Regularization of singular terms in the N¯ potential model

  • O. D. Dalkarov
  • A. Yu. VoroninEmail author
Original Article


We suggest a method of singular terms regularization in a potential model of the N¯ interaction. This method is free from uncertainties related to the usual cut-off procedure and is based on the fact that, in the presence of sufficiently strong short-range annihilation, N and ¯ never approach close enough to each other. In such a case the low-energy scattering is shown to be fully determined by the OBEP tail, while any details of the short-range core of the N¯ interaction are excluded from the observables. The obtained results for S- and P-wave scattering lengths are in agreement with the well-established theoretical models.


13.75.Cs Nucleon-nucleon interactions (including antinucleons, deuterons, etc.) 21.30.-x Nuclear forces 21.30.Fe Forces in hadronic systems and effective interactions 24.10.Ht Optical and diffraction models 


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  1. 1.
    R.J.N. Phillips, Rev. Mod. Phys. 39, 681 (1967).CrossRefGoogle Scholar
  2. 2.
    I.S. Shapiro, Phys. Rep. C 35, 129 (1978).CrossRefGoogle Scholar
  3. 3.
    O.D. Dalkarov, F. Myhrer, Nuovo Cimento A 40, 152 (1977).Google Scholar
  4. 4.
    T. Ueda, Prog. Theor. Phys. 62, 1670 (1979).Google Scholar
  5. 5.
    J. Cote, M. Lacombe, B. Loiseau, B. Moussallam, R. Vinh Mau, Phys. Rev. Lett. 48, 1319 (1982).CrossRefGoogle Scholar
  6. 6.
    J. Carbonell, O. Dalkarov, K. Protasov, I. Shapiro, Nucl. Phys. A 535, 651 (1991).CrossRefGoogle Scholar
  7. 7.
    M. Kohno, W. Weise, Nucl. Phys. A 454, 429 (1986).CrossRefGoogle Scholar
  8. 8.
    C.B. Dover, J.-M. Richard, Phys. Rev. C 21, 1466 (1980).CrossRefGoogle Scholar
  9. 9.
    M. Pignone, M. Lacombe, B. Loiseau, R. Vinh Mau, Phys. Rev. C 50, 2710 (1994). CrossRefGoogle Scholar
  10. 10.
    B. El-Bennich, M. Lacombe, B. Loiseau, R. Vinh Mau, Phys. Rev. C 59, 2313 (1999).CrossRefGoogle Scholar
  11. 11.
    W.W. Buck, C.B. Dover, J.-M. Richard, Ann. Phys. (N.Y.) 121, 47 (1979).CrossRefGoogle Scholar
  12. 12.
    A. Martin, Antinucleon-Nucleon Scattering at LEAR, Proceedings of the 8th Winter Course, Folgaria, Italy, edited by M. Gibilisco, G. Preparata, A. Zenoni (World Scientific, Singapore, 1994).Google Scholar
  13. 13.
    C. Amsler, Phys. Lett. B 297, 214 (1992).CrossRefGoogle Scholar
  14. 14.
    A. Abele, Eur. Phys. J. C 17, 583 (2000).CrossRefGoogle Scholar
  15. 15.
    D. Gotta, Nucl. Phys. A 660, 283 (1999).CrossRefGoogle Scholar
  16. 16.
    M. Augsburger, Nucl.Phys. A 658, 149 (1999).CrossRefGoogle Scholar
  17. 17.
    F. Iazzi, Phys. Lett B 475, 378 (2000).CrossRefGoogle Scholar
  18. 18.
    A. Bianconi, Phys. Lett B 483, 353 (2000).CrossRefGoogle Scholar
  19. 19.
    F. Nichitiu, Phys. Lett B 545, 261 (2002).CrossRefGoogle Scholar
  20. 20.
    P. Montagna, Nucl. Phys. A 700, 159 (2002).CrossRefGoogle Scholar
  21. 21.
    T. Walcher, Annu. Rev. Nucl. Part. Sci. 38, 67 (1988).CrossRefGoogle Scholar
  22. 22.
    E. Klempt, F. Bradamante, A. Martin, J.-M. Richard, Phys. Rep. 368, 119 (2002).CrossRefGoogle Scholar
  23. 23.
    J.Z. Bai, Phys. Rev. Lett. 91, 022001 (2003)CrossRefPubMedGoogle Scholar
  24. 24.
    L.D. Landau, E.M. Lifshitz, Quantum Mechanics (Pergamon Press, New York, 1977).Google Scholar
  25. 25.
    J. Carbonell, Rev. Mex. Fis. 47, 70 (2001)Google Scholar
  26. 26.
    A.Yu. Voronin, Phys. Rev. A 67, 062706 (2003)CrossRefGoogle Scholar
  27. 27.
    M.F. Mott, H.S.W. Massey, The Theory of Atomic Collisions (The Clarendon Press, Oxford, 1965).Google Scholar
  28. 28.
    G.N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge University Press, 1922).Google Scholar
  29. 29.
    J.E. Lennard-Jones, Proc. R. Soc. London, Ser. A 156, 6 (1936).Google Scholar
  30. 30.
    R. Cote, H. Friedrich, J. Trost, Phys. Rev. A 56, 1781 (1997).CrossRefGoogle Scholar
  31. 31.
    H.Friedrich, G. Jacoby, C.G. Meister, Phys. Rev. A 65, 032902.Google Scholar
  32. 32.
    V.V. Babikov, The Method of Phase Functions in Quantum Mechanics (Nauka, Moscow, 1967) (in Russian).Google Scholar
  33. 33.
    J. Carbonell, J.M. Richard, S. Wycech, Z. Phys. A 343, 325 (1992).CrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag 2005

Authors and Affiliations

  1. 1.P.N. Lebedev Physical InstituteMoscowRussia

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