Determination of Pion-Nucleon Parameters and Phase Shifts by Dispersion Relations

J. Hamilton; W. S. Woolcock

doi:10.1103/RevModPhys.35.737

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Determination of Pion-Nucleon Parameters and Phase Shifts by Dispersion Relations

J. Hamilton and W. S. Woolcock

J. Hamilton

Department of Physics, University College, Gower Street, London, W. C. 1

W. S. Woolcock

Department of Mathematics, University of Queensland, Brisbane, Australia

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Rev. Mod. Phys. 35, 737 – Published 1 October, 1963

DOI: https://doi.org/10.1103/RevModPhys.35.737

References (139)

G. F. Chew and F. E. Low, Phys. Rev. 101, 1570 (1956) J. Hamilton, P. Menotti, G. C. Oades, and L. L. J. Vick, 128, 1881 (1962)
G. F. Chew, M. L. Goldberger, F. E. Low, and Y. Nambu, Phys. Rev. 106, 1337 (1957)
W. S. Woolcock, Ph.D. thesis, Cambridge University (1961) (unpublished)
Omitted endnote
S. Mandelstam, Phys. Rev. 112, 1344 (1958) ibid.115, 1741, 1752 (1959)
J. Hamilton, Theory of Elementary Particles (Oxford University Press, New York, 1959), Chap. VI, paragraph 5
H. J. Bremermann, R. Oehme, and J. G. Taylor, Phys. Rev. 109, 2178 (1958) H. Lehmann, Nuovo Cimento 10, 579 (1958)
M. Jacob and G. C. Wick, Ann. Phys. 7, 404 (1959)
Omitted endnote
J. Hamilton, T. D. Spearman, and W. S. Woolcock, Ann. Phys. 17, 1 (1962) [Sec. V(B)]
Omitted endnote
Omitted endnote
E. C. Titchmarsh, Theory of Fourier Integrals (Oxford University Press, New York, 1948), theorem 101
Omitted endnote
Omitted endnote
D. Atkinson, P. Menotti, G. C. Oades, and L. L. J. Vick (private communication)
F. G. Tricomi, Integral Equations (Interscience Publishers, Inc., New York, 1957), Chapter 4 N. I. Muskheliskvili, Singular Integral Equations (P. Noordhoff Ltd., Groningen, the Netherlands, 1953), Chapter 4
Omitted endnote
H. Lehmann, Hamburg University (1961) (to be published)
Omitted endnote
Omitted endnote
Omitted endnote
B. M. Udgaonkar, Phys. Rev. Letters 8, 142 (1962)
R. Cool, O. Piccioni, and D. Clarke, Phys. Rev. 103, 1082 (1956)
R. G. Thomas. Phys. Rev. 120, 1015 (1960)
Proceedings of the International Conference on High-Energy Nuclear Physics, Geneva, 1962 (CERN Scientific Information Service, Geneva, Switzerland, 1962), edited by J. Prentk and A. Taylor
reference 26
Omitted endnote
J. W. Cronin, Phys. Rev. 118, 824 (1960)
I.Ia Pomeranchuk, Soviet Phys.—JETP 7, 499 (1958)
I. Ia. Pomeranchuk, Soviet Phys.—JETP 3, 306, 307 (1956) S. Z. Belenki, 6, 960 (1958)
G. F. Chew and S. C. Frautschi, Phys. Rev. 7, 394 (1961) ibid.8, 41 (1962) B. M. Udgaonkar Phys. Rev. Letters 8, 142 (1962)
J. Hamilton and T. D. Spearman, Ann. Phys. 12, 172 (1961)
Omitted endnote
D. Amati, M. Fiertz, and V. Glaser, Phys. Rev. Letters 4, 59 (1960)
Omitted endnote
Omitted endnote
G. H. Hardy and D. E. Littlewood, Proc. Math. Soc. (London) 30, 23 (1930)
Omitted endnote
Omitted endnote
Omitted endnote
Omitted endnote
S. Weinberg, Phys. Rev. 124, 2049 (1961)
M. L. Goldberger, H. Miyazawa, and R. Oehme, Phys. Rev. 99, 986 (1955)
J. Hamilton and W. S. Woolcock, Phys. Rev. 118, 291 (1960)
T. D. Spearman, Nucl. Phys. 16, 402 (1960)
G. von Dardel, D. Dekkers, R. Mermod, M. Vivargent, G. Weber, and K. Winter, Phys. Rev. Letters 8, 173 (1962)
J. Hamilton, Proceedings of the International Conference on Very High-Energy Physics, Geneva, 1961 (CERN Scientific Information Service, Geneva, Switzerland, 1961), p. 151
Omitted endnote
Omitted endnote
A. C. Finn, Phys. Rev. 119, 1786 (1960)
V. Singh and B. M. Udgaonkar, Phys. Rev. 123, 1487 (1961)
A. C. Finn (reference 50)
Omitted endnote
Omitted endnote
S. C. Frautschi, M. Gell-Mann, and F. Zachariasen [Phys. Rev. 126, 2204 (1962)]
C. Lovelace, Nuovo Cimento 25, 730 (1962)
G. Cocconi in Proceedings of the International Conference on High-Energy Physics, Geneva, 1962 (CERN Scientific Information Service, Geneva, Switzerland, 1962)
S. C. Frautschi, M. Gell-Mann, and F. Zachariasen, Phys. Rev. 126, 2204 (1962)
Omitted endnote
H. Lehmann, Nuovo Cimento 10, 579 (1958)
Omitted endnote
Omitted endnote
Omitted endnote
W. R. Frazer and J. R. Fulco, Phys. Rev. 117, 1063 (1960)
