Electron exchange model potential: Application to positronium-helium scattering

Abstract

The formulation of a suitable nonlocal model potential for electron exchange is presented, checked with electron-hydrogen and electron-helium scattering, and applied to the study of elastic and inelastic scattering and ionization of orthopositronium ͑Ps͒ by helium. The elastic scattering and the nϭ2 excitations of Ps are investigated using a three-Ps-state close-coupling approximation. The higher (nу3) excitations and ionization of Ps atoms are treated in the framework of the Born approximation with present exchange. Calculations are reported of phase shifts and elastic, Ps excitation, and total cross sections. The present target elastic total cross section agrees well with experimental results at thermal to medium energies.

Effect of H-ion formation on positronium-hydrogen elastic scattering

“…In the last few years, we are addressing Ps scattering problems by using a model regularized exchange-correlation potential (non-local) [21] in the exact coupled LippmannSchwinger equation [17,18,19,20,21,22,23,24,25,26]. In these calculations, con- in the results and discussions).…”

“…Their roles are yet to be investigated for the scattering of positronium (Ps) atoman exotic bound state of electron and positron with singlet and triplet spins. This seems to be very important since, despite a long history of theoretical studies [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26], we are yet to produce converged scattering results in the ab initio coupled-channel (CC) framework, even for the simplest Ps-H system [10].…”

“…However, exchange constitutes only a part of the continuum and Ps exhibits a strong polarizability of 36a 3 0 , which is expected to make it vulnerable to continuum effects and charge transfer processes. Continuum effect can be simulated through pseudostates of Ps and target, group [12,13,14] and the São Paulo group [17,18,19,20,21,22,23,24,25,26]. While the Belfast and Calcutta groups use complete ab initio coupled-channel (CC) formalism, the São Paulo group indulges to model exchange correlation potentials (to enhance the correlation and continuum effects) in the ab initio CC formalism.…”

“…The exact form for B d ν ′ µ ′ ,νµ , is available in the literature [9,21] but here we follow the sign convention for the Ps-wave function as used in [18]. For B e , we consider both the exact form (Appendix I) as well as the regularized form [21] with appropriate sign convention [18].…”

“…Any elaborate wave function containing the r 12 term would certainly enhance the electron-electron correlation further. We estimate the effect of this charge-transfer recombination channel in the ab initio CC framework by taking exchange exactly and also by using the regularized model exchange [21] in the CC equations.…”