Two-Pion-Exchange Contribution to Nucleon-Nucleon Scattering

Judith Binstock

doi:10.1103/PhysRevD.3.1139

Access by Xinjiang University

Two-Pion-Exchange Contribution to Nucleon-Nucleon Scattering

Judith Binstock

Texas A & M University, College Station, Texas 77843

PDF

Phys. Rev. D 3, 1139 – Published 1 March, 1971

DOI: https://doi.org/10.1103/PhysRevD.3.1139

Abstract

The two-pion-exchange contribution to nucleon-nucleon scattering is calculated, following the method of Goldberger, Grisaru, MacDowell, and Wong. The results are shown for two cases. In the first case, the input $π π \to \bar{N} N$ amplitude is approximated by a nucleon pole term only; in the second case it is approximated by a nucleon pole term plus a $Δ (1236)$ pole term. It is found that for the physical value of the $Δ (1236)$ width, $Γ_{Δ} = 120$ MeV, there is very little difference for the two cases in the resulting effect on nucleon-nucleon scattering below 400 MeV. The model is mathematically equivalent to the Amati-Leader-Vitale approach for all but ${}^{1}S_{0}$ , ${}^{3}P_{0}$ , and ${}^{3}P_{1}$ $NN$ partial waves. The results are found to be sensitive to the value of $Γ_{Δ}$ .

References (34)

M. Taketani, S. Nakemura, and M. Sasaki, Progr. Theoret. Phys. (Kyoto) 28, 991 (1962) ibid.32, 380 (1964) G. F. Chew, Phys. Rev. 112, 1380 (1958)
R. E. Seamon, K. A. Friedman, G. Breit, R. D. Haracz, J. M. Holt, and A. Prakash, Phys. Rev. 165, 1579 (1968)
M. H. MacGregor, R. A. Arndt, and R. M. Wright, Phys. Rev. 182, 1714 (1969)
V. K. Samaranayake and W. S. Woolcock, Phys. Rev. Letters 15, 936 (1965)
N. Hoshizaki, S. Otsuki, W. Watari, and M. Yonezawa, Progr. Theoret. Phys. (Kyoto) 27, 1199 (1962)
S. Sawada, T. Ueda, W. Watari, M. Yonezawa, Progr. Theoret. Phys. (Kyoto) 28, 991 (1962) ibid.32, 380 (1964) ibid.Suppl. 39, 140 (1967)
R. S. McKean, Jr., Phys. Rev. 125, 1399 (1962)
R. A. Bryan, C. R. Dismukes, and W. Ramsey, Nucl. Phys. 45, 353 (1963)
A. Scotti and D. Y. Wong, Phys. Rev. Letters 10, 142 (1963) Phys. Rev. 138, B145 (1965)
J. S. Ball, A. Scotti, and D. Y. Wong, Phys. Rev. 142, 1000 (1966)
R. A. Bryan and B. L. Scott, Phys. Rev. 135, B434 (1964) ibid.164, 1215 (1967) ibid.177, 1435 (1969)
G. Köpp and G. Kramer, Phys. Letters 19, 593 (1965)
G. Köpp, Z. Physik 191, 273 (1966)
R. A. Arndt, R. A. Bryan, M. H. MacGregor, Phys. Rev. 152, 1490 (1966) ibid.184, 1966(E) (1969) Phys. Letters 21, 314 (1966)
R. A. Bryan and R. A. Arndt, Phys. Rev. 150, 1299 (1966)
A. E. S. Green and T. Sawada, Rev. Mod. Phys. 39, 594 (1967) Nucl. Phys. B2, 276 (1967)
T. Ueda and A. E. S. Green, Phys. Rev. 174, 1304 (1968)
R. W. Stagat, F. Riewe, and A. E. S. Green, Phys. Rev. Letters 24, 631 (1970)
R. A. Bryan, Nucl. Phys. A146, 359 (1970)
A. Gersten, R. H. Thompson, and A. E. S. Green, University of Florida Report, 1970 (unpublished)
[22]
E. B. Hughes, R. A. Griffy, M. R. Yearian, and R. Hofstadter, Phys. Rev. 139, B458 (1965)
M. L. Goldberger, M. T. Grisaru, S. W. MacDowell, and D. Y. Wong, Phys. Rev. 120, 2250 (1960)
G. F. Chew, M. L. Goldberger, F. E. Low, and Y. Nambu, Phys. Rev. 106, 1337 (1957)
J. W. Durso, Phys. Rev. 149, 1234 (1966)
[27]
D. Amati, E. Leader, and B. Vitale, Nuovo Cimento 17, 68 (1960) ibid.18, 409 (1960) Phys. Rev. 130, 750 (1963)
A. Barbaro-Galtieri, S. E. Derenzo, L. Price, A. Rittenberg, A. H. Rosenfeld, N. Barash-Schmidt, C. Bricman, M. Roos, P. Söding, and C. G. Wohl, Rev. Mod. Phys. 42, 87 (1970)
S. Furuichi and W. Watari, Progr. Theoret. Phys. (Kyoto) 34, 594 (1965) ibid.36, 348 (1966) S. Furuichi, ibid. Suppl. 39, 190 (1967)
Omitted endnote
Omitted endnote
B. M. Barker and R. D. Haracz, Phys. Rev. 186, 1624 (1969)
W. R. Wortman, Phys. Rev. 176, 1762 (1968)
Omitted endnote

