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Prog. Theor. Phys. Supplement No.56 (1974) pp. 6-31

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Chapter II. The ATMS Method and the Three-Nucleon System with Realistic Potentials

Yoshinori Akaishi, Motoki Sakai, Jun Hiura* and Hajime Tanaka

Department of Physics, Hokkaido University, Sapporo
*College of Liberal Arts, Iwate University, Morioka

(Received February 3, 1975)

Abstract:

The ATMS method, which is a variational one, is explained. The wave function is constructed from the two-body scattering correlations on the basis of the multiple scattering theory. The triton is treated with the Hamada-Johnston (H-J), the Tamagaki (OPEH and OPEG) and Wada and Obinata's (OBEV) potentials. The upper-bound energies are -6.00 MeV for H-J, -6.59 MeV for OPEH, -6.64 MeV for OPEG and -5.91 MeV for OBEV. The kinetic energies are 66 MeV for H-J and 33 MeV for OBEV. The tensor force in the triplet-even state has the largest contribution which amounts to -38 MeV for H-J. The Coulomb energy of 3He is estimated. The two-body wave function is drawn out from the wave function of the triton. The ATMS method is powerful in solving the three-nucleon problem with realistic potentials.


URL : http://ptp.ipap.jp/link?PTPS/56/6/
DOI : 10.1143/PTPS.56.6

[ Full Text PDF : FREE ACCESS (1479K) ] Citation:


References:

  1. a) Y. Akaishi, J. Hiura, M. Sakai and H. Tanaka, Few Particle Problems in Nuclear Interaction, edited by I. Slaus, S. A. Moszkowski, R. P. Haddock and W.T.H. van Oers (Norh-Holland, 1972), p. 353.
    Y. Akaishi, M. Sakai, J. Hiura and H. Tanaka, Prog. Theor. Phys. 51 (1974), 134[PTP].
    b) M. Sakai, I. Shimodaya, Y. Akaishi, J. Hiura and H. Tanaka, Prog. Theor. Phys. 51 (1974), 155[PTP].
  2. T. Hamada and I. D. Johnston, Nucl. Phys. 34 (1962), 382[CrossRef].
  3. R. Tamagaki, Prog. Theor. Phys. 39 (1968), 91[PTP].
  4. T. Obinata and M. Wada, Prog. Theor. Phys. 53 (1975), 732[PTP].
  5. R. V. Reid, Ann. of Phys. 50 (1968), 411[CrossRef].
  6. a) M. A. Hennell and L. M. Delves, Phys. Lett. B 40 (1972), 20[CrossRef]; Nucl. Phys. A 168 (1971), 347[CrossRef]; ibid. 204 (1973), 552[CrossRef].
    b) L. M. Delves and J. M. Blatt, Nucl. Phys. A 98 (1967), 503[CrossRef].
  7. A. D. Jackson, A. Lande and P. U. Sauer, Nucl. Phys. A 156 (1970), 1[CrossRef]; Phys. Lett. B 35 (1971), 365[CrossRef].
  8. J. Bruinsma and R. Van Wageningen, Phys. Lett. B 44 (1973), 221[CrossRef].
  9. R. A. Malfliet and J. A. Tjon, Ann. of Phys. 61 (1970), 425[CrossRef].
    R. A. Brandenburg, Y. E. Kim and A. Tubis, Phys. Lett. B 49 (1974), 205.
    A. Laverne and C. Gignoux, Nucl. Phys. A 203 (1973), 597[CrossRef].
  10. a) Y. C. Tang, E. W. Schmid and R. C. Herndon, Nucl. Phys. 65 (1965), 203[CrossRef]; ibid. 42 (1963), 95[CrossRef].
    b) N. Austern and P. Iano, Nucl. Phys. 18 (1960), 672[CrossRef].
  11. Y. Akaishi and S. Nagata, Prog. Theor. Phys. 48 (1972), 133[PTP].
  12. L. C. Gomes, J. D. Walecka and V. F. Weisskopf, Ann. of Phys. 3 (1958), 241[CrossRef].
  13. K. M. Watson, Phys. Rev. 89 (1953), 575[APS].
    K. A. Brueckner and C. A. Levinson, Phys. Rev. 97 (1955), 1344[APS].
  14. H. A. Bethe, Phys. Rev. 103 (1956), 1353[APS].
    J. Goldstone, Proc. Roy. Soc. A 239 (1957), 267.
  15. Y. Akaishi, H. Bando, A. Kuriyama and S. Nagata, Prog. Theor. Phys. 40 (1968), 288[PTP].
    Y. Akaishi and S. Nagata, Prog. Theor. Phys. Suppl. Extra Number (1968), 476[PTP].
  16. G. H. Derrick and J. M. Blatt, Nucl. Phys. 8 (1958), 310[CrossRef].
    G. H. Derrick, Nucl. Phys. 16 (1960), 405[Elsevier].
  17. M. Bolsterli and E. Jezak, Phys. Rev. 135 (1964), B510[APS].
  18. J. P. Elliott, preprint.
  19. L. Cohen, Nucl. Phys. 20 (1960), 690[CrossRef].
  20. a) B. D. Day, Phys. Rev. 151 (1966), 826[APS].
    b) R. Rajaraman and H. A. Bethe, Rev. Mod. Phys. 39 (1967), 745[APS].
  21. R. Jastrow, Phys. Rev. 98 (1955), 1479[APS].
  22. A. H. Stroud and D. Secrest, Gaussian Quadrature Formulas (Prentice-Hall, Inc., 1966).
  23. J. J. Griffin and J. A. Wheeler, Phys. Rev. 108 (1957), 311[APS].
  24. C. Pask, Nucl. Phys. A 132 (1969), 234[CrossRef].
  25. C. de Vries, R. Hofstadter, A. Johansson and R. Herman, Phys. Rev. 134 (1964), B848[APS].
    H. Collard, R. Hofstadter, E. B. Hughes, A. Johansson, M. R. Yearian, R. B. Day and R. T. Wagner, Phys. Rev. 138 (1965), B57[APS].
  26. H. Bandō, S. Nagata and Y. Yamamoto, Prog. Theor. Phys. 44 (1970), 646[PTP]; ibid. 45 (1971), 1515[PTP].
    Y. Akaishi, H. Bandō and S. Nagata, Prog. Theor. Phys. Suppl. No. 52 (1972), 339, [PTP](Chapter VIII).
  27. K. Okamoto and C. Pask, Ann. of Phys. 68 (1971), 18.
  28. R. E. Schneider and R. M. Thaler, Phys. Rev. 137 (1965), B874[APS].
  29. S. Aranoff and J. K. Percus, Phys. Rev. 162 (1967), 878[APS].
  30. E. Hadjimichael, S. N. Yang and G. E. Brown, Phys. Lett. B 39 (1972), 594[CrossRef].

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