Low-energy positron–hydrogen molecule scattering

Abstract

The method of Hara using two centre formalism has been employed to investigate positron-hydrogen molecule scattering at low incident energies. Two model potentials have been used to see the importance of the choice of effective potential. It has been found that the total cross sections are sensitive to the details of the effect~ve potential. The present results are in qualitative agreement with measured values and other existing theoret~cal predictions.On a employe la mCthode de Hara utilisant un formalisme a deux centres pour ttudier la diffusion des positrons par I'hydrogene molCculaire, aux Cnergies d'incidence faibles. Deux potentiels modkles ont ete utilists, pour voir l'importance du choix de potentiel effectif. On a trouvC que les sections efficaces totales sont sens~bles aux ditails du potentiel effectif. Les resultats obtenus sont qualitativement en accord avec les valeurs mesurCes et les autres prkdictions thioriques existantes.[Traduit par le journal]Can. J. Phys.. 60. 597 (1982) Introduction Recently interests have been focused on positron-molecule scattering. Repeated measurements by different groups ( 1 -6), have given impetus to theoretical workers. The experimental situation has been reviewed recently by Griffith (7) and Ghosh et al. (8). Our knowledge of positron-molecule scattering is not satisfactory. The complexity of the problem forces theoretical workers to resort to certain approximations that may not be applicable to the case of positron-atom scattering. The fixed nuclei approximation enjoys the confidence of theoreticians for investigating the problem. By using this approximation, Hara (9) has investigated this problem, employing the two centre formalism. He has introduced the prolate spheroidal coordinates and has taken the 2 axis along the direction of the molecular axis. In his calculations, he has included the static, quadrupole tail of the static and the complete adiabatic polarization potential. He has also performed the calculations using only the dipole part of the polarization potential. The dramatic difference between the results obtained by using two different potentials suggests that the results depend on the details of the potential used. The results for the total cross sections are in fair agreement with the corresponding measured values below 6 eV. However, the position and magnitude of the maximum value of the cross sections are different from those of the experimental data.The York University group have performed a series of calculations (10-12). They have treated the problem in one centre formalism and used spherical polar coordinates. The results of Baille et al. (12) differ appreciably from those of Hara. This difference arises from the choice of their model potentials. A recent study by Darewych et al. ( 13) regarding the use of one and two

Polarisation potentials for positron-molecule collisions: positron-H2scattering

“…However, there is some indication of such a structure (at about 3.8 eV) in the results of Charlton et a1 (1980,1983). The theoretical cross sections of Lodge et al (1971), Baille et a1 (1974), Hara (1974) and Sur and Ghosh (1982), all of which were based on electron-H2 polarisation potentials, exhibit a minimum in the total cross section, although the energy at which this minimum occurs and the rapidity of the decrease of U,,, with increasing energy differ significantly among these results.…”

“…In a large number of positron-molecule studies the cut-off radius is taken without modification from scattering calculations on the corresponding electron-molecule system (Hara 1972, Bhattacharyya and Ghosh 1975, Sur and Ghosh 1982. In such calculations, no account is taken in the polarisation potential of the sign of q. Alternatively, the cut-off radius can be specified in some reasonable but ad hoc fashion; for example, Jain and Thompson ( 1983d) recently reported calculations of positron-CH4 collisions in which r, is chosen equal to the molecular bond length.…”

“…For example, the a b initio electron-H2 polarisation potential of Lane and Henry (1968)-in which the non-penetrating approximation (0 2.1.3(ii)) was implemented for the full adiabatic polarisation potential-has been used without alteration in positron-H2 calculations by Lodge et al (1971), Baille et al (1974), Bhattacharyya and Ghosh (1975), Pande and Singh (1978) and Sur and Ghosh (1982). The analogous electron-H2 potential of Hara (1 969)-which further implements the dipole approximation (9 2.1.2(ii))-has been used by Darewych et a1 (1974).…”