Eur. Phys. J. D 57, 187-196 (2010)
https://doi.org/10.1140/epjd/e2010-00028-5

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

¹ Institute of Theoretical Physics, V Holešovičkách 2, 180 00 Prague, Czech Republic
² J. Heyrovský Institute of Physical Chemistry of the ASCR, v. v. i., Dolejškova 3, 182 23 Prague, Czech Republic

Corresponding author: miroslav.sulc@jh-inst.cas.cz

Received: 25 November 2009
Revised: 15 January 2010
Published online: 16 February 2010

Abstract

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 Cs₂ or ⁴He₂ dimer ground state interaction). As demonstrated on these particular cases, our approach turns out to be very accurate in comparison with other computational methods.