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

Abstract

An approach based on splitting the reaction potential into a finite range part and a long range tail part to describe few-body scattering in the case of a Coulombic interaction is proposed. The solution to the Schrödinger equation for the long range tail of the reaction potential is used as an incoming wave. This reformulation of the scattering problem into an inhomogeneous Schrödinger equation with asymptotic outgoing waves makes it suitable for solving with the exterior complex scaling technique. The validity of the approach is analyzed from a formal point of view and demonstrated numerically, where the calculations are performed with the finite element method. The method of splitting the potential in this way is illustrated with calculations of the electron scattering on the hydrogen atom and the positive helium ion in energy regions where resonances appear.

Potential Splitting Approach for Atomic and Molecular Systems

“…The terms [A R 1 ] n, andà n, correspond to the functions Ψ R 1 and Φ = Φ 0 + Φ 1 , respectively. Projecting the representation (5) on the two body wave functions, the local representation for the partial amplitudesà n, can be derived [6]:…”

“…In several recent studies, we have reported a method which is capable to treat correctly the Coulomb scattering problem using exterior complex scaling [3][4][5][6]. The key point of this method is splitting the long-range Coulomb potential into the core and tail parts.…”

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

“…Even though the basic mathematical model for such a broad spectrum of physical systems is the Schrödinger equation, the diversity of model interactions and particular physical states leads to a variety of employed computational methods [12][13][14][15][16][17][18][19][20][21][22][23][24][25]. Thus, our ability to perform direct model-free calculations for such wide range of systems is of utmost importance for many branches of physics.…”

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

“…Even though the basic mathematical model for such a broad spectrum of physical systems is the Schrödinger equation, the diversity of model interactions and particular physical states leads to a variety of employed computational methods [12,13,14,15,16,17,18,19,20,21,22,23,24,25]. Thus, our ability to perform direct model-free calculations for such wide range of systems is of utmost importance for many branches of physics.…”