Time-dependent close-coupling calculations of positronium formation in positron-hydrogen collisions

Abstract

Positronium-formation cross sections from positron-hydrogen collisions are calculated by solving a set of close-coupled, time-dependent partial differential equations. These cross sections are determined by propagating a time-evolving wave packet on a two-dimensional radial lattice and then projecting the wave function onto the stationary states of the atom. Calculations are performed through Lϭ8 and are extrapolated for Lу9 at energies of 30, 40, and 50 eV. Using distorted-wave calculations to determine ionization cross sections at these higher energies, we are able to extract approximate positronium-formation cross sections from the transfer ionization cross sections. Comparisons are made with experiment.

The time-dependent close-coupling method for atomic and molecular collision processes

“…The TDCC method was used to calculate total cross sections for positron-impact transfer ionization of the hydrogen atom in its ground state [35]. The TDCC results were found to be in good agreement with standard close-coupling [36,37] calculations.…”

A computational scheme for the non-stationary treatment of two-electron processes

“…In the papers by Robicheaux (1996, 1998), Pindzola et al (1997), Robicheaux et al (1997), Plante and Pindzola (1998) the system was discretized on a uniform mesh. We make a substitution of the variables r = x 2 , and then discretize x uniformly.…”

“…In the last two years, a very promising non-stationary approach has been developed for the consideration of different processes with two interacting electrons in a central (in particular, Coulomb) field (Pindzola and Schulz 1996, Pindzola and Robicheaux 1996, 1998, Plante and Pindzola 1998. The well known universal advantage of the non-stationary methods is that they do not need any information on the boundary conditions and therefore are completely self-sufficient.…”

“…In the papers by Robicheaux (1996, 1998), Pindzola et al (1997), Robicheaux et al (1997), Plante and Pindzola (1998) the 'staggered leapfrog' algorithm with a uniform mesh has been used. This algorithm is not explicitly unitary and the accuracy of the calculations performed with a uniform mesh is not rather high.…”

Quantum dynamics of positron-hydrogen scattering and three-body bound state formation with an assisting laser field: predictions of a reduced-dimensionality model

“…Similar to the standard close-coupling methods, the time-dependent close-coupling (TDCC) method has been developed to follow the dynamic time-evolution of the system and extract scattering amplitudes from the final system wave function [28]. To our knowledge, the first successful application of the TDCC method to positron-hydrogen collisions was performed by Plante and Pindzola [29], where good agreement with experimental measurements and time-independent theoretical calculations was obtained. The later TDCC works of Yamanaka and Kino [30,31] have explicitly extracted Ps formation and direct positron annihilation cross sections in positron-hydrogen collisions.…”