The European Physical Journal A

, Volume 40, Issue 2, pp 121–126 | Cite as

Non-empirical pairing energy density functional

First order in the nuclear plus Coulomb two-body interaction
  • T. Lesinski
  • T. Duguet
  • K. Bennaceur
  • J. Meyer
Open Access


We perform systematic calculations of pairing gaps in semi-magic nuclei across the nuclear chart using the Energy Density Functional method and a non-empirical pairing functional derived, without further approximation, at lowest order in the two-nucleon vacuum interaction, including the Coulomb force. The correlated single-particle motion is accounted for by the SLy4 semi-empirical functional. Rather unexpectedly, both neutron and proton pairing gaps thus generated are systematically close to experimental data. Such a result further suggests that missing effects, i.e. higher partial waves of the NN interaction, the NNN interaction and the coupling to collective fluctuations, provide an overall contribution that is sub-leading as for generating pairing gaps in nuclei. We find that including the Coulomb interaction is essential as it reduces proton pairing gaps by up to 40%.


21.60.Jz Nuclear Density Functional Theory and extensions (includes Hartree-Fock and random-phase approximations) 21.30.Cb Nuclear forces in vacuum 21.30.Fe Forces in hadronic systems and effective interactions 21.60.De Ab initio methods 


  1. 1.
    A. Bohr, B.R. Mottelson, D. Pines, Phys. Rev. 110, 936 (1958).Google Scholar
  2. 2.
    J. Dobaczewski, W. Nazarewicz, Prog. Theor. Phys. Suppl. 146, 70 (2003).Google Scholar
  3. 3.
    P. Avogadro, F. Barranco, R.A. Broglia, E. Vigezzi, Phys. Rev. C 75, 012805 (2007).Google Scholar
  4. 4.
    H. Heiselberg, M. Hjorth-Jensen, Phys. Rep. 328, 237 (2000).Google Scholar
  5. 5.
    D.J. Dean, M. Hjorth-Jensen, Rev. Mod. Phys. 75, 607 (2003).Google Scholar
  6. 6.
    M. Baldo, H.J. Schulze, Phys. Rev. C 75, 025802 (2007).Google Scholar
  7. 7.
    K. Hebeler, A. Schwenk, B. Friman, Phys. Lett. B 648, 176 (2007).Google Scholar
  8. 8.
    M. Bender, P.-H. Heenen, P.-G. Reinhard, Rev. Mod. Phys. 75, 121 (2003).Google Scholar
  9. 9.
    P. Ring, P. Schuck, The Nuclear Many-Body Problem (Springer, Berlin, Heidelberg, 2000).Google Scholar
  10. 10.
    T. Duguet, K. Bennaceur, T. Lesinski, J. Meyer, in Opportunities with Exotic Beams, Proceedings of the 3rd ANL/MSU/JINA/INT RIA Workshop, edited by T. Duguet, H. Esbensen, K.M. Nollett, C.D. Roberts (World Scientific, 2007) p. 21Google Scholar
  11. 11.
    S.K. Bogner, T.T.S. Kuo, A. Schwenk, Phys. Rep. 386, 1 (2003).Google Scholar
  12. 12.
    A.A. Abrikosov, L.P. Gorkov, I.E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Prentice-Hall, 1963).Google Scholar
  13. 13.
    P. Nozières, Le problème à N corps (Dunod, Paris, 1963).Google Scholar
  14. 14.
    M. Baldo, M. Farine, U. Lombardo, E. Saperstein, P. Schuck, M. Zverev, Eur. Phys. J. A 18, 17 (2003).Google Scholar
  15. 15.
    S. Pankratov, M. Baldo, U. Lombardo, E. Saperstein, M. Zverev, Phys. At. Nucl. 70, 658 (2007).Google Scholar
  16. 16.
    F. Barranco, R.A. Broglia, G. Coló, G. Gori, E. Vigezzi, P.F. Bortignon, Eur. Phys. J. A 21, 57 (2004).Google Scholar
  17. 17.
    J. Terasaki, F. Barranco, R.A. Broglia, E. Vigezzi, P.F. Bortignon, Nucl. Phys. A 697, 127 (2002).Google Scholar
