Variational calculations of s-wave positronium hydrogen scattering

Abstract

A detailed investigation is made of low energy positronium–hydrogen s-wave elastic scattering, using the Kohn variational method, with very flexible scattering wavefunctions including all inter-particle correlations. The singlet and triplet scattering lengths are calculated and found to be a+ = 4.311a 0 and a− = 2.126a 0 respectively. The phase shifts are believed to be within less than 0.5% of the exact values, and they are in good agreement with the results of previous calculations.

Detailed investigation of low-energy positronium-hydrogen scattering

“…Ps-H scattering is a fundamental four-body Coulomb process. The Kohn and inverse Kohn variational methods have previously been applied to Ps-H collisions by Van Reeth and Humberston [21,22], who computed 1,3 S and 1,3 P phase shifts. We extend their 1,3 S and 1,3 P variational calculations in multiple ways.…”

“…Another extension that we consider is to use the procedure by Todd [26] to systematically remove short-range terms that cause linear dependence. This enables us to compute the phase shifts with more short-range Hylleraas terms than the earlier Kohn and inverse Kohn variational calculations [21,22]. We add the asymptotic expansion of Drake and Yan [27,28] to improve the accuracy of matrix elements containing only short-range terms.…”

Higher-lying resonances in Ps-H scattering below thee+-H−threshold

“…2, we use the fitted δ in Eq. (11) to calculate the energy levels of the lowest eight members of the Rydberg series, including the ground state (in this case n = 1−δ) of positronium hydride [2]. The fitted energies are also shown in Table I.…”

“…Triply excited S-wave resonances in Ps-H scattering lying below the doubly excited 2s 2 1 S e state were calculated [10]. An investigation on nonresonance Ps-H scattering was also performed [11]. Recently, an effective potential approach was used by Di Rienzi and Drachman [12] to study higher-lying resonances in Ps-H scattering below the Ps − -H + threshold, and the resonance energies for the Rydberg series of S, P, and D symmetries were located.…”

A comparative study of target ionization between hydrogen and hydrogenic ion by positronium impact

“…Development of suitable mathematical tools is necessary for solving the many body Schrodinger equation that appears in this particular single ionization process. Various approximation models like close coupling [3][4][5], R-matrix theory [6,7], different variational methods [8][9][10] have been developed for solving the Ps-H elastic and inelastic scattering processes. From such investigations one can make a comparative study of the different theoretical models with relative merits and demerits and their agreements with the available experimental data.…”