Eur. Phys. J. D (2016) 70: 207
https://doi.org/10.1140/epjd/e2016-70259-5

Regular Article

Benchmark for two-photon ionization of atoms with generalized Sturmian functions

¹ Departamento de Física, Universidad Nacional del Sur, 8000 Bahía Blanca, Buenos Aires, Argentina
² Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Buenos Aires, Argentina
³ Instituto de Astronomía y Física del Espacio (IAFE) and Departamento de Física, Universidad de Buenos Aires, C1428 EGA Buenos Aires, Argentina
⁴ Théorie, Modélisation, Simulation, SRSMC, UMR CNRS 7565, Université de Lorraine, 57078 Metz, France

^a e-mail: aigmz.1985@gmail.com

Received: 12 April 2016
Received in final form: 22 June 2016
Published online: 18 October 2016

Abstract

The description with traditional methods of the single or multiple ionization of atoms and molecules by two or more successive photons requires some special treatment. Difficulties occur when a spatially non-decaying driven term appears in the Schrödinger-like non-homogeneous equation for the scattering wave function. We propose using the intrinsic physical and mathematical properties of generalized Sturmian functions to efficiently deal with the Dalgarno-Lewis second order equation. In contrast to other approaches, our methodology provides a practical way to extract the transition amplitude from the asymptotic behavior of the scattering wave function, and this without requiring any further projection onto some final approximate state. As an illustration, the hydrogen case is studied in details, for both pulsed and monochrome laser radiation fields. The successful comparison with analytical and time-dependent solutions provides a benchmark, and allows us to master the numerical aspects of the methodology. Appropriately chosen generalized Sturmian functions manage to easily reproduce the beat-type asymptotic behavior observed in the photoelectron wave function after absorption by the atom of two successive photons.