J.M.: Computational methods for generalized Sturmians basis

The computational techniques needed to generate a two-body Generalized Sturmian basis are described. These basis are obtained as a solution of the Schrödinger equation, with two-point boundary conditions. This equation includes two central potentials: A general auxiliary potential and a short-range generating potential. The auxiliary potential is, in general, long-range and it determines the asymptotic behavior of all the basis elements. The short-range generating potential rules the dynamics of the inner region. The energy is considered a fixed parameter, while the eigenvalues are the generalized charges. Although the finite differences scheme leads to a generalized eigenvalue matrix system, it cannot be solved by standard computational linear algebra packages. Therefore, we developed computational routines to calculate the basis with high accuracy and low computational time. The precise charge eigenvalues with more than 12 significant figures along with the corresponding wave functions can be computed on a single processor within seconds

Double photoionization of helium: a generalized Sturmian approach

In this work we study the double photoionization of helium induced by low intensities laser fields in the regime where only one photon absorption occurs. The method proposed here is based on a Generalized Sturmian Functions (GSF) spectral approach which allows the imposition of outgoing boundary conditions for both ejected electrons. These, in turn, construct an hyperspherical flux characteristic of double continuum wave functions. We compare our calculated cross sections at 20 and 40 eV above threshold with absolute and relative measurements, and with other calculations. Our results definitively demonstrate the applicability of the GSF approach for dealing with break-up Coulomb problems

Beat structure in the solution of scattering problems with nondecaying sources

In this contribution we study mathematical properties of scattering solutions of Schrödinger-type equations with nondecaying, outgoing type, driven terms. We analyze in some details the two-body frame, where an analytical treatment is possible, and find how the scattering solution is expected to contain a beating type structure. The analytical formulation is first presented, and then fully and successfully confirmed with two numerical implementations: the Exterior Complex Scaling and the Generalized Sturmian Functions methods. Our results illustrate the underlying mathematical structure that can be found in, for example, the photoionization of atoms or molecules, in the case when several photons are absorbed or in second order calculations for a single photon absorption. A test case within the three-body frame is also presented, illustrating numerically the presence of beat structures in separately the single and double continuum channels

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

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

Double ionization of helium by proton impact: from intermediate to high momentum transfer

We study theoretically the double ionization of helium by 6 MeV proton impact. For such fast projectiles, when considering the projectile-target interaction to first order, the four-body Schrödinger equation reduces to solving a three-body driven equation. We solve it with a generalized Sturmian functions approach and, without evaluating a transition matrix element, we extract the transition amplitude directly from the asymptotic limit of the first order scattering solution. Fivefold differential cross sections (FDCS) are calculated for the double ionization process for a number of coplanar kinematical situations. We present a detailed theory-experiment comparison for intermediate momentum transfers (from 0.8 to 1.2 a.u. and from 1.4 to 2.0 a.u.). In spite of some experimental restrictions (energy and momentum ranges) and the low count rates, we found that our theoretical description provides a very satisfactory reproduction of the measured data on relative scale. We then explore how the binary, recoil and back-to-back structures change with increasing momentum transfers (0.853 to 1.656, to 3.0 a.u.). Within the impulsive regime, with a momentum transfer of 3.0 a.u., we also analyze the FDCS for different excess energies. Finally, in analogy to an experimentalist gathering electrons with different excess energies to obtain enough counts, we provide a collective FDCS prediction that hopefully will stimulate further measurements

Stopping cross sections of TiO2 for H and He ions

Stopping cross sections of TiO2 films were measured for H and He ions in the energy intervals 200–1500 keV and 250–3000 keV, respectively, using the Rutherford backscattering technique. Theoretical calculations were performed by means of two versions of the dielectric formalism and a non-linear model. Good agreement is found between the present experimental data and the theoretical results at intermediate and high energies, and also with the very limited experimental information available in the literature.We thank the financial support from the Spanish Ministerio de Economía y Competitividad (Projects FPA2009-14091-C02-01 and FIS2010-17225) and the European Regional Development Fund. This work was partially supported by the following Argentinian institutions: Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Agencia Nacional de Promoción Científica y Tecnológica (ANPCyT)