  18. 18.
    N. Giovanardi, F. Barranco, R.A. Broglia, E. Vigezzi, Phys. Rev. C 65, 041304 (2002).Google Scholar
  19. 19.
    G. Gori, F. Ramponi, F. Barranco, P.F. Bortignon, R.A. Broglia, G. Coló, E. Vigezzi, Phys. Rev. C 72, 011302 (2005).Google Scholar
  20. 20.
    A. Pastore, F. Barranco, R.A. Broglia, E. Vigezzi, Phys. Rev. C 78, 024315 (2008).Google Scholar
  21. 21.
    T. Duguet, T. Lesinski, Eur. Phys. J. ST 156, 207 (2008).Google Scholar
  22. 22.
    T. Lesinski, PhD Thesis, Université Lyon 1 (2008) 141-2008.Google Scholar
  23. 23.
    T. Lesinski, T. Duguet, K. Bennaceur, J. Meyer, in preparation.Google Scholar
  24. 24.
    R.B. Wiringa, V.G.J. Stoks, R. Schiavilla, Phys. Rev. C 51, 38 (1995).Google Scholar
  25. 25.
    S.K. Bogner, R.J. Furnstahl, S. Ramanan, A. Schwenk, Nucl. Phys. A 773, 203 (2006).Google Scholar
  26. 26.
    T. Duguet, Phys. Rev. C 69, 054317 (2004).Google Scholar
  27. 27.
    E. Chabanat, P. Bonche, P. Haensel, J. Meyer, R. Schaeffer, Nucl. Phys. A 635, 231 (1998).Google Scholar
  28. 28.
    K. Hebeler, T. Duguet, T. Lesinski, A. Schwenk, arXiv: 0904.3152.Google Scholar
  29. 29.
    T. Lesinski, BSLHFB code: HFB computer code in a spherical Bessel functions basis, 2008, unpublished.Google Scholar
  30. 30.
    T. Duguet, P. Bonche, P.-H. Heenen, J. Meyer, Phys. Rev. C 65, 014310 (2001).Google Scholar
  31. 31.
    M. Stoitsov, J. Dobaczewski, R. Kirchner, W. Nazarewicz, J. Terasaki, Phys. Rev. C 76, 014308 (2007).Google Scholar
  32. 32.
    T. Lesinski, M. Bender, K. Bennaceur, T. Duguet, J. Meyer, Phys. Rev. C 76, 014312 (2007).Google Scholar
  33. 33.
    P.E. Nemirovsky, Y.V. Adamchuk, Nucl. Phys. 39, 551 (1962).Google Scholar
  34. 34.
    T. Lesinski, K. Bennaceur, T. Duguet, J. Meyer, Phys. Rev. C 74, 044315 (2006).Google Scholar
  35. 35.
    M. Anguiano, J.L. Egido, L.M. Robledo, Nucl. Phys. A 683, 227 (2001).Google Scholar
  36. 36.
    S. Goriely, M. Samyn, J.M. Pearson, Nucl. Phys. A 773, 279 (2006).Google Scholar
  37. 37.
    M. Yamagami, Y.R. Shimizu, Phys. Rev. C 77, 064319 (2008).Google Scholar
  38. 38.
    S.K. Bogner, A. Schwenk, R.J. Furnstahl, A. Nogga, Nucl. Phys. A 763, 59 (2005).Google Scholar
  39. 39.
    L. Coraggio, N. Itaco, A. Covello, A. Gargano, T.T.S. Kuo, Phys. Rev. C 68, 034320 (2003).Google Scholar
  40. 40.
    R. Roth, P. Papakonstatinou, N. Paar, H. Hergert, T. Neff, H. Feldmeier, Phys. Rev. C 73, 044312 (2006).Google Scholar
  41. 41.
    B.A. Brown, Phys. Rev. C 58, 220 (1998).Google Scholar
  42. 42.
    F. Barranco, P.F. Bortignon, R.A. Broglia, G. Coló, P. Schuck, E. Vigezzi, X. Viñas, Phys. Rev. C 72, 054314 (2005).Google Scholar

Copyright information

© The Author(s) 2009

Open Access This 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 source are credited.

Authors and Affiliations

  • T. Lesinski
    • 1
  • T. Duguet
    • 2
    • 3
  • K. Bennaceur
    • 1
  • J. Meyer
    • 1
  1. 1.Université de Lyon - Lyon; Université Lyon 1 - Villeurbanne; CNRS/IN2P3; Institut de Physique Nucléaire de LyonLyonFrance
  2. 2.CEA, Centre de SaclayIRFU/Service de Physique NucléaireGif-sur-YvetteFrance
  3. 3.National Superconducting Cyclotron Laboratory and Department of Physics and AstronomyMichigan State UniversityEast LansingUSA

Personalised recommendations