Double ionization of helium with a convoluted quasi Sturmian approach

  • Alexandr S. ZaytsevEmail author
  • Darya S. Zaytseva
  • Lorenzo Ugo Ancarani
  • Sergey A. Zaytsev
Regular Article
Part of the following topical collections:
  1. Topical Issue: Many Particle Spectroscopy of Atoms, Molecules, Clusters and Surfaces (2018)


The double ionization of Helium by fast electron impact is investigated through an ab initio approach based on an expansion on convoluted quasi Sturmian functions. The latter are dressed with an appropriately built phase factor that allows to represent adequately the delicate Coulomb phase associated with the electron-electron interaction. In so doing, these dressed basis functions possess the correct asymptotic behavior in the double continuum channel. They are used to solve, in the whole space, the driven Schrödinger equation corresponding to a first order treatment of the scattering process. Because of the asymptotic built in property of the basis, the ionization amplitudes are extracted directly from the Coulomb three-body scattering wave function, without the need to evaluate a six-dimensional matrix element. The calculated (e,3e) fully differential cross sections for two electrons escaping at 10 + 10 eV or 4 + 4 eV are in good shape agreement with those obtained by two other numerical approaches. However, for certain geometrical configurations a magnitude enhancement is observed for the lower energy case, and is ascribed to the different large distance descriptions of the long range Coulomb correlation in the scattering solution.

