The European Physical Journal A

, 48:153

Translationally invariant calculations of form factors, nucleon densities and momentum distributions for finite nuclei with short-range correlations included

Regular Article - Theoretical Physics

Abstract

Relying upon our previous treatment of the density matrices for nuclei (in general, nonrelativistic self-bound finite systems) we are studying a combined effect of center-of-mass motion and short-range nucleon-nucleon correlations on the nucleon density and momentum distributions in light nuclei (4He and 16O). Their intrinsic ground-state wave functions are constructed in the so-called fixed center-of-mass approximation, starting with mean-field Slater determinants modified by some correlator (e.g., after Jastrow or Villars). We develop the formalism based upon the Cartesian or boson representation, in which the coordinate and momentum operators are linear combinations of the creation and annihilation operators for oscillatory quanta in the three different space directions, and get the own “Tassie-Barker” factors for each distribution and point out other model-independent results. After this separation of the center-of-mass motion effects we propose additional analytic means in order to simplify the subsequent calculations (e.g., within the Jastrow approach or the unitary correlation operator method). The charge form factors, densities and momentum distributions of 4He and 16O evaluated by using the well-known cluster expansions are compared with data, our exact (numerical) results and microscopic calculations.

References

  1. 1.
    A.N. Antonov, P.E. Hodgson, J.Zh. Petkov, Nucleon Momentum and Density Distributions in Nuclei (Clarendon Press, Oxford, 1988).Google Scholar
  2. 2.
    M. Alvioli, C. Ciofi degli Atti, H. Morita, Phys. Rev. C 72, 054310 (2005).ADSCrossRefGoogle Scholar
  3. 3.
    S. Dementiji, V. Ogurtzov, A. Shebeko, Sov. J. Nucl. Phys. 22, 6 (1976).Google Scholar
  4. 4.
    A.Yu. Korchin, A.V. Shebeko, Z. Phys. A 321, 687 (1985).ADSCrossRefGoogle Scholar
  5. 5.
    S.V. Dementiji et al., J. Phys. Soc. Jpn. 57, 2988 (1988).ADSCrossRefGoogle Scholar
  6. 6.
    C. Ciofi degli Atti, E. Pace, G. Salme, in Proceedings of the 2nd Workshop on Perspectives in Nuclear Physics at Intermediate Energies (WS, Singapore, 1985).Google Scholar
  7. 7.
    S. Frullani, J. Mougey, in Adv. Nucl. Phys., edited by J. Negele, E. Vogt, Vol. 14 (New York, 1984).Google Scholar
  8. 8.
    C. Ciofi degli Atti, S. Liuti, Nucl. Phys. A 532, 235 (1991).ADSCrossRefGoogle Scholar
  9. 9.
    H.M. Hofmann, Nucl. Phys. A 209, 233 (1973).ADSCrossRefGoogle Scholar
  10. 10.
    R.I. Jibuti, R.Ya. Kezerashvili, Yad. Fiz. 22, 975 (1975).Google Scholar
  11. 11.
    T. Katayama, Y. Akaishi, H. Tanaka, Prog. Theor. Phys. 67, 236 (1982).ADSCrossRefGoogle Scholar
  12. 12.
    R. Schiavilla, V.R. Pandharipande, R.B. Wiringa, Phys. Rev. C 41, 309 (1990).ADSCrossRefGoogle Scholar
  13. 13.
    V.P. Berezovoj, Yu.P. Melʼnik, A.V. Shebeko, Nucl. Phys. A 404, 443 (1983).ADSCrossRefGoogle Scholar
  14. 14.
    A. Korchin, A. Shebeko, Ukr. J. Phys. 22, 1646 (1977) arXiv: nucl-th/0601014.Google Scholar
  15. 15.