A. R. Irwin, R. H. March, W. D. Walker, and E. West, Proceedings of the International Conference on Elementary Particles, Aix-en-Provence, 1961 (C.E.N. Saclay, France, 1961), Vol. I, p. 249 G. Puppi, in Proceedings of the International Conference on High-Energy Physics, Geneva, 1962, edited by J. Prentke and A. Taylor (CERN Scientific Information Service, Geneva, Switzerland, 1962)
Omitted endnote
J. H. Foote, O. Chamberlain, E. H. Rogers, and H. M. Steiner, Phys. Rev. 122, 959 (1961)
Omitted endnote
A. C. Finn, Plays. Rev. 119, 1786 (1960)
J. Hamilton, T. D. Spearman, and W. S. Woodcock, Ann. Phys. 17, 1 (1962) J. Hamilton, P. Menotti, G. C. Oades, and L. L. J. Vick, Phys. Rev. 128, 1881 (1962)
J. Hamilton and W. S. Woolcock, Phys. Rev. 118, 291 (1960)
Omitted endnote
W. S. Woolcock, Ph.D. thesis, University of Cambridge, 1961 (unpublished)
W. S. Woolcock, in Proceedings of the Tenth International Conference on High-Energy Physics, Rochester, edited by E. C. G. Sudarshan, J. H. Tinlot, and A. C. Melissinos (Interscience Publishers, Inc., New York, 1960), p. 302
J. Hamilton and W. S. Woolcock, Phys. Rev. 118, 291 (1960) J. H. Foote et al. (reference 67)
S. W. Barnes, B. Rose, G. Giacomelli, J. Ring, R. Miyake, and K. Kinsey, Phys. Rev. 117, 116 and 238 (1960)
D. N. Edwards and T. Massam (private communication)
J. H. Foote et al. (reference 67)
Omitted endnote
Omitted endnote
H. P. Noyes and D. N. Edwards, Phys. Rev. 118, 1409 (1960)
V. G. Zinov, S. M. Korenchenko, N. L. Polumordvinova, and G. N. Tentyukova, Soviet Phys.-JETP 11, 1016 (1960)
J. Hamilton and W. S. Woolcock, Phys. Rev. 118, 291 (1960)
J. Deahl, M. Derrick, J. Fetkovich, T. Fields, and G. B. Yodh, Phys. Rev. 124, 1987 (1961)
J. C. Brisson, R. Omnes, and G. Valladas, Nuovo Cimento 19, 210 (1961) Proceedings of the International Conference on Elementary Particles, Aix-en-Provence, 1961 (C.E.N. Saclay, France, 1961), Vol. I, p. 467
J. Hamilton, Phys. Rev. 110, 1134 (1958)
Omitted endnote
W. J. Willis, Phys. Rev. 116, 753 (1959)
M. E. Blevins, M. M. Block, and J. Leitner, Phys. Rev. 112, 1287 (1958) W. D. Walker, 118, 1612 (1960)
Omitted endnote
Omitted endnote
N. P. Klepikov, Dubna preprint (1960) W. N. Wong and M. Ross, Phys. Rev. Letters 3, 398 (1959)
R. Blanckenbeckler and M. L. Goldberger, Phys. Rev. 126, 766 (1962) W. M. Layson, CERN preprint (1961)
R. Omnes and G. Valladas (reference 85)
Omitted endnote
B. Udgaonkar, Phys. Rev. Letters 8, 142 (1962)
Omitted endnote
Omitted endnote
Omitted endnote
Omitted endnote
reference 74
M. Cini, R. Gatto, E. L. Goldwasser, and M. Ruderman, Nuovo Cimento 10, 242 (1958)
reference 73 [J. Hamilton and W. S. Woolcock, Phys. Rev. 118, 291 (1960)]
Omitted endnote
J. Hamilton, P. Menotti, G. C. Oades, and L. L. J. Vick, Phys. Rev. 128, 1881 (1962)
reference 75
Omitted endnote
G. F. Chew and S. C. Frautschi, Phys. Rev. Letters 7, 394 (1961) ibid.8, 41
reference 85)
S. W. Barnes et al. (cf. reference 76)
D. E. Knapp and K. F. Kinsev, Bull. Am. Phys. Soc. 6, 435 (1961)
Omitted endnote
Omitted endnote
D. N. Edwards, S. G. F. Frank, and J. R. Holt, Proc. Phys. Soc. (London) 73, 856 (1959) D. N. Edwards and T. Massam, private communications
W. S. Woolcock, Proceedings of the International Conference on High-Energy Physics, Aix-en-Provence, 1961 (C.E.N. Saclay, France, 1961), Vol. I, pp. 459 and 461
reference 75
J. Hamilton and W. S. Woolcock. Phys. Rev. 118, 29 (1960)
J. Hamilton, P. Menotti, G. C. Oades, and L. L. J. Vick, Phys. Rev. 128, 1881 (1962)
Sec. 3(xi) of reference (118)
Omitted endnote
Omitted endnote
Omitted endnote
Omitted endnote
J. H. Foote et al. (reference 67)
Omitted endnote
V. G. Zinov et al. (reference 82)
A. Loria et al., Nuovo Cimento 22, 820 (1961)
references 73 and 115
G. Höhler and K. Dietz, Z. Physik 160, 453 (1960)
J. Deahl et al. (reference 84)
Omitted endnote
Omitted endnote
Hamilton and T. D. Spearman, Ann. Phys. 12, 172 (1961)
D. Atkinson, Phys. Rev. 128, 1908 (1962)
Omitted endnote
Omitted endnote
Omitted endnote
Sec. 15.4 of E. T. Whittaker and G. N. Watson, Modern Analysis (Cambridge University Press, New York, 1952) Sec. 11.3 of E. T. Copson, Theory of Functions of a Complex Variable (Oxford University Press, New York, 1952)

