Electron impact excitation of atoms and positive ions

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Derivatives of any order of the hypergeometric function pFq(a1, ..., ap; b1, ..., bq; z) with respect to the parameters ai and bi

The derivatives of any order of the general hypergeometric function pFq(a1.....ap; b1.....bq;z) with respect to the parameters a; or bj are expressed, in compact form, in terms of generalizations of multivariable Kampe de Feriet functions. To achieve this, use is made of Babister's solution to nonhomogeneous differential equations for pFq(a1.....ap; b1.....bq;z). An application to Hahn polynomials, which are 3F2 functions, is given as an illustration.Fil: Ancarani, L.U.. Université Paul Verlaine-Metz; FranciaFil: 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; Argentin

Two-body Coulomb problems with sources

The two-body Coulomb Schrödinger equation with different types of nonhomogeneities are studied. The particular solution of these nonhomogeneous equations is expressed in closed form in terms of a two-variable hypergeometric function. A particular representation of the latter allows one to study efficiently the solution in the asymptotic limit of large values of the coordinate and hence the associated physics. Simple sources are first considered, and a complete analysis of scattering and bound states is performed. The solutions corresponding to more general (arbitrary) sources are then provided and written in terms of more general hypergeometric functions. © 2010 The American Physical Society.Fil: Gasaneo, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Sur. Departamento de Física; ArgentinaFil: Ancarani, L.U.. Université Paul Verlaine-Metz; Franci

A special asymptotic limit of a Kampé de Fériet hypergeometric function appearing in nonhomogeneous Coulomb problems

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.Fil: Ancarani, L.U.. Université Paul Verlaine-Metz; FranciaFil: Gasaneo, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Sur. Departamento de Física; Argentin

Ground and excited states for exotic three-body atomic systems

An Angular Correlated Configuration Interaction method is extended and applied to exotic threebody atomic systems with general masses. A recently proposed angularly correlated basis set is used to construct, simultaneously and with a single diagonalization, ground and excited states wave functions which: (i) satisfy exactly Kato cusp conditions at the two-body coalescence points; (ii) have only linear parameters; (iii) show a fast convergency rate for the energy; (iv) form an orthogonal set. The efficiency of the construction is illustrated by the study a variety of three-body atomic systems [m1− m2− m3z3+ ] with two negatively charged light particles, with 123 diverse masses m1− and m2−, and a heavy positively charged nucleus m3z3+. The calculated ground 11S and several excited n1,3S state energies are compared with those given in the literature, when available. We also present a short discussion on the critical charge necessary to get a stable three-body system supporting two electrons, an electron and a muon, or two muons

Theoretical predictions for (e,2e) processes on positive ions : Direct application of new analytical formulae for Coulomb integrals

Triple differential cross sections for (e, 2e) processes on positive ions are calculated within the Coulomb Projected Born model. The partial wave formalism generates radial matrix elements of multipole type involving products of two Coulomb functions related to different charges. We first present results for the ionization of the valence electron of Mg+, for electrons impinging at a relatively moderate incident energy, in an asymmetric coplanar geometry ; the quality of the WKB approximation is emphasized. Then, we consider ions of the Hydrogenlike and Lithiumlike isoelectronic sequences, and identify a scaling law

Derivatives of Horn hypergeometric functions with respect to their parameters

International audienceThe derivatives of eight Horn hypergeometric functions [four Appell F1, F2, F3, and F4, and four (degenerate) confluent Φ1, Φ2, Ψ1, and Ξ1] with respect to their parameters are studied. The first derivatives are expressed, systematically, as triple infinite summations or, alternatively, as single summations of two-variable Kampé de Fériet functions. Taking advantage of previously established expressions for the derivative of the confluent or Gaussian hypergeometric functions, the generalization to the nth derivative of Horn’s functions with respect to their parameters is rather straightforward in most cases; the results are expressed in terms of n + 2 infinite summations. Following a similar procedure, mixed derivatives are also treated. An illustration of the usefulness of the derivatives of F1, with respect to the first and third parameters, is given with the study of autoionization of atoms occurring as part of a post-collisional process. Their evaluation setting the Coulomb charge to zero provides the coefficients of a Born-like expansion of the interaction

Ground state for two-electron and electron-muon three-body atomic systems

In this article, the angular correlated configuration interaction method previously introduced by some of the authors is extended to three-body atomic systems with general masses. A recently proposed angularly correlated basis set is used to construct ground state wave functions which: (i) satisfy exactly Kato cusp conditions atthe two-body coalescence points; (ii) have only linear coefficients; and (iii) show a fast convergency rate for the energy. The efficiency of the construction is illustrated by the study of the negatively charged hydrogen-like systems (∞H-, T-, D-, 1H-, and Mu-), neutral helium-like systems (e-e- ∞He +2,e-e- 4He+2, e -e- 3He+2, e-μ - ∞He+2, e-μ -4He+2, and e-μ- 3He+2), and positively charged lithium-like systems (e-e- ∞Li+3,e -e- 7Li+3, e-e - 6Li+3, e-μ- ∞Li+3, e-μ- 7Li+3, and e-μ- 6Li+3). The ground state energies and other mean values are compared with those given in the literature, when available. Wave functions with a moderate number of (20 maximum) linear coefficients are given explicitly; they are sufficiently simple and accurate to be used in practical calculations of atomic collision in which multidimensional integrations are involved.Fil: 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; ArgentinaFil: Ancarani, L.U.. Universite Paul Verlaine–Metz,; FranciaFil: 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; ArgentinaFil: 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; Argentin

Analysis of semi-relativistic approximations for relativistic (e,2e) experiments

We analyse the validity of using semi-relativistic approximations in the Coulomb Born approach, for both bound and continuum wave-functions, when describing theoretically relativistic (e, 2e) experiments. A comparison with absolute experimental data is made for the ionization of the K-shell of gold and silver, in coplanar symmetric and asymmetric geometries