Hyperfine Interactions

, Volume 228, Issue 1–3, pp 85–89 | Cite as

Four-body calculations of elastic scattering in H–H̄ collisions

  • Konrad PiszczatowskiEmail author
  • Alexei Voronin
  • Piotr Froelich


We present a nonadiabatic treatment of the hydrogen-antihydrogen system. The technique used to describe H- H̄ collisions is based on the coupled rearrangement channels method. Within this approach the total, nonadiabatic wave function of the system is divided into two parts: an inner and an outer one. To describe the inner part a set of square-integrable 4-body functions is used. These functions are obtained by a diagonalization of the total Hamiltonian projected on a chosen L 2 subspace, they explicitly contain components of various arrangement channels expressed in terms of corresponding Jacobi coordinates. The outer part of the total wave function reflects its asymptotic character. Our procedure leads to the system of non-local integro-differential equations that are solved iteratively and simultaneously determine both the shape of the outer part of the wave function and the coefficients in the four-body expansion of the inner part. Using this formalism we perform the one-channel calculation of the elastic scattering to obtain the S-matrix and nonadiabatic scattering length.


Hydrogen-antihydrogen interaction Hydrogen-antihydrogen collisions Nonadiabatic scattering theory 


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  1. 1.
    The ALPHA Collaboration: Nat. Phys. 7, 558 (2011)Google Scholar
  2. 2.
    Amole, C., Ashkezari, M.D., Baquero-Ruiz, M., Bertsche, W., Bowe, P.D., Butler, E., Capra, A., Cesar, C.L., Charlton, M., Deller, A., et al.: Nature 483, 439 (2012)CrossRefADSGoogle Scholar
  3. 3.
    The ALPHA Collaboration, Charman, A.E.: Nat. Commun. 4, 1785 (2013)Google Scholar
  4. 4.
    Froelich, P.: Adv. Quantum Chem. 41, 185 (2002)CrossRefADSGoogle Scholar
  5. 5.
    Kołos, W., Morgan, D.L., Schrader, D.M., Wolniewicz, L.: Phys. Rev. A 11, 1792 (1975)CrossRefADSGoogle Scholar
  6. 6.
    Froelich, P., Jonsell, S., Saenz, A., Zygelman, B., Dalgarno, A.: Phys. Rev. Lett. 84, 4577 (2000)CrossRefADSGoogle Scholar
  7. 7.
    Jonsell, S., Saenz, A., Froelich, P., Zygelman, B., Dalgarno, A.: Phys. Rev. A 64, 052712 (2001)CrossRefADSGoogle Scholar
  8. 8.
    Froelich, P., Jonsell, S., Saenz, A., Eriksson, S., Zygelman, B., Dalgarno, A.: Phys. Rev. A 70, 022509 (2004)CrossRefADSGoogle Scholar
  9. 9.
    Zygelman, B., Saenz, A., Froelich, P., Jonsell, S.: Phys. Rev. A 69, 042715 (2004)CrossRefADSGoogle Scholar
  10. 10.
    Armour, E., Chamberlain, C.: Few-Body Syst. 31, 101 (2002)Google Scholar
  11. 11.
    Liu, Y., Martin, G.D.R., Armour, E.A.D., Chamberlain, C.W.: Nucl. Instr. Meth. B 221, 1 (2004)CrossRefADSGoogle Scholar
  12. 12.
    Sinha, P., Ghosh, A.: Europhys. Lett. 49, 558 (2000)CrossRefADSGoogle Scholar
  13. 13.
    Voronin, A., Carbonell, J.: Hyperfine Interact 115, 143 (1998)CrossRefADSGoogle Scholar
  14. 14.
    Voronin, A., Carbonell, J.: Nucl. Inst. Methods B 214, 139 (2004)CrossRefADSGoogle Scholar
  15. 15.
    Zhao, J., Corless, R.M.: App. Math. Comput. 177, 271 (2006)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Open AccessThis article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

Authors and Affiliations

  • Konrad Piszczatowski
    • 1
    Email author
  • Alexei Voronin
    • 2
  • Piotr Froelich
    • 1
  1. 1.Department of Chemistry – Ångström LaboratoryUppsala UniversityUppsalaSweden
  2. 2.P.N. Lebedev Physical InstituteMoscowRussia

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