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J-Matrix Green’s Operators and Solving Faddeev Integral Equations for Coulombic Systems

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The J-Matrix Method

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Abstract

The two-body Coulomb Hamiltonian, in the Coulomb-Sturmian basis, has an infinite symmetric tridiagonal (Jacobi) matrix structure. This allows us to construct the Green’s operator in terms of 2F1 hypergeometric function, which can be evaluated by a continued fraction. Using this two-body Coulomb Green’s matrix, we developed an approximation method for solving Faddeev-type integral equations of the three-body Coulomb problem. The corresponding three-body Green’s operators are calculated as a convolution integral of the two-body Coulomb Green’s operators. As examples, the electron-hydrogen scattering and the resonances of the e-Ps system are presented.

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Author information

Authors and Affiliations

  1. Department of Physics and Astronomy, California State University, Long Beach, CA 90840, USA

    Z. Papp

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  1. Z. Papp
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Editor information

Editors and Affiliations

  1. Shura Council, Riyadh 11212, Saudi Arabia

    Abdulaziz D. Alhaidari

  2. Ministry of Commerce&Industry, Riyadh 11127, Saudi Arabia

    Hashim A. Yamani

  3. Dept. of Chemistry&Physics, Harvard University, 17 Oxford street, Cambridge, MA 02138-2901, USA

    Eric J. Heller

  4. Dept. of Physics, King Fahd University of Petroleum&Minerals, Dhahran 31261, Saudi Arabia

    Mohamed S. Abdelmonem

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Papp, Z. (2008). J-Matrix Green’s Operators and Solving Faddeev Integral Equations for Coulombic Systems. In: Alhaidari, A.D., Yamani, H.A., Heller, E.J., Abdelmonem, M.S. (eds) The J-Matrix Method. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6073-1_9

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