Merkuriev Cut-off in e+ − H Multichannel Scattering Calculations

Abstract

We present the results of positron-Hydrogen multichannel scattering calculations performed on the base of Faddeev-Merkuriev equations. We discuss an optimal choice of the Merkuriev's Coulomb splitting parameters. Splitting the Coulomb potential in two-body configuration space is applicable for a limited energy range. Splitting the potential in three-body configuration space makes it possible to perform calculations in a broader range of energies and to optimize the numerical convergence. Scattering cross sections for zero total angular momentum for all processes between the positronium formation threshold and the third excitation threshold of the Hydrogen atom are reported.

Solving the Faddeev-Merkuriev Equations in Total Orbital Momentum Representation via Spline Collocation and Tensor Product Preconditioning

“…The parameters x 0α , y 0α and ν α > 2 can in principle be chosen arbitrarily, but their choice changes the properties of components ψ α that are important from both theoretical and computational points of view [31]. In the papers [33,34] we have discussed the choice of the cut-off function and have presented some practical algorithm of how to choose its parameters efficiently. In the bound state calculations the splitting can be omitted, that is one can take V [33].…”

Solving the Faddeev-Merkuriev equations in total orbital momentum representation via spline collocation and tensor product preconditioning

“…The parameters x 0α , y 0α and ν α > 2 can in principle be chosen arbitrarily, but their choice changes the properties of components ψ α that are important from both theoretical and computational points of view [28]. In the papers [30,31] we have discussed the choice of the cut-off function and have presented some practical algorithm of how to choose its parameters efficiently. In the bound state calculations the splitting can be omitted, that is one can take V (s) α = V α and V (l) α = 0.…”

High resolution calculations of low energy scattering in e−e+p¯ and e+e−He++ systems via Faddeev–Merkuriev equations

“…= si n ,n 0 0 sin (ϑ (y α , p n )) + co n ,n 0 0 cos (ϑ (y α , p n )) (24) and using extrapolation. We obtain N ch solutions ψ α…”

“…Typically, splitting of the Coulomb potentials is done by an artificial functional parameter in the three-body configuration space, the Merkuriev cut-off function. Recently, we showed in [24], that the splitting procedure can be made simpler and easier for implementing into FM equations. In this contribution we give practical advices for the choice of the cut-off function in the form of a smoothed Heaviside step function in the two-body configuration space, thus minimising the number of free parameters of the splitting procedure.…”