On the Regularization in J-Matrix Methods

  • J. Broeckhove
  • V.S. Vasilevsky
  • F. Arickx
  • A.M. Sytcheva

Abstract

We investigate the effects of the regularization procedure used in the J-Matrix method. We show that it influences the convergence, and propose an alternative regularization approach.We explicitly perform some model calculations to demonstrate the improvement.

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References

  1. 1.
    E. J. Heller and H. A. Yamani, “J-matrix method: Application to s-wave electron-hydrogen scattering,” Phys. Rev., vol. A9,pp. 1209–1214, 1974.ADSGoogle Scholar
  2. 2.
    W. P. Reinhardt, D. W. Oxtoby, and T. N. Rescigno, “Computation of elastic scattering phase shifts via analytic continuation of fredholm determinants constructed using an L 2 basis,” Phys. Rev. Lett.,vol. 28, p. 401–403, 1972.CrossRefADSGoogle Scholar
  3. 3.
    D. A. Konovalov and I. E. McCarthy, “Convergent J-matrix calculation of electron-helium resonances,” J. Phys. B Atom. Mol. Phys., vol. 28, pp. L139–L145, Mar. 1995.Google Scholar
  4. 4.
    J. T. Broad and W. P. Reinhardt, “One- and two-electron photoejection from H-: A multichannel J-matrix calculation,” Phys. Rev. A, vol. 14, pp. 2159–2173, Dec. 1976.Google Scholar
  5. 5.
    V. A. Knyr and L. Y. Stotland, “The three-body problem and J-matrix method,” Phys. Atom. Nucl., vol. 56, pp. 886–889, July 1993.Google Scholar
  6. 6.
    V. A. Knyr, V. V. Nasyrov, and Y. V. Popov, “Application of the J-matrix method for describing the (e, 3e) reaction in the Helium Atom,” J. Exp. Theor. Phys., vol. 92, pp. 789–794, May 2001.Google Scholar
  7. 7.
    I. Cacelli, R. Moccia, and A. Rizzo, “Gaussian-type-orbital basis sets for the calculation of continuum properties in molecules: The differential photoionization cross section of molecular nitrogen,” Phys. Rev. A, vol. 57, pp. 1895–1905, Mar. 1998.Google Scholar
  8. 8.
    V. S. Vasilevsky and I. Y. Rybkin, “Astrophysical S-factor of the t(t,2n)4 He 3 H(3 H,2n)4 He reactions,” Sov. J. Nucl. Phys., vol. 50, p. 411, 1989.Google Scholar
  9. 9.
    V. S. Vasilevsky, I. Y. Rybkin, and G. F. Filippov, “Theoretical analysis of the mirror reactions d(d,n)3 He and d(d,p)3 H and resonance states of the 4 He nucleus,” Sov. J. Nucl.Phys., vol. 51, p. 71, 1990.Google Scholar
  10. 10.
    V. Vasilevsky, G. Filippov, F. Arickx, J. Broeckhove, and P. V.Leuven,“Coupling of collective states in the continuum: An application to 4He,” J. Phys. G: Nucl. Phys., vol. G18,pp. 1227–1242, 1992.ADSGoogle Scholar
  11. 11.
    V. S. Vasilevsky, A. V. Nesterov, F. Arickx, and P. V. Leuven,“Three-cluster model of six-nucleon system,” Phys. Atom. Nucl., vol. 60,pp. 343–349, 1997.ADSGoogle Scholar
  12. 12.
    V. S. Vasilevsky, A. V. Nesterov, F. Arickx, and J. Broeckhove,“Algebraic model for scattering in three-s-cluster systems. I.Theoretical background,” Phys. Rev., vol. C63,p.034606, 2001.ADSGoogle Scholar
  13. 13.
    V. S. Vasilevsky, A. V. Nesterov, F. Arickx, and J. Broeckhove,“Algebraic model for scattering in three-s-cluster systems. II.Resonances in three-cluster continuum of 6 He and 6 Be,” Phys. Rev., vol. C63, p. 034607, 2001.ADSGoogle Scholar
  14. 14.
    V. S. Vasilevsky, A. V. Nesterov, F. Arickx, and J. Broeckhove,“S factor of the 3 H(3 H,2n)4 He and 3 He(3 He,2p)4 He reactions using a three-cluster exit channel,” Phys. Rev., vol. C63, p. 064604, 2001.ADSGoogle Scholar
  15. 15.
    A. Sytcheva, J. Broeckhove, F. Arickx, and V. S. Vasilevsky,“Influence of monopole and quadrupole channels on the cluster continuum of the lightest p-shell nuclei,” J. Phys. G Nucl. Phys., vol. 32,pp. 2137–2155, Nov 2006.Google Scholar
  16. 16.
    V. Vasilevsky, F. Arickx, J. Broeckhove, and T. Kovalenko, “A microscopic model for cluster polarization, applied to the resonances of 7Be and the reaction 6 Li(p,3 He) 4 He,” in Proc. of the 24 International Workshop on Nuclear Theory, Rila Mountains, Bulgaria, June 20–25, 2005 (S. Dimitrova, ed.) pp. 232–246, Sofia, Bulgaria: Heron Press, 2005.Google Scholar
