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Self-consistent theory of finite Fermi systems and radii of nuclei

  • Nuclei
  • Theory
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Abstract

Present-day self-consistent approaches in nuclear theory were analyzed from the point of view of describing distributions of nuclear densities. The generalized method of the energy density functional due to Fayans and his coauthors (this is the most successful version of the self-consistent theory of finite Fermi systems) was the first among the approaches under comparison. The second was the most successful version of the Skyrme-Hartree-Fock method with the HFB-17 functional due to Goriely and his coauthors. Charge radii of spherical nuclei were analyzed in detail. Several isotopic chains of deformed nuclei were also considered. Charge-density distributions ρ ch(r) were calculated for several spherical nuclei. They were compared with model-independent data extracted from an analysis of elastic electron scattering on nuclei.

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References

  1. A. B. Migdal, Theory of Finite Fermi Systems and Applications to Atomic Nuclei (Nauka, Moscow, 1965; Intersci., New York, 1967).

    Google Scholar 

  2. L. D. Landau, Zh. Eksp. Teor. Fiz. 35, 97 (1958) [Sov. Phys. JETP 8, 70 (1958)].

    Google Scholar 

  3. G.G. Bunatyan and M. A. Mikulinskii, Yad. Fiz. 1, 38 (1965) [Sov. J. Nucl. Phys. 1, 26 (1965)].

    Google Scholar 

  4. E. E. Sapershtein, M. A. Troitskii, Yad. Fiz. 1, 400 (1965) [Sov. J. Nucl. Phys. 1, 284 (1965)].

    Google Scholar 

  5. V. A. Khodel’, Pis’ma Zh. Eksp. Teor. Fiz. 16, 410 (1972) [JETP Lett. 16, 291 (1972)].

    Google Scholar 

  6. V. A. Khodel’, Yad. Fiz. 23, 282 (1976) [Sov. J. Nucl. Phys. 23, 147 (1976)].

    Google Scholar 

  7. A. Bohr and B. R. Mottelson, Nuclear Structure, vol. 2: Nuclear Deformations, (Mir, Moscow, 1977; Benjamin, New York, Amsterdam, 1974).

    Google Scholar 

  8. V. G. Soloviev, Theory of Complex Nuclei (Nauka, Moscow, 1971; Pergamon Press, Oxford, 1976).

    Google Scholar 

  9. S. A. Fayans and V. A. Khodel’, Pis’ma Zh. Eksp. Teor. Fiz. 17, 633 (1973) [JETP Lett. 17, 444 (1973)].

    Google Scholar 

  10. D. Vautherin and D. M. Brink, Phys. Rev. C 5, 626 (1972).

    Article  ADS  Google Scholar 

  11. S. Goriely, N. Chamel, and J. M. Pearson, Phys. Rev. Lett. 102, 152503 (2009).

    Article  ADS  Google Scholar 

  12. J. Dechargé and D. Gogny, Phys. Rev. C 21, 1568 (1980).

    Article  ADS  Google Scholar 

  13. S. Goriely, S. Hilaire, M. Girod, and S. Péru, Phys. Rev. Lett. 102, 242501 (2009).

    Article  ADS  Google Scholar 

  14. W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).

    Article  MathSciNet  ADS  Google Scholar 

  15. P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964).

    Article  MathSciNet  ADS  Google Scholar 

  16. P. Ring and P. Schuck, The Nuclear Many-Body Problem (Springer, Berlin, 1980).

    Google Scholar 

  17. V. A. Khodel and E. E. Saperstein, Phys. Rep. 92, 183 (1982).

    Article  ADS  Google Scholar 

  18. A. B. Migdal, Theory of Finite Fermi Systems and Applications to Atomic Nuclei, 2nd ed. (Nauka, Moscow, 1981).

    Google Scholar 

  19. V. A. Khodel, E. E. Saperstein, and M. V. Zverev, Nucl. Phys. A 465, 397 (1987).

    Article  ADS  Google Scholar 

  20. P. Klüpfel, P.-G. Reinhard, T. J. Bürvenich, and J. A. Maruhn, Phys. Rev. C 79, 034310 (2009).

    Article  ADS  Google Scholar 

  21. M. V. Zverev, V. I. Kuprikov, E. E. Sapershtein, et al., Yad. Fiz. 46, 466 (1987) [Sov. J. Nucl. Phys. 46, 249 (1987)].

