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Beat structure in the solution of scattering problems with nondecaying sources*

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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.

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Authors and Affiliations

  1. Instituto de Astronomía y Física del Espacio (IAFE), Universidad de Buenos Aires, C1428, EGA Buenos Aires, Argentina

    Marcelo J. Ambrosio & Darío M. Mitnik

  2. Departamento de Física, Universidad de Buenos Aires, C1428, EGA Buenos Aires, Argentina

    Marcelo J. Ambrosio & Darío M. Mitnik

  3. Théorie, Modélisation, Simulation, SRSMC, UMR CNRS 7565, Université de Lorraine, 57078, Metz, France

    Lorenzo U. Ancarani

  4. IFISUR, Universidad Nacional del Sur, CONICET, Departamento de Física – UNS, Av. L. N. Alem 1253, B8000, CPB – Bahía Blanca, Argentina

    Antonio I. Gómez & Gustavo Gasaneo

  5. Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET), Buenos Aires, Argentina

    Marcelo J. Ambrosio, Antonio I. Gómez, Gustavo Gasaneo & Darío M. Mitnik

Authors
  1. Marcelo J. Ambrosio
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  2. Lorenzo U. Ancarani
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  3. Antonio I. Gómez
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  4. Gustavo Gasaneo
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  5. Darío M. Mitnik
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Correspondence to Marcelo J. Ambrosio.

Additional information

Contribution to the Topical Issue “Many Particle Spectroscopy of Atoms, Molecules, Clusters and Surfaces”, edited by A.N. Grum-Grzhimailo, E.V. Gryzlova, Yu V. Popov, and A.V. Solov’yov.

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Ambrosio, M.J., Ancarani, L.U., Gómez, A.I. et al. Beat structure in the solution of scattering problems with nondecaying sources*. Eur. Phys. J. D 71, 54 (2017). https://doi.org/10.1140/epjd/e2017-70542-y

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  • DOI: https://doi.org/10.1140/epjd/e2017-70542-y

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