Ab-Initio Sturmian method for three-body quantum mechanical problems: Scattering states and ionizing collisions

A.L. FRAPICCINI, J.M. RANDAZZO, G.GASANEO, F.D. COLAVECCHIA, D.M. MITNIK, AND L.U. ANCARANI

Valparaiso

Conferencia; V Encuentro Sud Americano de Colisiones Inelasticas en la Materia; 2010

Universidad Tecnica Federico Santa Maria

In this work we present the general theory to compute scattering states with a novel ab initio method based on generalized Sturmians. These functions are solutions of aradial Schrödinger equation where the magnitude of a generating potential is assumed as the eigenvalue, while the energy is a parameter of the calculation. These Sturmians are versatile enough to include almost any arbitrary (atomic) asymptotic conditions in the radial electron coordinates, such as the outgoing flux conditions for Coulomb potentials which are the adequate ones for atomic collisions. The full three body Schrödinger equation is solved with a Configuration Interaction expansion of the wave function in these generalized Sturmians. The basis set is used to expand the scattering portion of the total wave function, which evolves from a separable state composed by a plane wave and the ground hydrogen state. By means of the Galerkin method, a linear system of equations is obtained for the expansion´s coefficients. We show that the scattering wave function has the appropriate outgoing behaviour in the radial hyperspherical coordinate. Single differential cross section for the simple problem of atomic ionization by electronic impact in the S-wave model is presented. Our results of the cross sections at 55 and 54.4 eV incident energy present an excellent agreement compared to Exterior Complex Scaling results and Time Dependent calculations from M. S. Pindzola and F. Robicheaux.