  17. 17.
    F. Arickx, J. Broeckhove, P. Hellinckx, V. Vasilevsky, and A. Nesterov, “A three-cluster microscopic model for the 5 H nucleus,” in Proc. of the 24 International Workshop on Nuclear Theory, Rila Mountains,Bulgaria, June 20–25, 2005 (S. Dimitrova, ed.), pp. 217–231, Sofia,Bulgaria: Heron Press 2005.Google Scholar
  18. 18.
    V. Vasilevsky, F. Arickx, J. Broeckhove, and V. Romanov, “Theoretical analysis of resonance states in 4 H, 4 He and 4 Li above three-cluster threshold,” Ukr. J. Phys., vol. 49, no. 11,pp. 1053–1059, 2004.Google Scholar
  19. 19.
    Z. Papp and W. Plessas, “Coulomb-Sturmian separable expansion approach:Three-body Faddeev calculations for Coulomb-like interactions,” Phys.Rev. C, vol. 54, pp. 50–56, July 1996.Google Scholar
  20. 20.
    G. Filippov and Y. Lashko, “Structure of light neutron-rich nuclei and nuclear reactions involving these nuclei,” El. Chast. Atom. Yadra,vol. 36, no. 6, pp. 1373–1424, 2005.Google Scholar
  21. 21.
    G. F. Filippov, Y. A. Lashko, S. V. Korennov, and K. Katō,“6 He + 6 He clustering of 12Be in a microscopic algebraic approach,” Few-Body Systems, vol. 34,pp. 209–235, 2004.Google Scholar
  22. 22.
    S. Korennov G. Filippov, Y. Lashko, and K. Katō,“ Microscopic Hamiltonian of 9 Li and 10Be and the SU(3) basis,” Progr. Theor. Phys. Suppl., vol. 146, pp. 579–580, 2002.Google Scholar
  23. 23.
    J. M. Bang, A. I. Mazur, A. M. Shirokov, Y. F. Smirnov, and S. A.Zaytsev, “P-matrix and J-matrix approaches: Coulomb asymptotics in the harmonic oscillator representation of scattering theory,” Ann. Phys., vol. 280, pp. 299–335, Mar. 2000.Google Scholar
  24. 24.
    V. S. Vasilevsky and F. Arickx, “Algebraic model for quantum scattering:Reformulation, analysis, and numerical strategies,” Phys. Rev.,vol. A55, pp. 265–286, 1997.CrossRefADSGoogle Scholar
  25. 25.
    W. Vanroose, J. Broeckhove, and F. Arickx, “Modified J-matrix method for scattering,” Phys. Rev. Lett., vol. 88, p. 10404, Jan.2002.Google Scholar
  26. 26.
    J. Broeckhove, F. Arickx, W. Vanroose, and V. S. Vasilevsky,“The modified J-matrix method for short range potentials,” J. Phys. A Math. Gen., vol. 37, pp. 7769–7781, Aug. 2004.Google Scholar
  27. 27.
    E. J. Heller and H. A. Yamani, “New L 2 approach to quantum scattering: Theory,” Phys. Rev., vol. A9,pp. 1201–1208, 1974.ADSGoogle Scholar
  28. 28.
    Y. I. Nechaev and Y. F. Smirnov, “Solution of the scattering problem in the oscillator representation,” Sov. J. Nucl. Phys., vol. 35,pp. 808–811, 1982.MATHGoogle Scholar
  29. 29.
    H. A. Yamani and L. Fishman, “J-matrix method: Extensions to arbitrary angular momentum and to Coulomb scattering,” J. Math. Phys., vol. 16, pp. 410–420, 1975.CrossRefADSGoogle Scholar
  30. 30.
    R. G. Newton, Scattering Theory of Waves and Particles. New-York: McGraw-Hill, 1966.Google Scholar
  31. 31.
    P. M. Morse and H. Feshbach, Methods of Theoretical Physics. New-York: McGraw-Hill Book Co., Inc., 1953.Google Scholar
  32. 32.
    M. Abramowitz and A. Stegun, Handbook of Mathematical Functions. New-York: Dover Publications, Inc., 1972.MATHGoogle Scholar
  33. 33.
    G. F. Filippov and I. P. Okhrimenko, “Use of an oscillator basis for solving continuum problems,” Sov. J. Nucl. Phys., vol. 32, pp. 480–484,1981.Google Scholar
  34. 34.
    F. Calogero, Variable Phase Approach to Potential Scattering. New-York and London: Academic Press, 1967.MATHGoogle Scholar
  35. 35.
    V. V. Babikov, Phase Function Method in Quantum Mechanics. Moscow: Nauka, 1976.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • J. Broeckhove
    • 1
  • V.S. Vasilevsky
  • F. Arickx
  • A.M. Sytcheva
  1. 1.University of Antwerp, Group Computational Modeling and ProgrammingAntwerpBelgium

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