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Recursion relations for the three-electron subsidiary integral W (l, m, n; α, β, γ)

Authors

  • Chun Li,

    Corresponding author
    1. Department of Mathematics, Nanjing University, Nanjing, Jiangsu 210093, People's Republic of China
    2. Department of Physics, University of New Brunswick, Fredericton, New Brunswick, Canada E3B 5A3
    • Department of Mathematics, Nanjing University, Nanjing, Jiangsu 210093, People's Republic of China
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  • Liming Wang,

    1. Department of Physics, University of New Brunswick, Fredericton, New Brunswick, Canada E3B 5A3
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  • Zong-Chao Yan

    1. Department of Physics, University of New Brunswick, Fredericton, New Brunswick, Canada E3B 5A3
    2. Center for Cold Atom Physics, Chinese Academy of Sciences, Wuhan 430071, China
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Abstract

The subsidiary integral W (l, m, n; α, β, γ) is a key integral that appears in the variational calculation of a three-electron atomic system using Hylleraas coordinates. For the case where the ratio α/(α + β + γ) ∼ 1, an important special situation that may occur in the evaluation of the Bethe logarithm, existing approaches for calculating the W integral become impractical due to the problem of slow convergence. In this article, we present a computationally efficient and numerical stable method, in which the W integral can be expressed in terms of either a finite series or a finite recursion relation. Numerical tests are given. © 2012 Wiley Periodicals, Inc.

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