Scattering Problem and Resonances for Three-Body Coulomb Quantum Systems: Parallel Calculations

Abstract

Abstract. An approach to the solution of scattering and resonance problems based on splitting the potential into a finite range part and a long range tail part is proposed. The explicit solution to the Schrödinger equation for the long range tail Hamiltonian is used as an incoming wave. This reformulation of the scattering problem makes it suitable for treatment by the exterior complex scaling. The same technique is used to determine resonances of the system. Calculations are performed with the finite element method which allows efficient parallel computations. The approach is illustrated with calculations of the electron resonant scattering on the hydrogen and the helium ion.

Potential splitting approach to e–H and e–He+scattering

“…The numerical solution of the driven Schrödinger equation (29) is performed by the finite element method (FEM), which is described in details in [14]. The FEM grid used in the calculations resembles one of [12] for the coordinates r 1 and r 2 , and coincides with the grid in [20]. As we need the solution of (18) with the ECS radius ¢ > Q R, we first discuss the results for the calculations of the cross sections with different splitting R and ECS Q radii.…”