[c1] M. Taketani, S. Nakemura, and M. Sasaki, Progr. Theoret. Phys. (Kyoto) 28, 991 (1962) ibid.32, 380 (1964) G. F. Chew, Phys. Rev. 112, 1380 (1958)

[c2] R. E. Seamon, K. A. Friedman, G. Breit, R. D. Haracz, J. M. Holt, and A. Prakash, Phys. Rev. 165, 1579 (1968)

[c3] M. H. MacGregor, R. A. Arndt, and R. M. Wright, Phys. Rev. 182, 1714 (1969)

[c4] V. K. Samaranayake and W. S. Woolcock, Phys. Rev. Letters 15, 936 (1965)

[c5] N. Hoshizaki, S. Otsuki, W. Watari, and M. Yonezawa, Progr. Theoret. Phys. (Kyoto) 27, 1199 (1962)

[c6] S. Sawada, T. Ueda, W. Watari, M. Yonezawa, Progr. Theoret. Phys. (Kyoto) 28, 991 (1962) ibid.32, 380 (1964) ibid.Suppl. 39, 140 (1967)

[c7] R. S. McKean, Jr., Phys. Rev. 125, 1399 (1962)

[c8] R. A. Bryan, C. R. Dismukes, and W. Ramsey, Nucl. Phys. 45, 353 (1963)

[c9] A. Scotti and D. Y. Wong, Phys. Rev. Letters 10, 142 (1963) Phys. Rev. 138, B145 (1965)

[c10] J. S. Ball, A. Scotti, and D. Y. Wong, Phys. Rev. 142, 1000 (1966)

[c11] R. A. Bryan and B. L. Scott, Phys. Rev. 135, B434 (1964) ibid.164, 1215 (1967) ibid.177, 1435 (1969)

[c12] G. Köpp and G. Kramer, Phys. Letters 19, 593 (1965)

[c13] G. Köpp, Z. Physik 191, 273 (1966)

[c14] R. A. Arndt, R. A. Bryan, M. H. MacGregor, Phys. Rev. 152, 1490 (1966) ibid.184, 1966(E) (1969) Phys. Letters 21, 314 (1966)

[c15] R. A. Bryan and R. A. Arndt, Phys. Rev. 150, 1299 (1966)

[c16] A. E. S. Green and T. Sawada, Rev. Mod. Phys. 39, 594 (1967) Nucl. Phys. B2, 276 (1967)

[c17] T. Ueda and A. E. S. Green, Phys. Rev. 174, 1304 (1968)

[c18] R. W. Stagat, F. Riewe, and A. E. S. Green, Phys. Rev. Letters 24, 631 (1970)

[c19] R. A. Bryan, Nucl. Phys. A146, 359 (1970)

[c20] A. Gersten, R. H. Thompson, and A. E. S. Green, University of Florida Report, 1970 (unpublished)

[c21] [22]

[c22] E. B. Hughes, R. A. Griffy, M. R. Yearian, and R. Hofstadter, Phys. Rev. 139, B458 (1965)

[c23] M. L. Goldberger, M. T. Grisaru, S. W. MacDowell, and D. Y. Wong, Phys. Rev. 120, 2250 (1960)

[c24] G. F. Chew, M. L. Goldberger, F. E. Low, and Y. Nambu, Phys. Rev. 106, 1337 (1957)

[c25] J. W. Durso, Phys. Rev. 149, 1234 (1966)

[c26] [27]

[c27] D. Amati, E. Leader, and B. Vitale, Nuovo Cimento 17, 68 (1960) ibid.18, 409 (1960) Phys. Rev. 130, 750 (1963)

[c28] A. Barbaro-Galtieri, S. E. Derenzo, L. Price, A. Rittenberg, A. H. Rosenfeld, N. Barash-Schmidt, C. Bricman, M. Roos, P. Söding, and C. G. Wohl, Rev. Mod. Phys. 42, 87 (1970)

[c29] S. Furuichi and W. Watari, Progr. Theoret. Phys. (Kyoto) 34, 594 (1965) ibid.36, 348 (1966) S. Furuichi, ibid. Suppl. 39, 190 (1967)

[c30] Omitted endnote

[c31] Omitted endnote

[c32] B. M. Barker and R. D. Haracz, Phys. Rev. 186, 1624 (1969)

[c33] W. R. Wortman, Phys. Rev. 176, 1762 (1968)

[c34] Omitted endnote

Physical Review D

Export citation

Export citation

Two-Pion-Exchange Contribution to Nucleon-Nucleon Scattering

Abstract

References (34)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation