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Prog. Theor. Phys. Vol. 49 No. 3 (1973) pp. 800-824

[ Full Text PDF : FREE ACCESS (2307K) ]

A Molecular-Orbital Model of the Atomic Nuclei

Yasuhisa Abe, Jun Hiura and Hajime Tanaka

Department of Physics, Hokkaido University

(Received September 4, 1972)

Abstract:

A new nuclear model is proposed that describes the cluster and the shell structures unifiedly. By the present model one can investigate characteristics of one-particle orbitals in clustering states and also polarizations of constituent clusters. The model has its base on the Hartree-Fock (H. F.) approximation for nuclear intrinsic states. The basis wave functions used in the present H. F. calculations are constructed from single-particle wave functions around each “cluster center”, which can well describe possible large eccentric nuclear deformations in light nuclei. The model is analogous to the LCAO-MO-SCF method in the molecular physics. Numerical calculations are performed using an effective two-nucleon force (Volkov No. 1) for the ground states of 8Be and 12C nuclei, and interesting results are obtained about the stability of α-cluster structures. Polarizations are smallest at the equilibrium distance between α-clusters, determined by Brink's α-particle model. An artifical collapse or an extreme decomposition of the α-cluster structures brings about large polarizations. By those polarizations of constituent α-clusters themselves, the α-cluster structure recovers their density distributions. Comparisons of the results are made with those of two-center shell model, usual H. F. calculation and α-particle model.


URL : http://ptp.ipap.jp/link?PTP/49/800/
DOI : 10.1143/PTP.49.800

[ Full Text PDF : FREE ACCESS (2307K) ] Citation:

References:

