2016 
Ambrosio, M. J., Mitnik, D. M., Dorn, A., Ancarani, L. U., & Gasaneo, G. (2016). Double ionization of helium by 2keV electrons in equal and unequalenergy configurations. Physical Review A, 93(3).


Ancarani, L. U., & Jouin, H. (2016). Efficient technique to evaluate the Lindhard dielectric function. Eur. Phys. J. Plus, 131(4), 1–6.


Zaytsev, A. S., Ancarani, L. U., & Zaytsev, S. A. (2016). Quasi Sturmian basis for the twoelecton continuum. The European Physical Journal Plus, 131(2).


2015 
Aleshin, M. S., Zaitsev, S. A., Gasaneo, G., & Ancarani, L. U. (2015). Quasi Sturmian Functions in Problems of a ThreeParticle Coulomb Continuum. Russian Physics Journal, 58(7), 941–951.


Ambrosio, M. J., Colavecchia, F. D., Gasaneo, G., Mitnik, D. M., & Ancarani, L. U. (2015). Double ionization of helium by fast electrons with the Generalized Sturmian Functions method. J. Phys. B: At. Mol. Opt. Phys., 48(5), 055204.
Résumé: The double ionization of helium by high energy electron impact is studied. The corresponding fourbody Schrödinger equation is transformed into a set of driven equations containing successive orders in the projectile–target interaction. The first order driven equation is solved with a generalized Sturmian functions approach. The transition amplitude, extracted from the asymptotic limit of the first order solution, is equivalent to the familiar first Born approximation. Fivefold differential cross sections are calculated for ( e , 3 e ) processes within the high incident energy and small momentum transfer regimes. The results are compared with other numerical methods, and with the only absolute experimental data available. Our cross sections agree in shape and magnitude with those of the convergent close coupling method for the (10+10) eV and (4+4) eV emission energies. To date this had not been achieved by any two different numerical schemes when solving the three–body continuum problem for the fast projectile ( e , 3 e ) process. Though agreement with the experimental data, in particular with respect to the magnitude, is not achieved, our findings partly clarify a long standing puzzle.


Ambrosio, M. J., Colavecchia, F. D., Mitnik, D. M., Gasaneo, G., & Ancarani, L. U. (2015). Generalized Sturmian Functions applied to double continuum problems. J. Phys.: Conf. Ser., 601(1), 012004.
Résumé: The Generalized Sturmian Functions method aims to deal with atomic physics problems. It has seen application to two and threebody problems, and its flexibility enables one to work with bound systems as well as with particles in the continuum. In the present contribution we analyze how the method expands the atomic double continuum in collision problems, using the double ionization of Helium by fast electrons as a showcase. We first test the robustness of the method in a particularly challenging situation, the zero energy case. We then present fully differential cross sections for a scattering problem which after 15 years of continued efforts has not been satisfactorily solved: the double ionization of Helium by electron impact in the fast projectile regime, as measured by the Orsay group.


Ambrosio, M. J., Mitnik, D. M., Ancarani, L. U., Gasaneo, G., & Gaggioli, E. L. (2015). Double ionization of helium by proton impact: A generalizedSturmian approach. Phys. Rev. A, 92(4), 042704.
Résumé: We present ab initio calculations for the double ionization of helium by fast proton impact, using the generalizedSturmianfunctions methodology and within a perturbative treatment of the projectiletarget interaction. The crosssection information is extracted from the asymptotic behavior of the numerical threebody function that describes the emission process. Our goal is to provide benchmark firstorder Born fully differential cross sections with which one may investigate the suitability of transition matrices calculated using approximate analytictype solutions for the double continuum (the choice of effective charges or effective momenta to partially account for the internal target interactions being, to some extent, arbitrary). We also provide fully differential cross sections for the lowejectionenergy regime, which is beyond the suitable range of such perturbative methods. We find, however, that the effective momentum approach allows one to get at least a rough characterization of the most dominant physical process involved. We also compare our calculations with the only available relative experimental set, showing an agreement in shape that can be well understood within the given momentum transfer regime.


