Advertisement

Internal clusterization in the Coulomb few-body systems and stability of the five- and six-body systems with unit charges

  • Alexei M. FrolovEmail author
Regular Article
  • 17 Downloads

Abstract

Stability of the bound ground states in the six five-body muonic abμe2 ions (or (abμe2)) and ten six-body abcμe2 quasi-molecules is investigated. The notations a, b, c stand for the bare nuclei of three hydrogen isotopes – protium (p), deuterium (p) and tritium (t). All these systems are the Coulomb five- and six-body systems with unit charges. It is found that the ground bound S(L = 0) states are stable in all six five-body abμe2 ions and in ten six-body abcμe2 quasi-molecules. As follows from accurate variational computations of the five-body abμe2 ions their internal structure is similar to the internal structure of the negatively charged hydrogen ion H. Analogously, we show that the internal structures of the six-body neutral abcμe2 quasi-molecules are similar to the structure of the two-center H2 molecule which contains two heavy hydrogen nuclei and two bound electrons.

Graphical abstract

Keywords

Atomic Physics 

References

  1. 1.
    K. Langanke, C.A. Barnes, in Advances in Nuclear Physics, edited by J.W. Negie, E. Wogt (Spinger-Verlag, Berlin, 1998), Chap. 5 Google Scholar
  2. 2.
    R.J. Drachman, Can. J. Phys. 60, 494 (1982) ADSCrossRefGoogle Scholar
  3. 3.
    R.D. Poshusta, J. Phys. B 18, 1887 (1985) ADSCrossRefGoogle Scholar
  4. 4.
    D.M. Bishop, A.M. Frolov, Phys. Rev. A 45, 6236 (1992) ADSCrossRefGoogle Scholar
  5. 5.
    D.M. Bishop, A.M. Frolov, J. Phys. B 25, 3049 (1992) [Part II, J. Phys. B 25, 3059 1992] ADSCrossRefGoogle Scholar
  6. 6.
    A.M. Frolov, Eur. Phys. J. D 66, 212 (2012) ADSCrossRefGoogle Scholar
  7. 7.
    A.M. Frolov, Eur. Phys. J. D 63, 339 (2011) ADSCrossRefGoogle Scholar
  8. 8.
    A.M. Frolov, Eur. Phys. J. D 69, 132 (2015) ADSCrossRefGoogle Scholar
  9. 9.
    N.N. Kolesnikov, V.I. Tarasov, Yad. Fiz. 35, 609 (1982) [Sov. J. Nucl. Phys. 35, 354 1982] Google Scholar
  10. 10.
    A.M. Frolov, D.M. Wardlaw, Phys. Rev. A 78, 042506 (2008) ADSCrossRefGoogle Scholar
  11. 11.
    A.M. Frolov, D.M. Wardlaw, JETP 138, 5 (2010) Google Scholar
  12. 12.
    L.D. Landau, E.M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory, 3rd edn. (Pergamon Press, New York, 1976) Google Scholar
  13. 13.
    V.A. Fock, in Foundations of Quantum Mechanics (Nauka (Science), Moscow, 1976), Part II, Chaps. V and IV Google Scholar
  14. 14.
    H. Eyring, J. Walter, G.E. Kimball, Quantum Chemistry (John Wiley & Sons, Inc., New York, 1946) Google Scholar
  15. 15.
    R. McWeeny, B.T. Sutcliffe, in Methods of Molecular Quantum Mechanics (Academic Press, New York, 1969), Chap. 7 Google Scholar
  16. 16.
    L.W. Alvarez, H. Bradner, F.S. Crawford, Jr. J.A. Crawford, P. Falk-Vairant, M.L. Good, J.D. Gow, A.H. Rosenfeld, F. Solmitz, M.L. Stevenson, H.K. Ticho, R.D. Tripp, Phys. Rev. 105, 1127 (1957) ADSCrossRefGoogle Scholar
  17. 17.
    Ya.B. Zeldovich, A.D. Sakharov, JETP 32, 947 (1957) [Sov. Phys. JETP 5, 775 1957] Google Scholar
  18. 18.
    Ya.B. Zeldovich, S.S. Gershtein, Usp. Fiz. Nauk 71, 581 (1960) [Sov. Phys. Usp. 3, 593 1961] CrossRefGoogle Scholar
  19. 19.
    S.E. Jones, Nature 321, 127 (1986) ADSCrossRefGoogle Scholar
  20. 20.
    S.S. Gerstein, Yu.V. Petrov, L.I. Ponomarev, Usp. Fiz. Nauk 160, 3 (1990) [Sov. Phys. Usp. 33, 591 1990] CrossRefGoogle Scholar
  21. 21.
    L.I. Menshikov, L.N. Somov, Usp. Fiz. Nauk 160, 47 (1990) [Sov. Phys. Usp. 33, 616 1990] CrossRefGoogle Scholar
  22. 22.
    J.M. Blatt, V.F. Weisskopf, Theoretical Nuclear Physics, (Springer-Verlag Inc., New York, 1979) Google Scholar
  23. 23.
    V.B. Bel’jaev, S.S. Gerstein, B.N. Zakhariev, S.P. Lomnev, Zh. Eksp. Teor. Fiz. 37, 1652 (1959) [Sov. Phys. JETP 10, 1171 1959] Google Scholar
  24. 24.
    V.P. Dzhelepov, P.F. Ermolov, V.I. Moskalev, V.V. Filchenkov, Zh. Eksp. Teor. Fiz. 50, 1235 (1966) Google Scholar
  25. 25.
    V.M. Bystritsky, V.P. Dzelepov, V.I. Petruchin, A.I. Rudenko, L.N. Somov, V.M. Suvorov, V.V. Filchenkov, G. Hemnitz, N.M. Khovansky, B.A. Kohmenko, D. Horvath, Zh. Eksp. Teor. Fiz. 76, 460 (1979) Google Scholar
  26. 26.
    D.V. Balin, E.M. Maev, V.I. Medvedev, G.G. Semenchuk, Yu.N. Smirenin, A.A. Vorobyov, An.A. Vorobyov, Yu.K. Zalite, Phys. Lett. B 141, 173 1984 ADSCrossRefGoogle Scholar
  27. 27.
    W.H. Breunlich, M. Carnelli, P. Kammel, J. Marton, P. Pawlek, J. Werner, J. Emeskal, K.M. Crowe, J. Kurk, A. Janett, C. Petitjeau, R.H. Scherman, H. Bassy, W. Nauman, Phys. Rev. Lett. 53, 12 1984 CrossRefGoogle Scholar
  28. 28.
    A.I.Akhiezer, V.B. Beresteskii, in Quantum Electrodynamics, 4th edn. (Science, Moscow, 1981), Chap. 5 Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Applied MathematicsUniversity of Western OntarioLondonCanada

Personalised recommendations