    Google Scholar 

  22. A. V. Smirnov, S. V. Tolokonnikov, and S. A. Fayans, Yad. Fiz. 48, 1661 (1988) [Sov. J. Nucl. Phys. 48, 995 (1988)].

    Google Scholar 

  23. S. T. Belyaev, A. V. Smirnov, S. V. Tolokonnikov, and S. A. Fayans, Yad. Fiz. 45, 1263 (1987) [Sov. J. Nucl. Phys. 45, 783 (1987)].

    Google Scholar 

  24. S. A. Fayans, E. L. Trykov, and D. Zawischa, Nucl. Phys. A 568, 523 (1994).

    Article  ADS  Google Scholar 

  25. D. J. Horen, G. R. Satchler, S. A. Fayans, and E. L. Trykov, Nucl. Phys. A 600, 193 (1996).

    Article  ADS  Google Scholar 

  26. S. A. Fayans and D. Zawischa, Phys. Lett. B 383, 19 (1996).

    Article  ADS  Google Scholar 

  27. S. A. Fayans, Pis’ma Zh. Eksp. Teor. Fiz. 68, 161 (1998) [JETP Lett. 68, 169 (1998)].

    Google Scholar 

  28. S. A. Fayans, S. V. Tolokonnikov, E. L. Trykov, and D. Zawischa, Nucl. Phys. A 676, 49 (2000).

    Article  ADS  Google Scholar 

  29. S. V. Tolokonnikov and E. E. Saperstein, Yad. Fiz. 73, 1731 (2010) [Phys. At. Nucl. 73, 1684 (2010)].

    Google Scholar 

  30. H. Grawe, in Proceedings of the Workshop on Nuclear Structure in 78 Ni Region, Leuven, 2009, Mar. 9–11.

  31. I. Angeli, Recommended Values of Nuclear Charge Radii, http://cdfe.sinp.msu.ru/services/radchart/radhelp.html#rad (2008).

  32. Yu. Gangrsky and K. Marinova, Nuclear Charge Radii, http://cdfe.sinp.msu.ru/services/radchart/radhelp.html#rad (2008).

  33. Database of the Lomonosov Moscow State University, Skobeltsyn Institute of Nuclear Physics, http://cdfe.sinp.msu.ru/services/radchart/radmain.html

