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Accurate Evaluation of the S-Matrix for Multi-Channel Analytic and Non-Analytic Potentials in Complex L2 Bases

  • H.A. Yamani
  • M.S. Abdelmonem

Abstract

We describe an efficient and accurate scheme to compute the S-matrix elements for a given multi-channel analytic and non-analytic potentials in complex-scaled orthonormal Laguerre or oscillator bases using the J-matrix method. As examples of the utilization of the scheme, we evaluate the cross section of two-channel square wells in an oscillator basis and find the resonance position for the same potential using the Laguerre basis. We also find resonance positions of a two-channel analytic potential for several angular momenta ℓ using both bases. Additionally, we evaluate the effect of including the Coulomb term (z/r) when employing the Laguerre basis.

Keywords

Matrix Element Coulomb Term Oscillator Basis Matrix Element Versus Laguerre Basis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Reference

  1. 1.
    For a review of this method see, Reinhardt W P 1982 Ann. Rev. Phys. Chem. 33, 223Google Scholar
  2. 2.
    Rescigno T N and Reinhardt W P 1973 Phys. Rev. A8, 2828ADSMathSciNetGoogle Scholar
  3. 3.
    Rescigno T N and McCurdy C W 1986 Phys. Rev. A34 1882Google Scholar
  4. 4.
    Yamani H A and Abdelmonem M S 1996 J. Phys. A: Math. Gen. 29, 6991Google Scholar
  5. 5.
    Arickx F, Broeckhove J, Van Leuven P, Vasilevsky V, and Filippov 1994 Am. J. Phys. 62, 362CrossRefADSGoogle Scholar
  6. 6.
    Alhaidari A D, Bahlouli H, Abdelmonem M S, Al-Ameen F, and Al-Abdulaal T (2007) Phys. Lett. A 364, 372CrossRefADSMathSciNetMATHGoogle Scholar
  7. 7.
    Igashov S Yu, “Oscillator basis in the J-matrix method: convergence of expansions, asymptotics of expansion coefficients and boundary conditions”, Part II, Chapter 1, this volumeGoogle Scholar
  8. 8.
    Magnus W, Oberhettinger F, and Soni R P 1966, Formulas and Theorems for the Special Functions of Mathematical Physics (New York: Springer-Verlag)Google Scholar
  9. 9.
    Yamani H A and Abdelmonem M S 1997 J. Phys. B: At. Mol. Opt. Phys. 30, 1633CrossRefADSGoogle Scholar
  10. 10.
    Akhiezer N I 1965, The Classical Moment Problem (Einburgh: Oliver and Boyd)Google Scholar
  11. 11.
    Szego G 1939, Orthogonal Polynomials (New York: American Mathematical Society)Google Scholar
  12. 12.
    Krylov V I 1962, Approximate Calculation of Integrals (New York: The Macmillan Company)Google Scholar
  13. 13.
    Newton R G 1966, Scattering Theory of Waves and Particles (New York: McGraw-Hill), p. 543Google Scholar
  14. 14.
    Noro T and Taylor H S 1980 J. phys. B13, L377ADSGoogle Scholar
  15. 15.
    Mandelshtam V.A. Ravuri T. R. and Taylor H. S. 1993 Phys. Rev. Lett. 70, 1932CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • H.A. Yamani
    • 1
  • M.S. Abdelmonem
  1. 1.Ministry of Commerce & IndustryRiyadh 11127Saudi Arabia

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