Granados—Castro, C. M., Ancarani, L. U., Gasaneo, G., & Mitnik, D. M. (2015). Sturmian approach to single photoionization of many electron atoms and molecules. J. Phys.: Conf. Ser., 601(1), 012009.
Résumé: The application of generalized Sturmian functions to the study of single photoionization of different atomic and molecular systems is illustrated using model potentials. Sturmian functions have been used successfully to study single and double ionization by electron impact on He, while their implementation to molecular systems is still under development. The radial part of the scattering function is expanded in a generalized Sturmian basis. The solution of the resulting matrix problem provides the expansion coefficients. The latter yield directly the photoionization transition amplitude and thus the cross sections. Here we show our preliminary results for He and Ne atoms on one hand, and for CH4 and H2O molecules on the other.


Randazzo, J. M., & Ancarani, L. U. (2015). Modification of the quantum mechanical flux formula for electronhydrogen ionization through Bohm's velocity field. Phys. Rev. A, 92(6), 062706.
Résumé: For the single differential cross section (SDCS) for hydrogen ionization by electron impact (eH problem), we propose a correction to the flux formula given by R. Peterkop [Theory of Ionization of Atoms by Electron Impact (Colorado Associated University Press, Boulder, 1977)]. The modification is based on an alternative way of defining the kinetic energy fraction, using Bohm's definition of velocities instead of the usual asymptotic kinematical, or geometrical, approximation. It turns out that the solutiondependent, modified energy fraction is equally related to the components of the probability flux. Compared to what is usually observed, the correction yields a finite and wellbehaved SDCS value in the asymmetrical situation where one of the continuum electrons carries all the energy while the other has zero energy. We also discuss, within the Swave model of the e−H ionization process, the continuity of the SDCS derivative at the equal energy sharing point, a property not so clearly observed in published benchmark results obtained with integral and Smatrix formulas with unequal final states.


Randazzo, J. M., Mitnik, D., Gasaneo, G., Ancarani, L. U., & Colavecchia, F. D. (2015). Double photoionization of helium: a generalized Sturmian approach. Eur. Phys. J. D, 69(8), 1–10.
Résumé: 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 breakup Coulomb problems. Graphical abstract
MotsClés: Atomic and Molecular Collisions; Atomic, Molecular, Optical and Plasma Physics; Nonlinear Dynamics; Physical Chemistry; Quantum Information Technology, Spintronics; Quantum Physics; Spectroscopy/Spectrometry


2014 
Aleshin, M. S., Zaitsev, S. A., Gasaneo, G., & Ancarani, L. U. (2014). QuasiSturm Functions in Problems of the Continuous Spectrum. Russ Phys J, 57(7), 888–897.
Résumé: QuasiSturm (QS) functions are proposed as basis functions in a description of the states of the continuous spectrum of a quantum system. A representation of QS functions in closed analytical form is obtained. The advantages of the method are illustrated by an example of the twoparticle scattering problem.
MotsClés: Condensed Matter Physics; Coulomb Green’s function; elastic scattering; inhomogeneous Schrödinger equation; Jmatrix method; Nuclear Physics, Heavy Ions, Hadrons; Optics, Optoelectronics, Plasmonics and Optical Devices; Physics, general; Sturm basis; Theoretical, Mathematical and Computational Physics


Ambrosio, M. J., Ancarani, L. U., Mitnik, D. M., Colavecchia, F. D., & Gasaneo, G. (2014). A Generalized Sturmian Treatment of (e, 3e) Processes Described as a ThreeBody Coulomb Problem. FewBody Syst, 55(810), 825–829.
Résumé: The double ionization of helium by high energy electron impact is investigated. The pure fourbody Coulomb problem may be reduced to a threebody one in accordance with the use of the first Born approximation. Even within this frame, major unexplained discrepancies subsist between several theoretical descriptions, and with available absolute experimental data. In this contribution we discuss an alternative formulation which allows to tackle the problem with a different methodology, the generalized Sturmian approach. We discuss some issues associated to the convergence of the calculated cross sections.
MotsClés: Atomic, Molecular, Optical and Plasma Physics; Nuclear Physics, Heavy Ions, Hadrons; Particle and Nuclear Physics


Ancarani, L. U., & Rodriguez, K. V. (2014). Correlated expansions of n1S and n3S states for twoelectron atoms in exponential cosine screened potentials. Phys. Rev. A, 89(1), 012507.
Résumé: Two–electron atoms embedded in a plasma environment are studied with screened and exponential cosine screened Coulomb model potentials. Within a configuration interaction approach, and using parameter–free explicitly correlated basis functions, we have calculated the groundstate and first excitedstate energies (and other mean values) for H−, He, and Li+. We analyze their evolution with the screening parameter and provide simple fits, which allow for practical and rapid evaluations for example in plasma applications.


