Abstract:

We study the double ionization by electron impact of the ground state of heliumlike atoms and propose a scaling law for fully differential (e,3e) cross sections. Within the first Born approximation, cross sections are calculated with a three-body Coulomb (3C) double-continuum wave function and initial states represented by highly accurate wave functions, which satisfy all two-body Kato cusp conditions. We first consider the helium atom in the kinematical and geometrical conditions of the only absolute, high incident energy, experimental data available: our calculations confirm unambiguously that satisfying or not Kato cusp conditions is not a relevant feature of the ground state. Other heliumlike atoms are then considered. Under similar conditions, cross sections for H- are much larger than for helium while the reverse is true for positive ions; a comparison with the rare other theoretical calculations is performed. Finally, within our theoretical framework, we propose an approximate scaling law for (e,3e) cross sections for heliumlike positive ions, and confirm it by calculations. © 2008 The American Physical Society.

Author affiliation: Ancarani, L. U.. Université Paul Verlaine-Metz; Francia

Author affiliation: Dal Cappello, C.. Université Paul Verlaine-Metz; Francia

Author affiliation: Charpentier, I.. Centre National de la Recherche Scientifique; Francia

Author affiliation: Rodriguez, Karina Viviana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; Argentina

Author affiliation: Gasaneo, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; Argentina

Abstract:

The double ionization of helium by high energy electron impact is investigated. The pure four-body Coulomb problem may be reduced to a three-body 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. © 2014 Springer-Verlag Wien.

Author affiliation: Ambrosio, Marcelo José. Universidad Nacional del Sur. Departamento de Física; Argentina

Author affiliation: Ancarani, L. U.. Universite Paul Verlaine-metz. Institut de Physique, Chimie Et Materiaux. Laboratorie de Physique Moleculaire Et Des Collisions; Francia

Author affiliation: Mitnik, Dario Marcelo. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; Argentina

Author affiliation: Gasaneo, Gustavo. Universidad Nacional del Sur. Departamento de Física; Argentina

Author affiliation: Colavecchia, Flavio Dario. Comisión Nacional de Energíâ­a Atómica. Gerencia del Area Investigación y Aplicaciones No Nucleares. Gerencia de Física (centro Atómico Balseiro). División Colisiones Atómicas; Argentina

Abstract:

In this article, we investigate discretization schemes to represent Sturmian functions for both positive and negative energies in the presence of a long range Coulomb potential.We explore two methods to obtain Sturmian functions for positive energy. The first one involves the expansion of the radial wave function in a L2 finite basis set, whereas the second one introduces the discretization of the radial coordinate domain of the Hamiltonian or, alternatively, the Green function. We apply them to find the bound states and scattering phase shift for N-electron atoms close to the critical charge. Both methods are able to describe bound states near threshold, as well as continuum states with very good convergence properties.

Author affiliation: Frapiccini, Ana Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina

Author affiliation: Randazzo, Juan Martin. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina

Author affiliation: Gasaneo, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; Argentina. Universidad Nacional del Sur. Departamento de Física; Argentina

Author affiliation: Colavecchia, Flavio Dario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina

Abstract:

In the investigation of two-body Coulomb Schrödinger equations with some types of nonhomogeneities, the particular solution can be expressed in terms of a two-variable Kampé de Fériet hypergeometric function. The asymptotic limit of the latter-for both variables being large but their ratio being a bound constant-is required in order to extract relevant physical information from the solutions. In this report the mathematical limit is provided. For that purpose, a particular series representation of the hypergeometric function-in terms of products of Kummer and Gauss functions-is first derived. © 2011 American Institute of Physics.

Author affiliation: Ancarani, L.U.. Université Paul Verlaine-Metz; Francia

Author affiliation: Gasaneo, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Sur. Departamento de Física; Argentina

Abstract:

A methodology based on generalized Sturmian functions is put forward to solve two- and three-body scattering problems. It uses a spectral method which allows for the inclusion of the correct asymptotic behavior when solving the associated driven Schroedinger equation. For the two-body case, we demonstrate the equivalence between the exterior complex scaling (ECS) and the Sturmian approaches and illustrate the latter by using Hulthen Sturmian functions. Contrary to the ECS approach, no artificial cut-off of the potential is required in the Surmian approach. For the three-body scattering problem, the theoretical framework is presented in hyperspherical coordinates and a set of hyperspherical generalized Sturmian functions possessing outgoing asymptotic behavior is introduced. The Sturmian procedure is a direct generalization of the method discussed for the two-body problem; thus, the comparison with the ECS method is similar. For both the two- and three-body cases, Sturmian bases are efficient as they possess the correct outgoing behavior, diagonalize part of the potentials involved and are essentially localized in the region where the unsolved interaction is not negligible. Moreover, with the Sturmian basis, the operator (H − E ) is represented by a diagonal matrix whose elements are simply the Sturmian eigenvalues.