Graphical abstract


Atomic and Molecular Collisions 


  1. 1.
    Z. Papp, C.-Y. Hu, Z.T. Hlousek, B. Kónya, S.L. Yakovlev, Phys. Rev. A 63, 062721 (2001)ADSCrossRefGoogle Scholar
  2. 2.
    C.W. McCurdy, M. Baertschy, T.N. Rescigno, J. Phys. B 37, R137 (2004)ADSCrossRefGoogle Scholar
  3. 3.
    I. Bray, D.I. Fursa, A.S. Kadyrov, A.T. Stelbovics, A. Kheifets, A.M. Mukhamedzhanov, Phys. Rep. 520, 135 (2012)ADSCrossRefGoogle Scholar
  4. 4.
    G. Gasaneo, L.U. Ancarani, D.M. Mitnik, J.M. Randazzo, A.L. Frapiccini, F.D. Colavecchia, Adv. Quantum Chem. 67, 153 (2013)CrossRefGoogle Scholar
  5. 5.
    A.S. Kadyrov, A.M. Mukhamedzhanov, A.T. Stelbovics, I. Bray, Phys. Rev. A 70, 062703 (2004)ADSCrossRefGoogle Scholar
  6. 6.
    J. Colgan, M.S. Pindzola, Eur. Phys. J. D 66, 284 (2012)ADSCrossRefGoogle Scholar
  7. 7.
    J.S. Briggs, Phys. Rev. A 41, 539 (1990)ADSCrossRefGoogle Scholar
  8. 8.
    S.P. Merkuriev, L.D. Faddeev, Quantum Scattering Theory for Several Particle Systems (Kluwer Academic, Dordrecht, 1993)Google Scholar
  9. 9.
    M.R.H. Rudge, Rev. Mod. Phys. 40, 564 (1968)ADSCrossRefGoogle Scholar
  10. 10.
    Yu. F. Smirnov, A.V. Pavlitchenkov, V.G. Levin, V.G. Neudatchin, J. Phys. B 11, 3587 (1978)ADSCrossRefGoogle Scholar
  11. 11.
    J.H. Macek, S. Jones, Radiat. Phys. Chem. 74, 7 (2005)ADSCrossRefGoogle Scholar
  12. 12.
    L.U. Ancarani, T. Montagnese, C. Dal Cappello, Phys. Rev. A 70, 012711 (2004)ADSCrossRefGoogle Scholar
  13. 13.
    C.R. Garibotti, J.E. Miraglia, Phys. Rev. A 21, 572 (1980)ADSCrossRefGoogle Scholar
  14. 14.
    M. Brauner, J.S. Briggs, H. Klar, J. Phys. B 22, 2265 (1989)ADSCrossRefGoogle Scholar
  15. 15.
    A. Lahmam-Bennani, I. Taouil, A. Duguet, M. Lecas, L. Avaldi, J. Berakdar, Phys. Rev. A 59, 3548 (1999)ADSCrossRefGoogle Scholar
  16. 16.
    A. Kheifets, I. Bray, A. Lahmam-Bennani, A. Duguet, I. Taouil, J. Phys. B 32, 5047 (1999)ADSCrossRefGoogle Scholar
  17. 17.
    S. Jones, D.H. Madison, Phys. Rev. Lett. 91, 073201 (2003)ADSCrossRefGoogle Scholar
  18. 18.
    A.S. Zaytsev, L.U. Ancarani, S.A. Zaytsev, Eur. Phys. J. D 71, 177 (2017)ADSCrossRefGoogle Scholar
  19. 19.
    M.J. Ambrosio, L.U. Ancarani, Interdisciplianry Research on Particle Collisions and Quantitative Spectroscopy (World Scientific Publishing, Singapore, in press)Google Scholar
  20. 20.
    S.A. Zaytsev, V.A. Knyr, Yu.V Popov, A. Lahmam-Bennani, Phys. Rev. A 75, 022718 (2007)ADSCrossRefGoogle Scholar
  21. 21.
    M.S. Mengoue, M.G. Kwato Njock, B. Piraux, Yu.V Popov, S.A. Zaytsev, Phys. Rev. A 83, 052708 (2011)ADSCrossRefGoogle Scholar
  22. 22.
    M. Silenou Mengoue, H.M. Tetchou Nganso, Phys. Rev. A 94, 062705 (2016)ADSCrossRefGoogle Scholar
  23. 23.
    I. Bray, D.V. Fursa, A. Kheifets, A.T. Stelbovics, J. Phys. B 35, R117 (2002)ADSCrossRefGoogle Scholar
  24. 24.
    M.J. Ambrosio, F.D. Colavecchia, G. Gasaneo, D.M. Mitnik, L.U. Ancarani, J. Phys. B 48, 055204 (2015)ADSCrossRefGoogle Scholar
  25. 25.
    M.J. Ambrosio, F.D. Colavecchia, D.M. Mitnik, G. Gasaneo, Phys. Rev. A 91, 012704 (2015)ADSCrossRefGoogle Scholar
  26. 26.
    A.S. Zaytsev, L.U. Ancarani, S.A. Zaytsev, Eur. Phys. J. Plus 131, 48 (2016)CrossRefGoogle Scholar
  27. 27.
    M. Baertschy, T.N. Rescigno, C.W. McCurdy, Phys. Rev. A 64, 022709 (2001)ADSCrossRefGoogle Scholar
  28. 28.
    H. Bräuning, R. Dörner, C.L. Cocke, M.H. Prior, B. Krässig, A.S. Kheifets, I. Bray, A. Bräuning-Demian, K. Carnes, S. Dreuil, V. Mergel, J. Phys. B 31, 5149 (1998)ADSCrossRefGoogle Scholar
  29. 29.
    A.S. Kheifets, I. Bray, Phys. Rev. A 69, 050701(R) (2004)ADSCrossRefGoogle Scholar
  30. 30.
    J.M. Randazzo, D.M. Mitnik, G. Gasaneo, L.U. Ancarani, F.D. Colavecchia, Eur. Phys. J. D 69, 189 (2015)ADSCrossRefGoogle Scholar
  31. 31.
    C.W. McCurdy, D.A. Horner, T.N. Rescigno, F. Martín, Phys. Rev. A 69, 032707 (2004)ADSCrossRefGoogle Scholar
  32. 32.
    J. Colgan, M.S. Pindzola, F. Robicheaux, J. Phys. B 34, L457 (2001)ADSCrossRefGoogle Scholar
  33. 33.
    R.G. Newton, Scattering Theory of Waves and Particles (McGraw-Hill, New-York, 1966).Google Scholar
  34. 34.
    M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972)Google Scholar
  35. 35.
    A.D. Alhaidari, E.J. Heller, H.A. Yamani, M.S. Abdelmonem, eds., The J-Matrix Method: Developments and Applications (Springer Science, Business Media, 2008)Google Scholar
  36. 36.
    G. Gasaneo, D.M. Mitnik, J.M. Randazzo, L.U. Ancarani, F.D. Colavecchia, Phys. Rev. A 87, 042707 (2013)ADSCrossRefGoogle Scholar
  37. 37.
    M.L. Goldberger, K.M. Watson, Collision Theory (John Wiley & Sons Inc, New York, London, Sydney, 1964)Google Scholar
  38. 38.
    L.U. Ancarani, C.D. Cappello, G. Gasaneo, J. Phys.: Conf. Ser. 212, 012025 (2010)Google Scholar
  39. 39.
    Shared Facility Center “Data Center of FEB RAS” (Khabarovsk, Russia), http://lits.ccfebras.ruGoogle Scholar

Copyright information

© EDP Sciences / Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Alexandr S. Zaytsev
    • 1
    Email author
  • Darya S. Zaytseva
    • 1
  • Lorenzo Ugo Ancarani
    • 2
  • Sergey A. Zaytsev
    • 1
  1. 1.Pacific National UniversityKhabarovskRussia
  2. 2.Université de Lorraine, CNRS, LPCTMetzFrance

Personalised recommendations