GranadosCastro, C. M., Ancarani, L. U., Gasaneo, G., & Mitnik, D. M. (2014). Sturmian Approach to Single Photoionization of CH4. FewBody Syst, 55(810), 1029–1032.
Résumé: Single photoionization cross sections for two different ground state orbitals of the molecule CH4 are presented. An angular averaged molecular model potential is used to represent the interaction of the ionized electrons, whose continuum wave functions are calculated within a generalized Sturmian functions approach.
MotsClés: Atomic, Molecular, Optical and Plasma Physics; Nuclear Physics, Heavy Ions, Hadrons; Particle and Nuclear Physics


Mitnik, D. M., Gasaneo, G., Ancarani, L. U., & Ambrosio, M. J. (2014). Collision problems treated with the Generalized Hyperspherical Sturmian method. J. Phys.: Conf. Ser., 488(1), 012049.
Résumé: An hyperspherical Sturmian approach recently developed for threebody breakup processes is presented. To test several of its features, the method is applied to two simplified models. Excellent agreement is found when compared with the results of an analytically solvable problem. For the TemkinPoet model of the double ionization of He by high energy electron impact, the present method is compared with the Spherical Sturmian approach, and again excellent agreement is found. Finally, a study of the channels appearing in the breakup threebody wave function is presented.


Punta, J. A. D., Ambrosio, M. J., Gasaneo, G., Zaytsev, S. A., & Ancarani, L. U. (2014). Nonhomogeneous solutions of a Coulomb Schrödinger equation as basis set for scattering problems. Journal of Mathematical Physics, 55(5), 052101.
Résumé: We introduce and study twobody Quasi Sturmian functions which are proposed as basis functions for applications in threebody scattering problems. They are solutions of a twobody nonhomogeneous Schrödinger equation. We present different analytic expressions, including asymptotic behaviors, for the pure Coulomb potential with a driven term involving either Slatertype or Laguerretype orbitals. The efficiency of Quasi Sturmian functions as basis set is numerically illustrated through a twobody scattering problem.
MotsClés: Ionization; Lagrangian mechanics; Numerical solutions; Signal generators; Wave functions


2013 
Ancarani, L. U., & Randazzo, J. M. (2013). SDCS quantum mechanical flux formula revisited for electronhydrogen ionization. Journal of Atomic and Molecular Sciences, 4(3), 193–209.


Gasaneo, G., Mitnik, D. M., Randazzo, J. M., Ancarani, L. U., & Colavecchia, F. D. (2013). Smodel calculations for highenergyelectronimpact double ionization of helium. Phys. Rev. A, 87(4), 042707.
Résumé: In this paper the double ionization of helium by highenergy electron impact is studied. The corresponding fourbody Schrodinger equation is transformed into a set of driven equations containing successive orders in the projectiletarget interaction. The transition amplitude obtained from the asymptotic limit of the firstorder solution is shown to be equivalent to the familiar first Born approximation. The firstorder driven equation is solved within a generalized Sturmian approach for an Swave (e, 3e) model process with high incident energy and small momentum transfer corresponding to published measurements. Two independent numerical implementations, one using spherical and the other hyperspherical coordinates, yield mutual agreement. From our ab initio solution, the transition amplitude is extracted, and single differential cross sections are calculated and could be taken as benchmark values to test other numerical methods in a previously unexplored energy domain.
MotsClés: atoms; closecoupling method; crosssections; he; hydrogen scattering