Author affiliation: Gasaneo, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; Argentina

Abstract:

Simple and accurate wavefunctions for the He atom and He-like isoelectronic ions are presented. These functions—the product of hydrogenic one-electron solutions and a fully correlated part—satisfy all the coalescence cusp conditions at the Coulomb singularities. Functions with different numbers of parameters and different degrees of accuracy are discussed. Simple analytic expressions for the wavefunction and the energy, valid for a wide range of nuclear charges, are presented. The wavefunctions are tested, in the case of helium, through the calculations of various cross sections which probe different regions of the configuration space, mostly those close to the two-particle coalescence points.

Author affiliation: Rodriguez, Karina Viviana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; Argentina

Author affiliation: Gasaneo, Gustavo. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina

Author affiliation: Mitnik, Dario Marcelo. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; Argentina

Abstract:

The angularly correlated basis functions proposed by Gasaneo and Ancarani (Phys Rev, A 77:012705, 2008) are used to construct approximated wavefunctions, satisfying all two-body cusp conditions, for several three-body systems. The focus here is on the study of the following negatively charged hydrogen-like ions:  ∞ H − , 1H − , D − , T −  and Mu − , the negative positronium ion Ps − , and the exotic systems e−e−(nme)+e−e−(nme)+ in which one of the particles is heavier than the other two. Accurate results for the mean of the ground state energy and of other radial quantities are compared with those given in the literature, when available.

Author affiliation: Rodriguez, Karina Viviana. Universidad Nacional del Sur. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina

Author affiliation: Gonzalez, Y. V.. Universidad Nacional del Sur. Departamento de Física; Argentina

Author affiliation: Gasaneo, Gustavo. Universidad Nacional del Sur. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina

Author affiliation: Ancarani, L. U.. Université Paul Verlaine-Metz. Institut de Physique, Chimie et Materiaux. Laboratorie de Physique Moléculaire et des Collisions; Francia

Author affiliation: Mitnik, Dario Marcelo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina

Abstract:

An analytic wavefunction is proposed for the ground state of general atomic three-body systems in which two light particles are negatively charged and the third (heavy) is positively charged. By construction the wavefunction (i) has the same analytical form for all systems; (ii) is parameter-free; (iii) is nodeless; (iv) satisfies all two-particle cusp conditions; and (v) yields reasonable ground state energies for several three-body systems, including the prediction of a bound state for H-, D-, T- and Mu-. Simple polynomial fits are provided for certain important subcases, allowing for a rapid estimate of the ground state energy and of the stability of three-body systems.

Author affiliation: Ancarani, L. U.. Université Paul Verlaine-Metz; Francia

Author affiliation: Gasaneo, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; Argentina

Abstract:

An analytically solvable S-wave model for three particles break-up processes is presented. The scattering process is represented by a non-homogeneous Coulombic Schrödinger equation where the driven term is given by a Coulomb-like 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 three-body scattering problem, e.g., non-separability 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 Temkin-Poet 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 three-body 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 S-wave three-body Coulomb problem. The model allows us to explore the typical structure of the solution of a three-body 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.

Author affiliation: Ancarani, L. U.. Universite de Lorraine; Francia

Author affiliation: Gasaneo, Gustavo. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina

Author affiliation: Mitnik, Dario Marcelo. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; Argentina

Abstract:

Abstract: 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. Graphical abstract: [Figure not available: see fulltext.]

Author affiliation: Ambrosio, Marcelo José. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; Argentina. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina

Author affiliation: Ancarani, Lorenzo U.. Universite de Lorrain; Francia

Author affiliation: Gómez, Antonio Ilán. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina

Author affiliation: Gasaneo, Gustavo. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina

Author affiliation: Mitnik, Dario Marcelo. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; Argentina. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina