Can the exterior complex scaling method be applied to pure Coulomb potentials?

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

Dublin

Conferencia; International Symposium on (e,2e), Double Photo-Ionization & Related Topics & 16th International Symposium on Polarization & Correlation in electronic & Atomic Collisions; 2011

Institute of Physics - Atomic and Molecular Interactions Group

where the interaction between the particles takes place.To test numerically the proposed Sturmian-hyperspherical approach we make use of ananalytically solvable model for three particles break up processes [2], as was done, e.g.,within the exterior complex scaling method [3]. In our fragmentation/ionization model,the scattering process is represented by a non-homogeneous Coulomb Schrodinger equationwhere the driven term is given by a Yukawa-like -dependent interaction multiplied by theproduct of a continuum wave function and a bound state in the particles coordinates r1 andr2. The scattering function     +sc is the solution of the following driven equation:[T 􀀀Z 􀀀 E]    +sc = 􀀀W    0; (1)where T is the kinetic energy, and W is the left-out interaction. Closed forms in hypersphericalcoordinates are derived for the solution with outgoing wave behavior and for thescattering transition amplitude. They compare very well with numerical results validatingthe use of the proposed Sturmian hyperspherical approach. Moreover, as all the Sturmianbasis functions possess the correct outgoing Coulombic asymptotic behavior and diagonalizenot only the kinetic energy but also the Coulomb interaction 􀀀Z=, the convergence rate isstrongly accelerated: only a few SF are necessary to reproduce the analytical solutions forboth the scattering wave function and the transition amplitude.References[1] G. Gasaneo et al, J. Phys. Chem. A 113? 14573 (2009).[2] G. Gasaneo, L.U. Ancarani and D. M. Mitnik (to be submitted)[3] C. W. McCurdy and T. N. Rescigno, Phys. Rev. A 56, R4369 (1997)