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Prog. Theor. Phys. Vol. 34 No. 4 (1965) pp. 594-631

[ Full Text PDF : FREE ACCESS (1982K) ]

Dispersion Theoretic Calculation of Two-Pion-Exchange Contribution in Nucleon-Nucleon Scattering. I

— Formulations and General Results of Numerical Calculation —

Susumu Furuichi and Wataro Watari

Department of Physics, Rikkyo University, Tokyo
*Research Institute for Atomic Energy, Osaka City University, Osaka

(Received June 10, 1965)

Abstract:

The two-pion-exchange contribution without pion-pion correlation in nucleon-nucleon scattering is investigated in detail using the partial-wave dispersion relation. With the aim to clarify the contribution we devide the amplitude into the contributions corresponding to the fourth order perturbation (N-part) and the additional effect from the pion-nucleon resonance in the (33) state (33 part), and each part is further divided with respect to the angular momentum of the exchanged two pions, L, so that the characteristics of quantities appearing in the intermediate steps of calculation such as the effective mass distribution functions may be presented in a somewhat concrete way.
Through the investigation of the effective mass distribution functions, we found (i) the 33 part contributions mostly to the L=0 and 1 parts, which are the lowest L contributions to h(a) and h(b) respectively, where we describe the whole amplitude as h(a)+τ(1)τ(2)h(b) for the isospin freedom; (ii) the relative order of magnitude of 33 part to N part shows that the (33) effect is considerably large for L=0 part at the large effective mass region. This means that the effects of (33) πN resonance in the two-pion-exchange contribution for the nucleon-nucleon scattering have a very similar behaviour to the one-scalar-boson exchange contributions, where relatively large effective masses are assumed. Consequently, such features of the 33 part is likely to specify the characteristics of the two-pion-exchange contributions.
In fact, the (33) effect is generally very large for lower partial wave amplitudes than the F wave, in the form of “proper” 2π contribution.
Comparison with other calculations and discussions of related problem are also given.


URL : http://ptp.ipap.jp/link?PTP/34/594/
DOI : 10.1143/PTP.34.594

[ Full Text PDF : FREE ACCESS (1982K) ] Citation:

References:

