Use of generalized hyperspherical Sturmian functions for a three?body break?up model problem

D. M. MITNIK, G. GASANEO AND L. U. ANCARANI

JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS

IOP PUBLISHING LTD

Lugar: Londres; Año: 2012

0953-4075

An hyperspherical Sturmian approach recently developed for three?body break?up processes is tested through an analytically solvable S?wave model. The scattering process is represented by a non-homogeneous Schr¨odinger equation in which the driven term is given by a Coulomb-like interaction multiplied by the product of a continuum wave function and a bound state in the particles coordinates. The model contains most of the difficulties encountered in real three?body scattering problem, e.g., non-separability in the electrons? spherical coordinates and Coulombic asymptotic behavior, and thus provides an interesting benchmark for numerical methods. Since the Sturmian basis functions are constructed as to include the correct asymptotic behavior, a very fast convergence of the scattering wave function is observed. Excellent agreement is found with the analytical results for the associated transition amplitude. This agreement is also found at very low energies, a region where the calculation is generally challenging since it requires the evaluation of the transition amplitudes at huge distances. Our method allows this kind of calculations without increasing significantly the computational requirements.