  1. Y. Abe, Proceegins of the International Conference on Clustering Phenomena in Nuclei, Bochum, 1969, ed. E. R. A. Beck (IAEA, Vienna, 1969), p. 303.
    H. Tanaka, p. 137 in the above book.
  2. Y. Abe, J. Hiura and H. Tanaka, Prog. Theor. Phys. 46 (1971), 352[PTP].
  3. J. A. Wheeler, Phys. Rev. 52 (1937), 1083[APS]; ibid. 52 (1937), 1107[APS].
  4. L. R. Hofstad and E. Teller, Phys. Rev. 54 (1938), 681[APS].
  5. K. Wildermuth and Th. Kanellopolos, Nucl. Phys. 7 (1958), 150[CrossRef].
    K. Wildermuth and W. McClure, Cluster Representations of Nuclei (Springer-Verlag, Berlin, 1969).
  6. Yu. A. Kudeyarov, Z. Matties, V. G. Neudatchin and Yu. F. Smirnov, Nucl. Phys. 65 (1965), 529[CrossRef].
    V. G. Neudatchin and Yu. F. Smirnov, Atomic Energy Reviews (IAEA, Vienna) 3 (1965), 157.
    V. G. Neudatchin and Yu. F. Smirnov, Prog. Nucl. Phys. 10 (1969), 275.
  7. E. W. Schmid and K. Wildermuth, Nucl. Phys. 26 (1961), 463[CrossRef].
    I. Shimodaya, R. Tamagaki and H. Tanaka, Prog. Theor. Phys. 27 (1962), 793[PTP].
    O. Endo, I. Shimodoaya and J. Hiura, Prog. Theor. Phys. 31 (1964), 1157[PTP].
    For later works, see also R. Tamagaki, Prog. Theor. Phys. 34 (1965), 191[PTP]; Prog. Theor. Phys. Suppl. Extra Number (1968), 242[PTP];
    S. Okai and S. C. Park, Phys. Rev. 145 (1966), 787[APS].
  8. J. Hiura and I. Shimodaya, Prog. Theor. Phys. 30 (1963), 585[PTP]; ibid. 36 (1966), 977[PTP].
  9. J. Hiura, Y. Abe, S. Saito and O. Endo, Prog. Theor. Phys. 42 (1969), 555[PTP].
  10. G. C. Phillips and T. A. Tombrello, Nucl. Phys. 19 (1960), 555[CrossRef].
  11. K. Ikeda, N. Takigawa and H. Horiuchi, Prog. Theor. Phys. Suppl. Extra Number (1968), 464[PTP].
  12. H. Horiuchi and K. Ikeda, Prog. Theor. Phys. 40 (1968), 277[PTP].
  13. Proceedings of the International Conference on Nuclear Reaction induced by Heavy Ion, eds. R. Bodk and W. R. Hering (Heidelberg, Germany, 1969).
  14. P. Chevallier, F. Scheibling, G. Goldring, I. Plesser and M. W. Sachs, Phys. Rev. 160 (1967), 827[APS].
  15. H. Morinaga, Phys. Rev. 101 (1956), 254[APS].
  16. D. M. Brink, International School of Physics “Enrico Fermi”, XXXVI (1966), p. 247.
  17. T. Yukawa and S. Yoshida, Phys. Lett. B 33 (1970), 334[CrossRef].
    H. Friedrich and A. Weiguny, Phys. Lett. B 35 (1971), 105[CrossRef].
    H. Friedrich, H. Hüsken and A. Weiguny, Phys. Lett. B 38 (1972), 199[CrossRef].
  18. R. Tamagaki, Prog. Theor. Phys. 42 (1969), 748[PTP].
  19. N. De Takacsy, Nucl. Phys. A 178 (1972), 469[CrossRef].
    H. Friedrich, L. Satpathy and A. Weiguny, Phys. Lett. B 36 (1971), 189[CrossRef].
  20. N. Takigawa and A. Arima, Nucl. Phys. A 168 (1971), 593[CrossRef].
  21. H. Horiuchi, Prog. Theor. Phys. 43 (1970), 375[PTP].
  22. M. G. Mayer and J. H. D. Jenesen, Elementary Theory of Nuclear Shell Structure (Wiley, New York, 1955).
  23. T. Inoue, T. Sebe, H. Hagiwara and A. Arima, Nucl. Phys. 59 (1964), 1[CrossRef].
    T. Inoue, T. Sebe, K. K. Huang and A. Arima, Nucl. Phys. A 99 (1967), 305[CrossRef].
    A. Arima, S. Cohen, R. D. Lawson and M. H. Macfarlane, Nucl. Phys. A 108 (1968), 94[CrossRef].
  24. E. C. Halbert, J. B. McGrory, B. H. Wildenthal and S. P. Pandya, Adv. Nucl. Phys. 4 (1971), 316.
  25. A. Arima, H. Horiuchi and T. Sebe, Phys. Lett. B 24 (1967), 129[CrossRef].
    T. Engeland and P. J. Ellis, Phys. Lett. B 25 (1967), 57[CrossRef].
  26. J. Eichler, K. Takada and T. Marumori, Prog. Theor. Phys. 40 (1968), 60[PTP].
  27. T. Marumori and K. Suzuki, Nucl. Phys. A 106 (1968), 610[CrossRef].
  28. M. Kamimura, T. Matsuse and K. Takada, Prog. Theor. Phys. 47 (1972), 1537[PTP].
  29. F. Nemoto and H. Bando, Prog. Theor. Phys. 47 (1972), 1210[PTP].
  30. I. Kelson and C. A. Levinson, Phys. Rev. 134 (1964), B269[APS].
    G. Ripka, Adv. Nucl. Phys. 1 (1968), p. 183.
    M. Bouten, Theory of Nuclear Structure: Trieste Lectures 1969 (IAEA, Vienna, 1970).
  31. C. C. J. Roothaan, Rev. Mod. Phys. 23 (1951), 69[APS].
  32. Y. Suzuki and K. Kubodera, Prog. Theor. Phys. 44 (1970), 617[PTP].
  33. O. Miyatake, M. Nozawa and M. Tohyama, Gensikaku Kenkyu (Circular in Japanese) 4 (1960), 138.
  34. K. Ikeda, Proceedings of the International Conference on Clustering Phenomena in Nuclei, Bachum, Germany (1969), p. 277.
  35. M. Bouten and P. van Leuven, Physica 34 (1967), 469[Elsevier].
  36. W. Wadia, Z. Phys. 224 (1969), 425.
  37. M. Hamermesh, Group Theory (Addison-Wesley, 1962).
  38. A. B. Volkov, Nucl. Phys. 74 (1965), 33[CrossRef].
  39. K. A. Brueckner and J. L. Gammel, Phys. Rev. 109 (1958), 1023[APS].
    Y. Akaishi and S. Nagata, Prog. Theor. Phys. Suppl. Extra Number (1968), 476, [PTP]and the related papers cited therein.
  40. H. Bando, S. Nagata and Y. Yamamoto, Prog. Theor. Phys. 44 (1970), 646[PTP]; ibid. 45 (1971), 1515[PTP].
  41. R. Hofstader, Ann. Rev. Nucl. Sci. 7 (1957), 231.
  42. U. Amaldi, Jr., Suppl. Nuovo Cim. 5 (1967), 1225.
    Th. A. J. Maris, P. Hillman and H. Tyren, Nucl. Phys. 7 (1958), 1[CrossRef].
    G. Jacob and Th. A. J. Maris, Rev. Mod. Phys. 38 (1966), 121[APS].
  43. K. Kubodera and K. Ikeda, Prog. Theor. Phys. 42 (1969), 740[PTP].
  44. T. Lauritsen and F. Ajzenberg-Selove, Nucl. Phys. 78 (1966), 82[Elsevier].
  45. A. Herzenberg and A. S. Roberts, Nucl. Phys. 3 (1957), 314[CrossRef].
    K. Itonaga and H. Bando, Prog. Theor. Phys. 44 (1970), 1232[PTP].
  46. J. Eichler and A. Faessler, Nucl. Phys. A 157 (1970), 166[CrossRef].
  47. Y. Suzuki, H. Horiuchi and K. Ikeda, Prog. Theor. Phys. 47 (1972), 1517[PTP].
  48. I. Shavitt, Method in Computational Physics 2 (1963), 1.

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  16. Progress of Theoretical Physics Supplement No.192 (2012) pp. 1-238 :
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