  1. M. Taketani, S. Nakamura and M. Sasaki, Prog. Theor. Phys. 6 (1951), 581[PTP].
  2. Prog. Theor. Phys. Suppl. No. 3 (1956).
  3. M. Taketani, S. Machida and S. Ohnuma, Prog. Theor. Phys. 6 (1951), 638[PTP].
    M. Konuma, H. Miyazawa and S. Otsuki, Prog. Theor. Phys. 19 (1958), 17[PTP].
  4. S. Machida and K. Senba, Prog. Theor. Phys. 13 (1955), 389[PTP].
  5. J. L. Gammel and R. M. Thaler, Phys. Rev. 107 (1957), 291[APS].
    P. Signell and R. M. Marshak, Phys. Rev. 109 (1958), 1229[APS].
    R. A. Bryan, Nuovo Cim. 16 (1960), 895.
    T. Hamada and I. D. Johnston, Nucl. Phys. 34 (1962), 382[CrossRef].
  6. N. Hoshizaki and S. Machida, Prog. Theor. Phys. 24 (1960), 1325[PTP]; ibid. 27 (1962), 288[PTP].
    S. Otsuki, R. Tamagaki and W. Watari, Prog. Theor. Phys. 27 (1962), 315[PTP].
  7. S. Furuichi and S. Machida, Nuovo Cim. 19 (1961), 396.
  8. S. Furuichi, Prog. Theor. Phys. 27 (1962), 51[PTP].
  9. S. Furuichi, Prog. Theor. Phys. 29 (1963), 235[PTP].
  10. M. Matsumoto and W. Watari, Prog. Theor. Phys. 11 (1954), 63[PTP].
  11. I. Sato, Phys. Rev. 127 (1962), 1325 [APS][ Errata; 128 (1962), 2925[APS]].
  12. D. Amati, E. Leader and B. Vitale, Phys. Rev. 130 (1963), 750[APS].
  13. J. Bowcock, N. Cottingham and D. Lurié, Nuovo Cim. 16 (1960), 918; ibid. 19 (1961), 142.
  14. J. W. Durso and P. Signell, Phys. Rev. 135 (1964), B1057[APS].
  15. N. Hoshizaki, S. Otsuki, W. Watari and M. Yonezawa, Prog. Theor. Phys. 27 (1962), 1199[PTP].
  16. S. Sawada, T. Ueda, W. Watari and M. Yonezawa, Prog. Theor. Phys. 28 (1962), 991[PTP].
  17. S. Sawada, T. Ueda, W. Watari and M. Yonezawa, Prog. Theor. Phys. 32 (1964), 380[PTP].
  18. A. Scotti and D. Y. Wong, Phys. Rev. Lett. 10 (1963), 142[APS]; Phys. Rev. 138 (1965), B145[APS].
    V. V. Babikov, Prog. Theor. Phys. 29 (1963), 712[PTP].
    R. A. Bryan, C. R. Dismukes and W. Ramsey, Nucl. Phys. 45 (1963), 353[CrossRef].
    P. B. Kantor, Phys. Rev. Lett. 12 (1964), 52[APS].
    M. H. MacGregor, Phys. Rev. Lett. 12 (1964), 403[APS].
    R. A. Bryan and B. L .Scott, Phys. Rev. 135 (1964), B434[APS].
  19. S. Furuichi and M. Yonezawa, Prog. Theor. Phys. 33 (1965), 238[PTP].
  20. D. Amati, E. Leader and B. Vitale, Nuovo Cim. 17 (1960), 68.
  21. G. F. Chew, M. L. Goldberger, F. E. Low and Y. Nambu, Phys. Rev. 106 (1957), 1337[APS].
  22. W. R. Frazer and J. R. Fulco, Phys. Rev. 117 (1960), 1603[APS].
  23. H. P. Stapp, T. J. Ipsilantis and N. Metropolis, Phys. Rev. 105 (1957), 302[APS].
  24. D. Amati, E. Leader and B. Vitale, Nuovo Cim. 18 (1960), 409.
  25. For example, M. Roos, Rev. Mod. Phys. 35 (1963), 314[APS].
  26. S. Matsuyama and H. Miyazawa, Prog. Theor. Phys. 19 (1958), 517[PTP].
  27. J. Goto and S. Machida, Prog. Theor. Phys. 25 (1961), 64[PTP].
  28. S. Furuichi, S. Sawada, T. Ueda, W. Watari and M. Yonezawa, Prog. Theor. Phys. 32 (1964), 966[PTP].
  29. G. Breit, M. H. Hull, Jr., K. E. Lassila and K. D. Pyatt, Jr., Phys. Rev. 120 (1960), 2227[APS].

