Density Functional Formalism in Relativistic Nuclear Mean Field Theory

  • M. Centelles
Part of the NATO ASI Series book series (NSSB, volume 337)


The description of nuclear structure has been traditionally approached by solving a non-relativistic many-body Schrödinger equation which involves nucleons interacting through static potentials. This has been done within the Hartree-Fock (HF) approximation, where the many-body wave function of the system is replaced by a Slater determinant of single-particle wave functions obtained in a self-consistent way from the mean field produced by the nucleons themselves. Important progress has also been made in the microscopic approach to nuclear matter, mainly along the lines of the Brueckner-Bethe-Goldstone many-body theory [1]. A quantitative microscopic description of finite nuclei, however, has so far only been possible on a phenomenological level. Effective density-dependent interactions with only a few free adjustable parameters, like the Skyrme force [2], have been constructed in order to account for the observed nuclear properties. Such density-dependent Hartree-Fock (DDHF) scheme has been able not only to yield excellent ground-state properties of both spherical and deformed nuclei, but also to describe dynamical phenomena, like fission, heavy ion collisions at low and intermediate energy or nuclear excitation spectra [3].


Nuclear Matter Skyrme Force Gradient Expansion Gradient Correction Relativistic Mean Field 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    D. W. L. Sprung, Adv. Nucl. Phys. 5, 225 (1972).CrossRefGoogle Scholar
  2. R. Machleidt, Adv. Nucl. Phys. 19, 189 (1989).CrossRefGoogle Scholar
  3. [2]
    T. H. R. Skyrme, Philos. Mag. 1, 1043 (1956).ADSzbMATHCrossRefGoogle Scholar
  4. D. Vautherin and D. M. Brink, Phys. Rev. C5, 626 (1972).ADSGoogle Scholar
  5. [3]
    P. Quentin and H. Flocard, Ann. Rev. Nucl. Part. Sci. 28, 523 (1978).ADSCrossRefGoogle Scholar
  6. J. W. Negele, Rev. Mod. Phys. 54, 913 (1982).ADSCrossRefGoogle Scholar
  7. [4]
    J. D. Walecka, Ann. Phys. (N.Y.). 83, 491 (1974).ADSCrossRefGoogle Scholar
  8. [5]
    S. A. Chin, Ann. Phys. (N.Y.). 108, 301 (1977).ADSCrossRefGoogle Scholar
  9. [6]
    B. D. Serot and J. D. Walecka, Adv. Nucl. Phys. 16, 1 (1986).Google Scholar
  10. [7]
    C. J. Horowitz and B. D. Serot, Nucl. Phys. A368, 503 (1981).ADSGoogle Scholar
  11. [8]
    A. Bouyssy, S. Marcos, and Pham Van Thieu, Nucl. Phys. A422, 541 (1984).ADSGoogle Scholar
  12. [9]
    P.-G. Reinhard, M. Rufa, J. Maruhn, W. Greiner, and J. Friedrich, Z. Phys. A323, 13 (1986).ADSGoogle Scholar
  13. [10]
    Y. K. Gambhir, P. Ring, and A. Thimet, Ann. Phys. (N.Y.). 198, 132 (1990).ADSCrossRefGoogle Scholar
  14. [11]
    P.-G. Reinhard, Rep. Prog. Phys. 52, 439 (1989).ADSCrossRefGoogle Scholar
  15. [12]
    B. D. Serot, Rep. Prog. Phys. 55, 1855 (1992).ADSCrossRefGoogle Scholar
  16. [13]