    A. Shebeko, P. Papakonstantinou, E. Mavrommatis, Eur. Phys. J. A 27, 143 (2006).ADSCrossRefGoogle Scholar
  16. 16.
    H. Morita, Y. Akaishi, O. Endo, H. Tanaka, Prog. Theor. Phys. 78, 1117 (1987).ADSCrossRefGoogle Scholar
  17. 17.
    H. Morita, Y. Akaishi, H. Tanaka, Prog. Theor. Phys. 79, 863 (1988) H. Morita, private communication to A. Shebeko.ADSCrossRefGoogle Scholar
  18. 18.
    S.E. Massen, Ch.C. Moustakidis, Phys. Rev. C 60, 024005 (1999).ADSCrossRefGoogle Scholar
  19. 19.
    Ch.C. Moustakidis, S.E. Massen, Phys. Rev. C 62, 034318 (2000).ADSCrossRefGoogle Scholar
  20. 20.
    J.L. Friar, Nucl. Phys. A 173, 257 (1971).ADSCrossRefGoogle Scholar
  21. 21.
    C. Ciofi degli Atti, L. Lanto, P. Toropainen, Phys. Lett. B 42, 443 (1972).Google Scholar
  22. 22.
    C.M. Vincent, Phys. Rev. C 8, 929 (1973).ADSCrossRefGoogle Scholar
  23. 23.
    A.E.L. Dieperink, T. de Forest, Jr., Phys. Rev. C 10, 543 (1974).ADSCrossRefGoogle Scholar
  24. 24.
    D. Van Neck et al., Phys. Rev. C 57, 2308 (1998).ADSCrossRefGoogle Scholar
  25. 25.
    B. Mihaila, J. Heisenberg, Phys. Rev. C 60, 054303 (1999).ADSCrossRefGoogle Scholar
  26. 26.
    K.W. Schmid, Eur. Phys. J. A 12, 29 (2001).ADSCrossRefGoogle Scholar
  27. 27.
    K.W. Schmid, Eur. Phys. J. A 13, 319 (2002).ADSCrossRefGoogle Scholar
  28. 28.
    K.W. Schmid, Eur. Phys. J. A 14, 413 (2002).ADSCrossRefMATHGoogle Scholar
  29. 29.
    K.W. Schmid, Eur. Phys. J. A 16, 475 (2003).ADSCrossRefGoogle Scholar
  30. 30.
    P. Navratil, Phys. Rev. C 70, 014317 (2004).ADSCrossRefGoogle Scholar
  31. 31.
    K. Ypsilantis, M. Grypeos, J. Phys. G.: Nucl. Part. Phys. 21, 1701 (1995).ADSCrossRefGoogle Scholar
  32. 32.
    R. Jastrow, Phys. Rev. 98, 1497 (1955).ADSCrossRefGoogle Scholar
  33. 33.
    F.M.H. Villars, in Proceedings of the International School of Physics “Enrico Fermi”, 1961, Varenna, Italy, edited by V.F. Weisskopf (Academic Press, New York, 1963).Google Scholar
  34. 34.
    J. Da Providencia, C.M. Shakin, Ann. Phys. 30, 95 (1964).ADSCrossRefGoogle Scholar
  35. 35.
    C.M. Shakin, Y.R. Waghmare, M.H. Hull, Jr., Phys. Rev. 161, 1006 (1967).ADSCrossRefGoogle Scholar
  36. 36.
    H. Feldmeier et al., Nucl. Phys. A 632, 61 (1998).ADSCrossRefGoogle Scholar
  37. 37.
    R. Roth, T. Neff, H. Feldmeier, Prog. Part. Nucl. Phys. 65, 50 (2010).ADSCrossRefGoogle Scholar
  38. 38.
    H. Kümmel, K.H. Lührmann, J.G. Zabolitzky, Phys. Rep. C 36, 1 (1978).ADSCrossRefGoogle Scholar
  39. 39.
    F. Iwamoto, M. Yamada, Prog. Theor. Phys. 17, 543 (1957).MathSciNetADSCrossRefMATHGoogle Scholar
  40. 40.
    J.B. Aviles, Ann. Phys. 5, 251 (1958).MathSciNetADSCrossRefMATHGoogle Scholar
  41. 41.
    C.D. Hartogh, M.A. Tolhoek, Physica 24, 721 (1958).MathSciNetADSCrossRefGoogle Scholar
  42. 42.
    N.G. Van Kampen, Physica 27, 783 (1961).MathSciNetADSCrossRefMATHGoogle Scholar
  43. 43.
    J.W. Clark, J. Westhouse, Math. Phys. 9, 131 (1968).ADSCrossRefGoogle Scholar
  44. 44.
    J.W. Clark, M.L. Ristig, Nuovo Cimento A LXX, 313 (1970).ADSCrossRefGoogle Scholar
  45. 45.
    M. Gaudin, J. Gillespie, G. Ripka, Nucl. Phys. A 176, 237 (1971).ADSCrossRefGoogle Scholar
  46. 46.
    Dal Ri, S. Stringari, O. Bohigas, Nucl. Phys. A 376, 81 (1982).ADSCrossRefGoogle Scholar
