Shell Structure



Although the bulk properties of nuclei such as the mass and size, and also fission and the compound nucleus reactions suggest that the nucleus behaves like a liquid, there exist characteristic properties which cannot be understood from such a point of view. The existence of magic numbers in various phenomena is the most evident example, suggesting the shell structure. The magic numbers appear in various systems in nature. The existence of the noble gases in the periodic table of the elements is the most popular example. Contrary to those magic numbers for atoms, which are associated with the long range Coulomb interaction, the magic numbers for nuclei which originate from the short range force differ in numbers. Also, the spin–orbit interaction plays a crucial role in the magic numbers for nuclei. In this chapter we discuss how the magic numbers arise, and discuss the spin and parity properties of the nuclei in the vicinity of magic numbers. Although the shell model which is based on the mean-field theory succeeds, it is suggested that it is important to take into account the effects of the residual interaction, i.e., the pairing correlation in order to explain the details of the nuclear phenomena. As an example of the current topics, we also discuss the present status of the research of superheavy elements which are stabilized by shell effects.


Orbit Interaction Magic Number Neutron Number Superheavy Nucleus Superheavy Element 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    D.R. Tilley et al., Nucl. Phys. A 708, 3 (2002)ADSCrossRefGoogle Scholar
  2. 2.
    National Nuclear Data Center.
  3. 3.
    C.M. Lederer, V. Shirley, Table of Isotopes, 7th edn. (Wiley, New York, 1978)Google Scholar
  4. 4.
    A. Csótó, G.M. Hale, Phys. Rev. C 55, 536 (1997)ADSCrossRefGoogle Scholar
  5. 5.
    M.A. Preston, Physics of the Nucleus (Addison-Wesley, London, 1962)MATHGoogle Scholar
  6. 6.
    A.M. Lane, R.G. Thomas, Rev. Mod. Phys. 30, 257 (1958)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    T. Otsuka, T. Suzuki, R. Fujimoto, H. Grawe, Y. Akaishi, Phys. Rev. Lett. 95, 232502 (2005)ADSCrossRefGoogle Scholar
  8. 8.
    W.D. Knight et al., Phys. Rev. Lett. 52, 2141 (1984)ADSCrossRefGoogle Scholar
  9. 9.
    I. Hamamoto, Nucl. Phys. A 126, 545 (1969); 141, 1 (1970); 155, 362 (1970)Google Scholar
  10. 10.
    A. Bohr, B.R. Mottelson, Nuclear Structure, vol. II (Benjamin, New York, 1975)MATHGoogle Scholar
  11. 11.
    N.J. Stone, At. Data Nucl. Data Tables 90, 75 (2005)ADSCrossRefGoogle Scholar
  12. 12.
    A. Arima, H. Horie, Prog. Theor. Phys. 12, 623 (1954)ADSCrossRefGoogle Scholar
  13. 13.
    T. Yamazaki, T. Nomura, S. Nagamiya, T. Katou, Phys. Rev. Lett. 25, 547 (1970)ADSCrossRefGoogle Scholar
  14. 14.
    F. Halzen, A.D. Martin, QUARKS and LEPTONS (Wiley, New York, 1984)Google Scholar
  15. 15.
    A. Bohr, B.R. Mottelson, Nuclear Structure, vol. I (Benjamin, New York, 1969)MATHGoogle Scholar
  16. 16.
    A. Molinari, M.B. Johnson, H.A. Bethe, W.M. Alberico, Nucl. Phys. A 239, 45 (1975)ADSCrossRefGoogle Scholar
  17. 17.
    G.E. Brown, Unified Theory of Nuclear Models and Forces (North-Holland, Amsterdam, 1967)Google Scholar
  18. 18.
    Yu. Oganessian, J. Phys. G 34, R165 (2007)ADSCrossRefGoogle Scholar
  19. 19.
    Here, we quote some of the related theoretical papers. (a) Papers concerning stochastic differential equations: Y. Aritomo, T. Wada, M. Ohta, Y. Abe, Phys. Rev. C 59, 796 (1999); C. Shen, G. Kosenko, Y. Abe, Phys. Rev. C 66, 061602 (2002); Y. Abe, D. Boilley, G. Kosenko, C. Shen, Acta Phys. Pol. B 34, 2091 (2003); Y. Aritomo, Phys. Rev. C 80, 064604 (2009); V. Zagrebaev, W. Greiner, Phys. Rev. C 78, 034610 (2008); (b) Paper on the quantum diffusion theory: N. Takigawa, S. Ayik, K. Washiyama, S. Kimura, Phys. Rev. C 69, 054605 (2004); (c) Paper using coupled-channels calculations: N. Rowley, N. Grar, K. Hagino, Phys. Lett. B 632, 243 (2006)Google Scholar
  20. 20.
    K. Morita et al., J. Phys. Soc. Jpn. 81, 103201 (2012)ADSCrossRefGoogle Scholar

Copyright information

© Springer Japan 2017

Authors and Affiliations

  1. 1.Department of PhysicsGraduate School of Science, Tohoku UniversitySendaiJapan
  2. 2.Center for Computational SciencesUniversity of TsukubaTsukubaJapan

Personalised recommendations