    A. Bouyssy, J.-F. Mathiot, N. Van Giai, and S. Marcos, Phys. Rev. C36, 380 (1987).ADSGoogle Scholar
  17. P. Bernardos, V. N. Fomenko, N. Van Giai, et al., Phys. Rev. C (in press).Google Scholar
  18. [14]
    L. S. Celenza and C.M. Shakin, Relativistic Nuclear Physics: Theories of Structure and Scattering (World Scientific, Singapore, 1986).Google Scholar
  19. H. Müther, R. Machleidt, and R. Brockmann, Phys. Rev. C42, 1981 (1990).ADSGoogle Scholar
  20. S. Lundqvist and N. H. March (eds.), Theory of the Inhornogeneous Electron Gas (Plenum, New York, 1983).Google Scholar
  21. R. O. Jones and O. Gunnarsson, Rev. Mod. Phys. 61, 689 (1989).Google Scholar
  22. [16]
    R. M. Dreizler and J. da Providencia (eds.), Density Functional Methods in Physics, Vol. 123 NATO ASI Series B (Plenum, New York, 1985).Google Scholar
  23. [17]
    R. M. Dreizler and E. K. U. Gross, Density Functional Theory (Springer, Berlin, 1990).zbMATHCrossRefGoogle Scholar
  24. [18]
    R. W. Hasse, R. Arvieu, and P. Schuck (eds.), Workshop on Semiclassical Methods in Nuclear Physics, J. de Phys. Colloque C6 (1984).Google Scholar
  25. I. Zh. Petkov and M. V. Stoitsov, Nuclear Density Functional Theory (Clarendon Press, Oxford, 1991).Google Scholar
  26. [19]
    P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964).MathSciNetADSCrossRefGoogle Scholar
  27. [20]
    R. A. Berg and L. Wilets, Phys. Rev. 101, 201 (1956).ADSzbMATHCrossRefGoogle Scholar
  28. R. J. Lombard, Ann. Phys. (N.Y.) 77, 380 (1973).ADSCrossRefGoogle Scholar
  29. [21]
    P. Ring and P. Schuck, The Nuclear Many-Body Problem (Springer, Berlin, 1980).CrossRefGoogle Scholar
  30. [22]
    O. Bohigas, X. Campi, H. Krivine, and J. Treiner, Phys. Lett. B64, 381 (1976).ADSGoogle Scholar
  31. [23]
    M. Brack, C. Guet, and H.-B. Håkansson, Phys. Rep. 123, 275 (1985).ADSCrossRefGoogle Scholar
  32. [24]
    M. Centelles, M. Pi, X. Vinas, F. Gardas, and M. Barranco, Nucl. Phys. A510, 397 (1990).ADSGoogle Scholar
  33. [25]
    W. D. Myers and W. J. Swiatecki, Ann. Phys. (N.Y.). 55, 395 (1969).ADSCrossRefGoogle Scholar
  34. W. D. Myers and W. J. Swiatecki, Ann. Phys. (N.Y.) 84, 186 (1974).ADSCrossRefGoogle Scholar
  35. [26]
    B. Grammaticos and A. Voros, Ann. Phys. (N.Y.). 123, 359 (1979).MathSciNetADSCrossRefGoogle Scholar
  36. B. Grammaticos and A. Voros, Ann. Phys. (N.Y.) 129, 153 (1980).MathSciNetADSCrossRefGoogle Scholar
  37. [27]
    D. R. Murphy, Phys. Rev. A24, 1682 (1981).ADSGoogle Scholar
  38. [28]
    M. S. Vallarta and N. Rosen, Phys. Rev. 41, 708 (1932).ADSzbMATHCrossRefGoogle Scholar
  39. [29]
    A. H. MacDonald and S. H. Vosko, J. Phys. C12, 2977 (1979).ADSGoogle Scholar
  40. M. V. Ramana and A. K. Rajagopal, Adv. Chem. Phys. 54, 231 (1983).CrossRefGoogle Scholar
  41. [30]
    E. Engel and R. M. Dreizler, Phys. Rev. A35, 3607 (1987).ADSGoogle Scholar
  42. E. Engel, H. Müller, and R. M. Dreizler, Phys. Rev. A39, 4873 (1989).ADSGoogle Scholar