  34. H. de Vries, C.W. de Jager, and C. de Vries, At. Data Nucl. Data Tables 36, 495 (1987).

    Article  ADS  Google Scholar 

  35. Yu. B. Ivanov, A. P. Platonov, and V. A. Khodel’, Yad. Fiz. 47, 1559 (1988) [Sov. J. Nucl. Phys. 47, 988 (1988)].

    Google Scholar 

  36. G. Audi, A. H. Wapstra, and C. Thibault, Nucl. Phys. A 729, 337 (2003).

    Article  ADS  Google Scholar 

  37. S. Goriely, http://www-astro.ulb.ac.be/Html/masses.html

  38. W. Bertozzi, J. Friar, J. Heisenberg, and J.W. Negele, Phys. Lett. B 41, 408 (1972).

    Article  ADS  Google Scholar 

  39. H. Chandra and G. Sauer, Phys. Rev. C 13, 245 (1976).

    Article  ADS  Google Scholar 

  40. M. Anselment, W. Faubel, S. Göring, et al., Nucl. Phys. A 451, 471 (1986).

    Article  ADS  Google Scholar 

  41. E. W. Otten, in Treatise on Heavy Ion Science, Ed. by D. A. Broemley (Plenum, New York, 1989), Vol. 8, p. 515.

    Google Scholar 

  42. S. B. Dutta, R. Kirchner, O. Klepper, et al., Z. Phys. A 341, 39 (1991).

    Article  ADS  Google Scholar 

  43. M. D. Seliverstov et al., Eur. Phys. J. A 41, 315 (2009).

    Article  ADS  Google Scholar 

  44. C.W. P. Palmer, P. E. G. Baird, S. A. Blundell, et al., J. Phys. B 17, 2197 (1984).

    Article  ADS  Google Scholar 

  45. L. Vermeeren, R. E. Silverans, P. Lievens, et al., Phys. Rev. Lett. 68, 1679 (1992).

    Article  ADS  Google Scholar 

  46. L. Vermeeren, P. Lievens, R. E. Silverans, et al., J. Phys. G 22, 1517 (1996).

    Article  ADS  Google Scholar 

  47. E. Chabanat, P. Bonche, P. Haensel, et al., Nucl. Phys. A 627, 710 (1997).

    Article  ADS  Google Scholar 

  48. I. Angeli, Yu. P. Gangrsky, K. P. Marinova, et al., J. Phys. G 36, 085102 (2009).

    Article  ADS  Google Scholar 

  49. V. A. Khodel, A. P. Platonov, and E. E. Saperstein, J. Phys. G 8, 967 (1982).

    Article  ADS  Google Scholar 

  50. P. Möller, J. R. Nix, W. D. Myers, and W. J. Swiatecki, At. Data Nucl. Data Tables 59, 185 (1995).

    Article  ADS  Google Scholar 

  51. S. Goriely, F. Tondeur, and J. M. Pearson, At. Data Nucl. Data Tables 77, 311 (2001).

    Article  ADS  Google Scholar 

  52. H. Euteneuer, J. Friedrich, and N. Voegler, Nucl. Phys. A 298, 452 (1978).

    Article  ADS  Google Scholar 

  53. J. L. Friar, J. Heisenberg, and J. W. Negele, in Proceedings of the June Workshop in Intermediate Energy Electromagnetic Interactions, Ed. by A. M. Bernstein (Massachusetts Inst. of Technology, 1977), p. 325.

  54. B. Frois, J. B. Bellicard, J. M. Cavedon, et al., Phys. Rev. Lett. 38, 152 (1977).

    Article  ADS  Google Scholar 

  55. J. Heisenberg, R. Hofstadter, J. S. McCarthy, et al., Phys. Rev. Lett. 23, 1402 (1969).

    Article  ADS  Google Scholar 

  56. G. J. C. van Niftrik, Nucl. Phys. A 131, 574 (1969).

    Article  ADS  Google Scholar 

  57. M. Nagao and Y. Torizuka, Phys. Lett. B 37, 383 (1971).

    Article  ADS  Google Scholar 

  58. J. Friedrich and F. Lenz, Nucl. Phys. A 183, 523 (1972).

    Article  ADS  Google Scholar 

  59. H. Euteneuer, J. Friedrich, and N. Voegler, Phys. Rev. Lett. 36, 129 (1976).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Russian Research Centre Kurchatov Institute, pl. Akademika Kurchatova 1, Moscow, 123182, Russia

    E. E. Saperstein & S. V. Tolokonnikov

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  1. E. E. Saperstein
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  2. S. V. Tolokonnikov
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Correspondence to E. E. Saperstein.

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Original Russian Text © E.E. Saperstein, S.V. Tolokonnikov, 2011, published in Yadernaya Fizika, 2011, Vol. 74, No. 9, pp. 1306–1325.

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Saperstein, E.E., Tolokonnikov, S.V. Self-consistent theory of finite Fermi systems and radii of nuclei. Phys. Atom. Nuclei 74, 1277–1298 (2011). https://doi.org/10.1134/S1063778811090109

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