Abstract
A version of the J-matrix method for solving three-body differential Faddeev-Merkuriev equations is proposed. This version permits taking into account the full spectrum of a two-body Coulomb subsystem. Laguerre functions are used as a basis in expanding the total wave function of the problem being considered. In order to test the efficiency of the proposed method, the differential cross section for single ionization of a helium atom is calculated where the emerging He+ ion remains in an excited state. The result agrees satisfactorily with experimental data both in the shape of the respective curve and in magnitude.
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References
E. J. Heller and H. A. Yamani, Phys. Rev. A 9, 1201 (1974); H. A. Yamani and L. Fishman, J. Math. Phys. 16, 410 (1975); J. T. Broad and W. P. Reinhardt, Phys. Rev. A 14, 2159 (1976).
G. F. Filippov and I. P. Okhrimenko, Yad. Fiz. 32, 932 (1980) [Sov. J. Nucl. Phys. 32, 480 (1980)]; G. F. Filippov, Yad. Fiz. 33, 928 (1981) [Sov. J. Nucl. Phys. 33, 488 (1981)]
Yu. F. Sminov and Yu. I. Nechaev, Kinam 4, 445 (1982); Yad. Fiz. 35, 1385 (1982) [Sov. J. Nucl. Phys. 35, 808 (1982)].
J. Revai, M. Sotona, and J. Zofka, J. Phys. G 11, 745 (1985).
V. A. Knyr, V. V. Nasyrov, Yu. V. Popov, and L. Ya. Stotland, Zh. Éksp. Teor. Fiz. 109, 361 (1996) [JETP 82, 190 (1996)].
Yu. V. Popov, V. A. Knyr, V. V. Nasyrov, and A. Lahmam-Bennani, Few-Body Syst., Suppl. 10, 235 (1999).
V. A. Knyr, V. V. Nasyrov, and Yu. V. Popov, Zh. Éksp. Teor. Fiz. 119, 906 (2001) [JETP 92, 789 (2001)].
A. M. Lane and R. G. Thomas, Rev. Mod. Phys. 30, 257 (1958).
J. Broad and W. P. Reinhardt, J. Phys. B 9, 1491 (1976).
V. A. Knyr and L. Ya. Stotland, Yad. Fiz. 55, 2908 (1992) [Sov. J. Nucl. Phys. 55, 1626 (1992)]; 59, 607 (1996) [Phys. At. Nucl. 59, 575 (1996)]; 56 (7), 54 (1993) [Phys. At. Nucl. 56, 886 (1993)].
I. Bray and A. T. Stelbovics, Phys. Rev. A 46, 6995 (1992).
Z. Papp, C.-Y. Hu, Z. T. Hlousek, et al., Phys. Rev. A 63, 62721 (2001).
Z. Papp, Phys. Rev. C 55, 1080 (1997).
S. P. Merkuriev and L. D. Faddeev, Quantum Scattering Theory for Few-Body Systems (Nauka, Moscow, 1985) [in Russian].
A. A. Kvitsinsky, A. Wu, and C.-Y. Hu, J. Phys. B 28, 275 (1995).
R. G. Newton, Scattering Theory of Waves and Particles (McGraw-Hill, New York, 1966; Mir, Moscow, 1969).
A. Erdélyi, Higher Transcendental Functions (Bateman Manuscript Project), Ed. by A. Erdélyi (McGraw-Hill, New York, 1953; Nauka, Moscow, 1973), Vol. 1.
J. T. Broad, Phys. Rev. A 31, 1494 (1985).
E. J. Heller, Phys. Rev. A 12, 1222 (1975).
Z. Papp and C.-Y. Hu, Phys. Rev. A 66, 052714 (2002).
C. Dupre, A. Lahmam-Bennani, A. Duguet, et al., J. Phys. B 25, 259 (1992).
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Original Russian Text © S.A. Zaitsev, V.A. Knyr, Yu. V. Popov, 2006, published in Yadernaya Fizika, 2006, Vol 69, No. 2, pp. 276–283.
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Zaitsev, S.A., Knyr, V.A. & Popov, Y.V. Solving Faddeev-Merkuriev equations within the J-matrix approach: Application to coulomb problems. Phys. Atom. Nuclei 69, 255–262 (2006). https://doi.org/10.1134/S1063778806020098
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DOI: https://doi.org/10.1134/S1063778806020098