Efficient solution of scattering equations by combination of R-matrix and Lanczos methods

We propose a fast and economical computational method for solving scattering Lippmann-Schwinger integral equation. Our approach benefits from the accurate construction of the Green's function based on the R-matrix theory combined with the Schwinger-Lanczos variational principle. No principal restrictions on the form of the potential are assumed. Theoretical description of our method in the first part of this paper is then followed by numerical examples. In particular we demonstrate how to adapt our method for computation of partial wave phase-shifts in the case of electron-hydrogen atom scattering. Then we also investigate the properties of a family of long-range potentials (emerging e.g. in the theoretical description of the Cs-2 or He-4(2) dimer ground state interaction). As demonstrated on these particular cases, our approach turns out to be very accurate in comparison with other computational methods.