energy positrons from molecular hydrogen

“…On the theoretical side, very few calculations of the total cross sections for the scattering of positrons by molecular hydrogen have been done. In the low-energy regime (below the positronium formation threshold of 8.63 eV), calculations of positron scattering by H 2 were done by Danby and Tennyson [26] using the R-matrix method, by Armour et al [27] using the generalized Kohn method, and by Gibson [28] using the distributed positron model. Contributions to the total cross section from partial cross sections of different symmetries, each symmetry corresponding to an irreducible representation of the molecular point group, were included.…”

Polarisation potentials for positron-molecule scattering processes

“…As one can see, these results are comparable to ours above ~ 2 eV of collision energy but show a Ramsauer minimum which is in worse agreement with the experimental data; (ii) the calculations marked by T are in marked disagreement with experiments, although coming from a rather sophisticated treatment using the R-matrix approach [35] and employ a very detailed description of long range forces. It is interesting to note that, even more recently, calculations which employed the Schwinger multichannel method adapting it to positron scattering [36], found again rather bad agreement with the experiments over the whole energy range below the threshold of Ps formation; (iii) another interesting set of data is provided by those obtained by Armour and coworkers [37], who have employed the theoretical approach provided by the Kohn variational method and treated the energy range below the threshold of 8.63 eV. They computed the Sg +, Z, +, H, and //q symmetries and their total integral cross sections are shown on the top part of Fig.…”