Advertisement

Energy Density Functional Theory in Atomic and Nuclear Physics

  • M. Baldo
Chapter

Abstract

Ab initio calculations have been developed in atomic and molecular physics, as well as in nuclear physics. They are based on theoretical and numerical methods that are common to all fields. One may mention the Monte Carlo method, in different formulations, and the Configuration Interaction scheme. Despite the enormous progress achieved along the years, these methods are limited to systems of not too large number of particles, because the numerical effort at increasing number of particles becomes rapidly too demanding even for the most advanced computers. At the same time, several accurate approximations to the many-body problem have been perfected and applied to different systems. One may mention the cluster expansion method and the variational method. The numerical complexity of these schemes becomes more and more demanding as the number of particle increases. At a more phenomenological level the Energy Density Functional (EDF) approach offers a simpler scheme that can be applied to systems of virtually arbitrary number of particles. For instance, in nuclear physics it is commonly applied throughout the nuclear mass table. In this paper, we will present a general discussion on the EDF method, the analogy and the differences between the atomic and molecular EDF on one hand and the nuclear EDF on the other. Special emphasis is devoted to the Kohn–Sham method and to nuclear structure studies.

References

  1. 1.
    P.C. Hohenberg, W. Kohn, Phys. Rev. 136, B864 (1964).  https://doi.org/10.1103/PhysRev.136.B864
  2. 2.
    J. Messud, M. Bender, E. Suraud, Phys. Rev. C 80, 054314 (2009).  https://doi.org/10.1103/PhysRevC.80.054314
  3. 3.
    J. Engel, Phys. Rev. C 75, 014306 (2007).  https://doi.org/10.1103/PhysRevC.75.014306
  4. 4.
    N. Barnea, Phys. Rev. C 76, 067302 (2007).  https://doi.org/10.1103/PhysRevC.76.067302
  5. 5.
    T. Lesinski, Phys. Rev. C 89, 044305 (2014).  https://doi.org/10.1103/PhysRevC.89.044305
  6. 6.
    M. Dutra, O. Lourenço, J.S. Sá Martins, A. Delfino, J.R. Stone, P.D. Stevenson, Phys. Rev. C 85, 035201 (2012).  https://doi.org/10.1103/PhysRevC.85.035201
  7. 7.
    J. Dechargé, D. Gogny, Phys. Rev. C 21, 1568 (1980).  https://doi.org/10.1103/PhysRevC.21.1568
  8. 8.
    J.P. Perdew, K. Burke, Y. Wang, Phys. Rev. B 54, 16533 (1996).  https://doi.org/10.1103/PhysRevB.54.16533
  9. 9.
    J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996); [Erratum Phys. Rev. Lett. 78, 1396 (1997)].  https://doi.org/10.1103/PhysRevLett.77.3865
  10. 10.
    S.A. Fayans, S.V. Tolokonnikov, E.L. Trykov, D. Zawischa, Nucl. Phys. A 676(1), 49 (2000).  https://doi.org/10.1016/S0375-9474(00)00192-5
  11. 11.
    S.A. Fayans, D. Zawischa, Int. J. Mod. Phys. B 15(10–11), 1684 (2001).  https://doi.org/10.1142/S0217979201006203
  12. 12.
    M. Baldo, P. Schuck, X.V. nas, Phys. Lett. B 663(5), 390 (2008).  https://doi.org/10.1016/j.physletb.2008.04.013
  13. 13.
    L.M. Robledo, M. Baldo, P. Schuck, X. Viñas, Phys. Rev. C 77, 051301 (2008).  https://doi.org/10.1103/PhysRevC.77.051301
  14. 14.
    X. Vinãs, L.M. Robledo, M. Baldo, P. Schuck, Int. J. Mod. Phys. E 18(04), 935 (2009).  https://doi.org/10.1142/S0218301309013075
  15. 15.
    L.M. Robledo, M. Baldo, P. Schuck, X. Viñas, Phys. Rev. C 81, 034315 (2010).  https://doi.org/10.1103/PhysRevC.81.034315
  16. 16.
    M. Baldo, L. Robledo, P. Schuck, X.V. nas, J. Phys. G 37(6), 064015 (2010).  https://doi.org/10.1088/0954-3899/37/6/064015
  17. 17.
    M. Baldo, L.M. Robledo, P. Schuck, X. Viñas, Phys. Rev. C 87, 064305 (2013).  https://doi.org/10.1103/PhysRevC.87.064305
  18. 18.
    M. Baldo, L.M. Robledo, P. Schuck, X. Viñas, Phys. Rev. C 95, 014318 (2017).  https://doi.org/10.1103/PhysRevC.95.014318
  19. 19.
    A. Akmal, V.R. Pandharipande, D.G. Ravenhall, Phys. Rev. C 58, 1804 (1998).  https://doi.org/10.1103/PhysRevC.58.1804
  20. 20.
    G. Audi, A.H. Wapstra, C. Thibault, Nucl. Phys. A 729(1), 337 (2003); The 2003 NUBASE and Atomic Mass Evaluations.  https://doi.org/10.1016/j.nuclphysa.2003.11.003
  21. 21.
    M. Baldo, P.F. Bortignon, G. Colò, D. Rizzo, L. Sciacchitano, J. Phys. G 42(8), 085109 (2015).  https://doi.org/10.1088/0954-3899/42/8/085109

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Istituto Nazionale di Fisica NucleareSezione di CataniaCataniaItaly

Personalised recommendations