  47. 47.
    C. Ciofi degli Atti, M.E. Grypeos, Lett. Nuovo Cimento 2, 587 (1969).CrossRefGoogle Scholar
  48. 48.
    Ch.C. Moustakidis et al., Phys. Rev. C 64, 014314 (2001).ADSCrossRefGoogle Scholar
  49. 49.
    A. Shebeko, N. Goncharov, Sov. J. Nucl. Phys. 18, 532 (1974).Google Scholar
  50. 50.
    M.L. Goldberger, K.M. Watson, Collision theory (John Wiley and Sons, 1964).Google Scholar
  51. 51.
    D. Van Neck, M. Waroquier, Phys. Rev. C 58, 3359 (1998).ADSCrossRefGoogle Scholar
  52. 52.
    V. Neudachin, Yu. Smirnov, Nucleon clusters in light nuclei (Nauka, Moscow, 1964).Google Scholar
  53. 53.
    R. Peierls, J. Yoccoz, Proc. Phys. Soc. A 70, 381 (1957).MathSciNetADSCrossRefMATHGoogle Scholar
  54. 54.
    D.J. Ernst, C.M. Shakin, R.M. Thaler, Phys. Rev. C 7, 925 (1973).ADSCrossRefGoogle Scholar
  55. 55.
    D.J. Ernst, C.M. Shakin, R.M. Thaler, Phys. Rev. C 7, 1340 (1973).ADSCrossRefGoogle Scholar
  56. 56.
    K.W. Schmid, F. Grümmer, Z. Phys. A 336, 5 (1990).ADSGoogle Scholar
  57. 57.
    K.W. Schmid, F. Grümmer, Z. Phys. A 337, 267 (1990).ADSGoogle Scholar
  58. 58.
    J.G. Zabolitzky, W. Ey, Phys. Lett. B 76, 527 (1978).ADSCrossRefGoogle Scholar
  59. 59.
    F. Coester, Nucl. Phys. 7, 421 (1958).CrossRefGoogle Scholar
  60. 60.
    F. Coester, H. Kümmel, Nucl. Phys. 17, 477 (1960).CrossRefMATHGoogle Scholar
  61. 61.
    V.Yu. Gonchar, E.V. Inopin, V.I. Kuprikov, Yad. Fiz. 25, 46 (1977).Google Scholar
  62. 62.
    S. Radhakant, S.B. Khadkikar, B. Banerjee, Nucl. Phys. A 142, 81 (1970).ADSCrossRefGoogle Scholar
  63. 63.
    H. Chandra, G. Sauer, Phys. Rev. C 13, 245 (1976).ADSCrossRefGoogle Scholar
  64. 64.
    H. de Vries, C.W. de Jager, C. de Vries, At. Data Nucl. Data Tables 36, 495 (1987).ADSCrossRefGoogle Scholar
  65. 65.
    A. Shebeko, P. Grigorov, Ukr. J. Phys. 52, 830 (2007).Google Scholar
  66. 66.
    R.F. Frosch et al., Phys. Rev. 160, 874 (1967).ADSCrossRefGoogle Scholar
  67. 67.
    R.G. Arnold et al., Phys. Rev. Lett. 40, 1429 (1978).ADSCrossRefGoogle Scholar
  68. 68.
    I. Sick, J.S. McCarthy, Nucl. Phys. A 150, 631 (1970).ADSCrossRefGoogle Scholar
  69. 69.
    C. Ciofi degli Atti, E. Pace, G. Salme, Phys. Rev. C 43, 1155 (1991).ADSCrossRefGoogle Scholar
  70. 70.
    S.C. Pieper, R.B. Wiringa, V.R. Pandharipande, Phys. Rev. C 46, 1741 (1992).ADSCrossRefGoogle Scholar
  71. 71.
    H. Batemann, A. Erdélyi, Tables of Integral Transforms, Vol. 1 (McGraw-Hill, New York, 1954).Google Scholar
  72. 72.
    H. Kamada, A. Nogga, W. Glöckle et al., Phys. Rev. C 64, 044001 (2001).ADSCrossRefGoogle Scholar
  73. 73.
    A. Deltuva, A.C. Fonseca, Phys. Rev. C 75, 014005 (2007).ADSCrossRefGoogle Scholar
  74. 74.
    A. Nogga, H. Kamada, W. Glöckle, B.R. Barrett, Phys. Rev. C 65, 054003 (2002).ADSCrossRefGoogle Scholar

Copyright information

© SIF, Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • A. V. Shebeko
    • 1
  • P. A. Grigorov
    • 2
  • V. S. Iurasov
    • 3
  1. 1.Institute for Theoretical PhysicsNSC “Kharkov Institute of Physics & Technology”KharkivUkraine
  2. 2.University of TübingenTübingenGermany
  3. 3.National Karazin UniversityKharkivUkraine

Personalised recommendations