Mitnik, D. M., Gasaneo, G., & Ancarani, L. U. (2013). Use of generalized hyperspherical Sturmian functions for a threebody breakup model problem. J. Phys. B: At. Mol. Opt. Phys., 46(1), 015202.
Résumé: A hyperspherical Sturmian approach recently developed for threebody breakup processes is tested through an analytically solvable Swave model. The scattering process is represented by a nonhomogeneous Schrödinger equation in which the driven term is given by a Coulomblike interaction multiplied by the product of a continuum wavefunction and a bound state in the particles' coordinates. The model contains most of the difficulties encountered in a real threebody scattering problem, e.g., nonseparability in the electrons' spherical coordinates and Coulombic asymptotic behaviour, and thus provides an interesting benchmark for numerical methods. Since the Sturmian basis functions are constructed so as to include the correct asymptotic behaviour, a very fast convergence of the scattering wavefunction is observed. Excellent agreement is found with the analytical results for the associated transition amplitude. This holds true down to very low energies, a domain which is usually challenging as it involves huge spatial extensions. Within our method, such calculations can be performed without increasing significantly the computational requirements.


2012 
Ancarani, L. U., Gasaneo, G., & Mitnik, D. M. (2012). An analytically solvable threebody breakup model problem in hyperspherical coordinates. Eur. Phys. J. D, 66(10), 1–11.
Résumé: An analytically solvable Swave model for three particles breakup processes is presented. The scattering process is represented by a nonhomogeneous Coulombic Schrödinger equation where the driven term is given by a Coulomblike interaction multiplied by the product of a continuum wave function and a bound state in the particles coordinates. The closed form solution is derived in hyperspherical coordinates leading to an analytic expression for the associated scattering transition amplitude. The proposed scattering model contains most of the difficulties encountered in real threebody scattering problem, e.g., nonseparability in the electrons’ spherical coordinates and Coulombic asymptotic behavior. Since the coordinates’ coupling is completely different, the model provides an alternative test to that given by the TemkinPoet model. The knowledge of the analytic solution provides an interesting benchmark to test numerical methods dealing with the double continuum, in particular in the asymptotic regions. An hyperspherical Sturmian approach recently developed for threebody collisional problems is used to reproduce to high accuracy the analytical results. In addition to this, we generalized the model generating an approximate wave function possessing the correct radial asymptotic behavior corresponding to an Swave threebody Coulomb problem. The model allows us to explore the typical structure of the solution of a threebody driven equation, to identify three regions (the driven, the Coulombic and the asymptotic), and to analyze how far one has to go to extract the transition amplitude.
MotsClés: Atomic and Molecular Collisions; Atomic, Molecular, Optical and Plasma Physics; Nonlinear Dynamics; Physical Chemistry; Quantum Information Technology, Spintronics; Quantum Physics; Spectroscopy/Spectrometry


Gasaneo, G., Ancarani, L. U., & Mitnik, D. M. (2012). On the applicability of the exterior complex scaling method for scattering problems including Coulombic potentials. Eur. Phys. J. D, 66(4), 1–13.
Résumé: We study some formal aspects of the exterior complex scaling (ECS) approach when implemented for both short and longrange potentials. In particular, we focus on the inconsistencies related to the requirement of an artificial cutoff of the potential in order to avoid exponential divergencies due to the complex rotation. For the pure twobody Coulomb potential we demonstrate analytically and numerically that the ECS inner solution is indeed the correct one, thus reinforcing the method; the extraction of the transition amplitude, however, remains problematic. We also show that a consistent application of the ECS method requires a distorted wave formulation, and two variants are proposed. Finally, we will propose an approach equivalent to the original ECS but that avoids all formal difficulties. It is based on performing the complex rotation on the basis functions rather than on the driven equation itself, and makes use of Sturmian functions with appropriately chosen outgoing boundary conditions. Our proposal differs from one of the original versions of the ECS method, through the use of physically based basis functions rather than pure numeric ones.
MotsClés: Atomic and Molecular Collisions; Atomic, Molecular, Optical and Plasma Physics; Nonlinear Dynamics; Physical Chemistry; Quantum Information Technology, Spintronics; Quantum Physics; Spectroscopy/Spectrometry

