Skip to main content
Log in

Potential Splitting Approach to Positron Scattering Off the Hydrogen Atom and the Positive Helium Ion

  • Published:
Few-Body Systems Aims and scope Submit manuscript

Abstract

The positron-hydrogen atom and the positron-positive helium ion scattering problems at the energies below the second excitation threshold of the positronium are solved by the potential splitting approach combined with the complex scaling technique. We solve the Schrödinger equation in the total angular momentum representation. The elastic scattering and excitation cross-sections are obtained.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. L.D. Faddeev, S.P. Merkuriev, Quantum Scattering Theory for Several Particle Systems (Kluwer, Dordrecht, 1993)

    Book  MATH  Google Scholar 

  2. J. Nuttall, H.L. Cohen, Method of complex coordinates for three-body calculations above the breakup threshold. Phys. Rev. 188, 1542 (1969)

    Article  ADS  Google Scholar 

  3. T.N. Rescigno, M. Baertschy, D. Byrum, C.W. McCurdy, Making complex scaling work for long-range potentials. Phys. Rev. A 55, 4253 (1997)

    Article  ADS  Google Scholar 

  4. C.W. McCurdy, F. Martin, Implementation of exterior complex scaling in B-splines to solve atomic and molecular collision problems. J. Phys. B At. Mol. Opt. Phys. 37, 917 (2004)

    Article  ADS  Google Scholar 

  5. I. Hornyak, A.T. Kruppa, Two-body Coulomb scattering and complex scaling. Phys. Rev. A 85, 022702 (2012)

    Article  ADS  Google Scholar 

  6. J. Mitroy, L. Berge, A. Stelbovics, Positron-hydrogen scattering at low energies. Phys. Rev. Lett. 73, 2966 (1994)

    Article  ADS  Google Scholar 

  7. Y. Zhou, C.D. Lin, Comparative studies of excitations and resonances in \(\text{ H }^{-}\), \(\text{ Ps }^{-}\), and \(e^{+}+\text{ H }\) systems. Phys. Rev. Lett. 75, 2296 (1995)

    Article  ADS  Google Scholar 

  8. B.H. Bransden, C.J. Noble, R.J. Whitehead, Positron scattering by singly charged helium ions in the ground state. J. Phys. B At. Mol. Opt. Phys. 34, 2267 (2001)

    Article  ADS  Google Scholar 

  9. N. Yamanaka, Y. Kino, Time-dependent coupled-channel calculation for elastic scattering of positrons by hydrogen atoms and helium ions. Phys. Rev. A 68, 052715 (2003)

    Article  ADS  Google Scholar 

  10. M.V. Volkov, N. Elander, E. Yarevsky, S.L. Yakovlev, Solving the Coulomb scattering problem using the complex-scaling method. Europhys. Lett. 85, 30001 (2009)

    Article  ADS  Google Scholar 

  11. N. Elander, M. Volkov, A. Larson, M. Stenrup, J.Z. Mezei, E. Yarevsky, S. Yakovlev, Quantum scattering with the driven Schrödinger approach and complex scaling. Few Body Syst. 45, 197 (2009)

    Article  ADS  Google Scholar 

  12. M.V. Volkov, S.L. Yakovlev, E.A. Yarevsky, N. Elander, Potential splitting approach to multichannel Coulomb scattering: the driven Schrödinger equation formulation. Phys. Rev. A 83, 032722 (2011)

    Article  ADS  Google Scholar 

  13. E. Yarevsky, S.L. Yakovlev, N. Elander, M.V. Volkov, On the scattering of the electron off the hydrogen atom and the helium ion below and above the ionization threshold: Temkin-Poet model. Few Body Syst. 55, 1057 (2014)

    Article  ADS  Google Scholar 

  14. E. Yarevsky, S.L. Yakovlev, Å. Larson, N. Elander, Potential-splitting approach applied to the Temkin-Poet model for electron scattering off the hydrogen atom and the helium ion. J. Phys. B At. Mol. Opt. Phys. 48, 115002 (2015)

    Article  ADS  Google Scholar 

  15. M.V. Volkov, E.A. Yarevsky, S.L. Yakovlev, Potential splitting approach to the three-body Coulomb scattering problem. Europhys. Lett. 110, 30006 (2015)

    Article  ADS  Google Scholar 

  16. E. Yarevsky, S.L. Yakovlev, N. Elander, Potential splitting approach to e - H and e - He\(^{+}\). J. Phys. B At. Mol. Opt. Phys. 50, 055001 (2017)

    Article  ADS  Google Scholar 

  17. M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, New-York, 1986)

    MATH  Google Scholar 

  18. S.L. Yakovlev, M.V. Volkov, E. Yarevsky, N. Elander, The impact of sharp screening on the Coulomb scattering problem in three dimensions. J. Phys. A Math. Theor. 43, 245302 (2010)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. D.A. Varshalovich, A.N. Moskalev, V.K. Khersonsky, Quantum Theory of Angular Momentum (World Scientific, Singapore, 1989)

    MATH  Google Scholar 

  20. V.V. Kostrykin, A.A. Kvitsinsky, S.P. Merkuriev, Faddeev approach to the three-body problem in total-angular-momentum representation. Few Body Syst. 6, 97 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  21. N. Elander, E. Yarevsky, Exterior complex scaling method applied to doubly excited states of helium. Phys. Rev. A 57, 3119 (1998)

    Article  ADS  Google Scholar 

  22. N. Elander, S.B. Levin, E. Yarevsky, Convergence and quantum number assignment studies of rovibrational eigenstates in a model of predissociating NeICl van der Waals complex. Int. J. Quantum Chem. 109, 459 (2009)

    Article  ADS  Google Scholar 

  23. T.T. Gien, Accurate calculation of phase shifts for positron-\(\text{ He }^{+}\) collisions. J. Phys. B At. Mol. Opt. Phys. 34, L535 (2001)

    Article  ADS  Google Scholar 

  24. S.A. Novikov, M.W.J. Bromley, J. Mitroy, Positron scattering and annihilation from hydrogenlike ions. Phys. Rev. A 69, 052702 (2004)

    Article  ADS  Google Scholar 

  25. D.G. Green, G.F. Gribakin, Positron scattering and annihilation in hydrogenlike ions. Phys. Rev. A 88, 032708 (2013)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to P. A. Belov.

Additional information

This article belongs to the Topical Collection “The 23rd European Conference on Few-Body Problems in Physics”.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Belov, P.A., Gradusov, V.A., Volkov, M.V. et al. Potential Splitting Approach to Positron Scattering Off the Hydrogen Atom and the Positive Helium Ion. Few-Body Syst 58, 114 (2017). https://doi.org/10.1007/s00601-017-1274-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00601-017-1274-6

Navigation