Scattering problems with nondecaying sources: Two-Photon ionization as a benchmark

A.I. GOMEZ, G. GASANEO, D.M. MITNIK, M.J. AMBROSIO, AND L.U. ANCARANI

Bordeaux

Congreso; Colloque commun de la division de Physique Atomique et Moleculaire et Optique de la SFP et des Journees de Spectroscopie Moleculaires PAMO{JSM; 2016

La Societe Francaise d'Optique

single or multiple ionization of atoms and molecules by two or more successive photons (see, e.g., [1]).Indeed, theoretical and numerical difficulties occur when a spatially non-decaying driven term appearsin the Schr¨odinger-like non-homogeneous equation for the scattering wave function. The simplest ofsuch situations is the two-photon double ionization of Helium. Although this process has been studiedextensively during the last decade, both theoretically [2] and experimentally [3], large discrepancies arestill observed. Two major theoretical challenges are the imposition of adequate asymptotic conditions,and how to extract the ionization amplitude from the calculated scattering wave function.Before addressing the full Helium problem within a Generalized Sturmian Functions (GSF) approach[4], we study here the two-photon ionization of Hydrogen that presents the main characteristicswe want to emphasize. This benchmark case [5] allows us to understand how the methodology works.The treatment of the second order equation is distinct due to the fact that its driven term does not vanishfor large distances r, as can be seen on Fig. 1(a). This non-vanishing behavior enforces on the secondorder scattering wave function a ?beat? type asymptotic behavior, as shown in Fig. 1(b). Within the methodologywe propose, a suitable set of GSFs can be easily constructed possessing, at large distances,precisely the correct ?beat? behavior (see Fig. 1(c)).