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 35 No. 2 (1966) pp. 333-335 :
    Pion-Pion Interaction
    Susumu Furuichi, Hiroyuki Kanada and Keiji Watanabe
  2. Progress of Theoretical Physics Vol. 35 No. 3 (1966) pp. 408-415 :
    Pion-Pion Correlation Effect in Two-Pion-Exchange Contribution for Nucleon-Nucleon Scattering
    Susumu Furuichi and Keiji Watanabe
  3. Progress of Theoretical Physics Vol. 36 No. 1 (1966) pp. 184-185 :
    Twp-Pion-Exchange Potential with Nucleon Pairs
    Noboru Hiroshige and Kei Senba
  4. Progress of Theoretical Physics Vol. 36 No. 2 (1966) pp. 348-365 :
    Dispersion Theoretic Calculation of the Two-Pion-Exchange Contribution in Nucleon-Nucleon Scattering. II
    Susumu Furuichi and Wataro Watari
  5. Progress of Theoretical Physics Vol. 37 No. 1 (1967) pp. 75-87 :
    Two-Pion-Exchange Potential with Nucleon-Pair Effects
    Noboru Hiroshige
  6. Progress of Theoretical Physics Vol. 37 No. 2 (1967) pp. 465-467 :
    Effect of Higher πN Resonances to Subtraction Constant in the ππ→NN Dispersion Relation
    Susumu Furuichi and Keiji Watanabe
  7. Progress of Theoretical Physics Vol. 37 No. 6 (1967) pp. 1147-1166 :
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    Masahiro Sato and Ryozo Tamagaki
  8. Progress of Theoretical Physics Vol. 38 No. 2 (1967) pp. 516-518 :
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    Susumu Furuichi and Tōru Sōkawa
  9. Progress of Theoretical Physics Vol. 38 No. 3 (1967) pp. 636-652 :
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  10. Progress of Theoretical Physics Vol. 38 No. 5 (1967) pp. 1200-1202 :
    Kinematical Considerations on Three-Pion-Exchange Contributions in Nucleon-Nucleon Scattering
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  11. Progress of Theoretical Physics Vol. 41 No. 1 (1969) pp. 105-130 :
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  12. Progress of Theoretical Physics Vol. 41 No. 2 (1969) pp. 461-472 :
    One-Boson-Exchange Modes and Two- and Three-Pion Exchange in Nucleon-Nucleon Scattering. II
    Susumu Furuichi, Hiroshi Suemitsu, Wataro Watari and Minoru Yonezawa
  13. Progress of Theoretical Physics Vol. 41 No. 3 (1969) pp. 850-852 :
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    Susumu Furuichi, Wataro Watari and Minoru Yonezawa
  14. Progress of Theoretical Physics Vol. 41 No. 6 (1969) pp. 1504-1514 :
    On the Effect of Higher π-N Resonances on N-N Scattering
    Susumu Furuichi and Tohru Sōkawa
  15. Progress of Theoretical Physics Vol. 43 No. 3 (1970) pp. 696-708 :
    Nuclear Force in the Inner Region and One-Boson-Exchange Model
    Tamotsu Ueda
  16. Progress of Theoretical Physics Vol. 43 No. 6 (1970) pp. 1560-1573 :
    A Multi-Channel Approach to High Energy Reactions by the One-Boson-Exchange Model
    Noboru Hiroshige and Wataro Watari
  17. Progress of Theoretical Physics Vol. 44 No. 1 (1970) pp. 183-192 :
    High Energy Proton-Proton Scattering and an Extended Particle Model
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  18. Progress of Theoretical Physics Vol. 44 No. 3 (1970) pp. 711-728 :
    Two-Pion-Exchange Contribution to Nucleon-Nucleon Scattering on the Basis of Pion-Pion Dynamics
    Susumu Furuichi, Hiroyuki Kanada and Keiji Watanabe
  19. Progress of Theoretical Physics Vol. 47 No. 6 (1972) pp. 1922-1934 :
    Regge-Like Behaviour of Necleon-Nucleon Scattering Amplitudes at Low Energy
    Hiroshi Suemitsu
  20. Progress of Theoretical Physics Vol. 49 No. 2 (1973) pp. 541-551 :
    Remarks on the Regge-Like Behaviour of the One-Boson-Exchange Amplitude in Low-Energy Nucleon-Nucleon Scattering
    Yoshinori Susuki
  21. Progress of Theoretical Physics Vol. 50 No. 4 (1973) pp. 1312-1333 :
    Nuclear Forces in Momentum Space with One-Boson-Exchange Model
    Norio Hoshizaki and Tsuyoshi Kadota
  22. Progress of Theoretical Physics Vol. 58 No. 3 (1977) pp. 850-863 :
    The Pauli Principle Effect in Nuclear Matter on the I = J = 0 Part of the Potential due to the Exchange of Interacting Two Pions
    Tamotsu Ueda and Shuji Takagi

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