Two?photon ionization as a benchmark for scattering problems with nondecaying sources

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

Frankfurt

Conferencia; 12th European Conference on Atoms Molecules and Photons; 2016

The description with traditional methods of single or multiple ionization of atoms and molecules by two ormore successive photons requires some special treatment (see, e.g., [1]). Difficulties occur when a spatially nondecayingdriven term appears in the Schrodinger-like non-homogeneous equation for the scattering wave function. ¨The simplest of such situations is the non-sequential two-photon double ionization of Helium which has beenstudied extensively during the last decade, both theoretically [2] and experimentally [3]. Nevertheless, there arestill large discrepancies between the different theoretical approaches, and with experimental data; as such, theprocess is not considered as fully understood. Two major theoretical difficulties are the imposition of adequateasymptotic conditions and how to extract the ionization amplitude from the solution.Before addressing the full Helium problem within a Generalized Sturmian Functions (GSF) approach [4,5],we study here the two-photon ionization of Hydrogen that presents the main characteristics we want to emphasize.This benchmark case allows us to understand how the methodology [6] works and to delve into some of thenumerical aspects of the general method we propose to address, i.e., the multiphoton double ionization problemin two?electron atoms. The GSF used to solve the first and second order equations are constructed possessingappropriate asymptotic conditions (outgoing Coulomb behavior). The treatment of the second order equation isparticular due to the fact that its driven term does not vanish for large distances r, as can be seen on Fig. 1(a). Thisnon-vanishing behavior enforces on the second order scattering wave function a ?beat? type asymptotic behavior,as shown in Fig. 1(b). Within the methodology we propose, a suitable set of GSFs can be easily constructedpossessing, at large distances, exactly that ?beat? behavior (see Fig. 1(c)).Fig. 1 For an Hydrogen atom interacting with a monochrome laser, we plot as a function of the emitted electron distance r: (a)the second order driven term; (b) the second order scattering wavefunction; (c) a suitable set of Generalized Sturmian Functions.When solving the second order equation using this adequate basis set, convergence is naturally increased.Moreover, in contrast to other approaches, our methodology provides a practical way to extract the ionizationamplitude directly from the asymptotic behavior of the scattering wave function, not as a matrix element, that isto say without the need for any ad hoc approach. We also briefly illustrate how similar situations are encountered,for example, in the multiphoton double ionization of helium.References[1] D.A. Horner, F. Morales, T.N. Rescigno, F. Mart´ın and W. McCurdy, Two-photon double ionization of helium above and below the thresholdfor sequential ionization, Phys. Rev. A, 76, 030701(R) (2007).[2] L.Malegat et al., A novel estimate of the two-photon double-ionization cross section of helium, J. Phys. B, 45, 175601 (2012).[3] Sh.A. Abdel-Naby et al., Nuclear-recoil differential cross sections for the two-photon double ionizatio of helium, Phys. Rev. A 87, 063425(2013).[4] G. Gasaneo, L.U. Ancarani, D.M. Mitnik, J.M. Randazzo, A.L. Frapiccini and F.D. Colavecchia, Three-Body Coulomb Problems withGeneralized Sturmian Functions, Adv. Quantum Chem. 67, 153 (2013).[5] D.M. Mitnik, F.D. Colavecchia, G. Gasaneo and J.M. Randazzo, Computational methods for Generalized Sturmians basis, Comp. Phys.Comm. 45, 1145 (2011).[6] A.I. Gomez, G. Gasaneo, D.M. Mitnik, M.J. Ambrosio and L.U. Ancarani, ´ submitted