  43. W. F. Pohlner and R. M. Dreizler, Phys. Rev. A44, 7165 (1991).ADSGoogle Scholar
  44. [31]
    J. Boguta and J. Rafelski, Phys. Lett. B71, 22 (1977).ADSGoogle Scholar
  45. [32]
    J. Boguta and A. R. Bodmer, Nucl. Phys. A292, 413 (1977).MathSciNetADSGoogle Scholar
  46. [33]
    W. Stocker and M. M. Sharma, Z. Phys. A339, 147 (1991).ADSGoogle Scholar
  47. [34]
    M. Centelles, X. Vinas, M. Barranco, and P. Schuck, Nucl. Phys. A519, 73c (1990).ADSGoogle Scholar
  48. [35]
    M. Centelles, X. Vinas, M. Barranco, and P. Schuck, Ann. Phys. (N.Y.). 221, 165 (1993).ADSCrossRefGoogle Scholar
  49. [36]
    M. K. Weigel, S. Haddad, and F. Weber, J. Phys. G17, 619 (1991).ADSGoogle Scholar
  50. D. Von-Eiff, S. Haddad, and M. K. Weigel, Phys. Rev. C46, 230 (1992).ADSGoogle Scholar
  51. [37]
    C. Speicher, R. M. Dreizler, and E. Engel, Ann. Phys. (N.Y.). 213, 312 (1992).MathSciNetADSCrossRefGoogle Scholar
  52. [38]
    M. Centelles, X. Vinas, M. Barranco, S. Marcos, and R. J. Lombard, Nucl. Phys. A537, 486 (1992).ADSGoogle Scholar
  53. [39]
    D. Von-Eiff and M. K. Weigel, Phys. Rev. C46, 1797 (1992).ADSGoogle Scholar
  54. [40]
    M. Centelles, X. Vinas, M. Barranco, N. Ohtsuka, Amand Faessler, Dao T. Khoa, and H. Müther, Phys. Rev. C47, 1091 (1993).ADSGoogle Scholar
  55. [41]
    C. Speicher, E. Engel, and R. M. Dreizler, Nucl. Phys. A562, 569 (1993).ADSGoogle Scholar
  56. [42]
    M. CenteUes and X. Vinas, Nucl. Phys. A563, 173 (1993).ADSGoogle Scholar
  57. [43]
    D. A. Kirzhnits, Field Theoretical Methods in Many-Body Systems (Pergamon, Oxford, 1967).Google Scholar
  58. [44]
    B. K. Jennings, R. K. Bhaduri, and M. Brack, Nucl. Phys. A253, 29 (1975).ADSGoogle Scholar
  59. [45]
    N. H. March, Self-consistent Fields in Atoms (Pergamon, Oxford, 1975).Google Scholar
  60. B.-G. Englert and J. Schwinger, Phys. Rev. A32, 26 (1985).ADSGoogle Scholar
  61. [46]
    M. M. Sharma, M. A. Nagarajan, and P. Ring, Phys. Lett. B312, 377 (1993).ADSGoogle Scholar
  62. [47]
    M. M. Sharma, G. A. Lalazissis, and P. Ring, Phys. Lett. B317, 9 (1993).ADSGoogle Scholar
  63. M. M. Sharma, G. A. Lalazissis, W. Hillebrandt, and P. Ring, Phys. Rev. Lett. (submitted).Google Scholar
  64. [48]
    M. Centelles, X. Vinas, and P. Schuck, Nucl. Phys. A (in press).Google Scholar
  65. [49]
    D. Von-Eiff and M. K. Weigel, Phys. Rev. C46, 1288 (1992).ADSGoogle Scholar
  66. H. Müller and R. M. Dreizler, Nucl. Phys. A563, 649 (1993).ADSGoogle Scholar
  67. [50]
    M. Durand, P. Schuck, and X. Vinas, Z. Phys. A346, 87 (1993).ADSGoogle Scholar
  68. [51]
    P. Schuck and X. Vinas, Phys. Lett. B302, 1 (1993).ADSGoogle Scholar
  69. [52]
    E. Ruiz Arriola and L. L. Salcedo, Mod. Phys. Lett. A8, 2061 (1993).ADSGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • M. Centelles
    • 1
  1. 1.Departament d’Estructura i Constituents de la Matèria Facultat de FísicaUniversitat de BarcelonaBarcelonaSpain

Personalised recommendations