Nuclear Level Calculation

Part of the Springer Theses book series (Springer Theses)


In this chapter, we will review the nuclear many-body physics needed in the study of the electric dipole moment (EDM). We will first see the ab initio calculations of the EDMs of light nuclei (deuteron and He). We will then review in detail the screening of the P, CP-odd nuclear EDM in atomic system pointed by Schiff and the formula of the nuclear Schiff moment as important P, CP-odd mechanism contributing to the atomic EDM. We will next present the derivation of the leading P, CP-odd nuclear moments (the nuclear EDM, Schiff moment and magnetic quadrupole moment) for heavy nuclei within a simple model. After this simple calculation, a sophisticated mean-field approach is reviewed, and its results for the evaluation of the nuclear Schiff moments of heavy nuclei (Xe, Hg, Rn and Ra) are presented. We finally summarize the nuclear level P, CP-odd moments for all nuclei relevant to the discussions in this chapter. Note that the electric charge \(e\) is defined as \(e=|e|>0\) in this chapter, in contrast to the previous chapters.


Electric Dipole Moment Atomic System Random Phase Approximation Valence Neutron Valence Nucleon 


  1. 1.
    I.B. Khriplovich, Phys. Lett. B 444, 98 (1998)Google Scholar
  2. 2.
    F.J.M. Farley et al., Phys. Rev. Lett. 93, 052001 (2004)Google Scholar
  3. 3.
    Y.K. Semertzidis et al., AIP Conf. Proc. 698, 200 (2004)Google Scholar
  4. 4.
    Y.F. Orlov, W.M. Morse, Y.K. Semertzidis, Phys. Rev. Lett. 96, 214802 (2006)Google Scholar
  5. 5.
    L.I. Schiff, Phys. Rev. 132, 2194 (1963)Google Scholar
  6. 6.
    C.-P. Liu, R.G.E. Timmermans, Phys. Rev. C 70, 055501 (2004)Google Scholar
  7. 7.
    I.B. Khriplovich, S.K. Lamoreaux, CP Vioaltion Without Strangeness (Springer, Berlin, 1997)CrossRefGoogle Scholar
  8. 8.
    J.S.M. Ginges, V.V. Flambaum, Phys. Rept. 397, 63 (2004)Google Scholar
  9. 9.
    I. Stetcu, C.-P. Liu, J.L. Friar, A.C. Hayes, P. Navratil, Phys. Lett. B 665, 168 (2008)Google Scholar
  10. 10.
    I.B. Khriplovich, R.A. Korkin, Nucl. Phys. A 665, 365 (2000)Google Scholar
  11. 11.
    R.B. Wiringa, V.G.J. Stoks, R. Schiavilla, Phys. Rev. C 51, 38 (1995)Google Scholar
  12. 12.
    V.G.J. Stoks, R.A.M. Klomp, C.P.F. Terheggen, J.J. de Swart, Phys. Rev. C 49, 2950 (1994)Google Scholar
  13. 13.
    P. Navratil, J.P. Vary, B.R. Barrett, Phys. Rev. Lett. 84, 5728 (2000)Google Scholar
  14. 14.
    P. Navratil, J.P. Vary, B.R. Barrett, Phys. Rev. C 62, 054311 (2000)Google Scholar
  15. 15.
    R. Machleidt, F. Sammarruca, Y. Song, Phys. Rev. C 53, 1483 (1996)Google Scholar
  16. 16.
    P. Navratil, Few Body Syst. 41, 117 (2007)Google Scholar
  17. 17.
    D.R. Entem, R. Machleidt, Phys. Rev. C 68, 041001(R) (2003)Google Scholar
  18. 18.
    U. van Kolck, Phys. Rev. C 49, 2932 (1994)Google Scholar
  19. 19.
    E. Epelbaum, A. Nogga, W. Glöckle, H. Kamada, U.-G. Meissner, H. Witala, Phys. Rev. C 66, 064001 (2002)Google Scholar
  20. 20.
    V. Spevak, N. Auerbach, V.V. Flambaum, Phys. Rev. C 56, 1357 (1997)Google Scholar
  21. 21.
    O.P. Sushkov, V.V. Flambaum, I.B. Khriplovich, Zh. Eksp. Teor. Fiz. 87, 1521 (1984) [Sov. Phys. JETP 60, 873 (1984)]Google Scholar
  22. 22.
    J. Bardeen, L.N. Cooper, J.R. Schrieffer, Phys. Rev. 106, 162 (1957)Google Scholar
  23. 23.
    J. Bardeen, L.N. Cooper, J.R. Schrieffer, Phys. Rev. 108, 1175 (1957)Google Scholar
  24. 24.
    V.V. Flambaum, I.B. Khriplovich, O.P. Sushkov, Phys. Lett. B 162, 213 (1985)Google Scholar
  25. 25.
    V.V. Flambaum, I.B. Khriplovich and O.P. Sushkov. Nucl. Phys. A 449, 750 (1985)Google Scholar
  26. 26.
    V.F. Dmitriev, R.A. Senkov, N. Auerbach, Phys. Rev. C 71, 035501 (2005)Google Scholar
  27. 27.
    V.F. Dmitriev, R.A. Senfkov, Phys. Rev. Lett. 91, 212303 (2003)Google Scholar
  28. 28.
    J.H. de Jesus, J. Engel, Phys. Rev. C 72, 045503 (2005)Google Scholar
  29. 29.
    S. Ban, J. Dobaczewski, J. Engel, A. Shukla, Phys. Rev. C 82, 015501 (2010)Google Scholar
  30. 30.
    J. Engel, M. Bender, J. Dobaczewski, J.H. de Jesus, P. Olbratowski, Phys. Rev. C 68, 025501 (2003)ADSCrossRefGoogle Scholar
  31. 31.
    J. Dobaczewski, J. Engel, Phys. Rev. Lett. 94, 232502 (2005)ADSCrossRefGoogle Scholar
  32. 32.
    J. Dobaczewski, W. Satula, B. Carlsson, J. Engel, P. Olbratowski, P. Powalowski, M. Sadziak, N. Schunk, A. Staszczak, M. Stoitsov et al., Comput. Phys. Commun. 180, 2361 (2009)ADSCrossRefGoogle Scholar
  33. 33.
    P.-G. Reinhard, D.J. Dean, W. Nazarewicz, J. Dobaczewski, J.A. Maruhn, M.R. Strayer, Phys. Rev. C 60, 014316 (1999)ADSCrossRefGoogle Scholar
  34. 34.
    J. Bartel, P. Quentin, M. Brack, C. Guet, H.B. Hakansson, Nucl. Phys. A 386, 70 (1982)ADSCrossRefGoogle Scholar
  35. 35.
    E. Chabanat, P. Bonche, P. Haensel, J. Meyer, R. Schaeffer, Nucl. Phys. A 635, 231 (1998)ADSCrossRefGoogle Scholar
  36. 36.
    M. Beiner, H. Flocard, N. Van Giai, P. Quentin, Nucl. Phys. A 238, 29 (1975)ADSCrossRefGoogle Scholar
  37. 37.
    N. Yoshinaga et al., Talk given at 4th International conference on "Fundamental Physics Using Atoms", Osaka University, August 2010 (URL:

Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Research Center for Nuclear PhysicsOsaka UniversityIbarakiJapan

Personalised recommendations