[c1] G. F. Chew and F. E. Low, Phys. Rev. 101, 1570 (1956) J. Hamilton, P. Menotti, G. C. Oades, and L. L. J. Vick, 128, 1881 (1962)

[c2] G. F. Chew, M. L. Goldberger, F. E. Low, and Y. Nambu, Phys. Rev. 106, 1337 (1957)

[c3] W. S. Woolcock, Ph.D. thesis, Cambridge University (1961) (unpublished)

[c4] Omitted endnote

[c5] S. Mandelstam, Phys. Rev. 112, 1344 (1958) ibid.115, 1741, 1752 (1959)

[c6] J. Hamilton, Theory of Elementary Particles (Oxford University Press, New York, 1959), Chap. VI, paragraph 5

[c7] H. J. Bremermann, R. Oehme, and J. G. Taylor, Phys. Rev. 109, 2178 (1958) H. Lehmann, Nuovo Cimento 10, 579 (1958)

[c8] M. Jacob and G. C. Wick, Ann. Phys. 7, 404 (1959)

[c9] Omitted endnote

[c10] J. Hamilton, T. D. Spearman, and W. S. Woolcock, Ann. Phys. 17, 1 (1962) [Sec. V(B)]

[c11] Omitted endnote

[c12] Omitted endnote

[c13] E. C. Titchmarsh, Theory of Fourier Integrals (Oxford University Press, New York, 1948), theorem 101

[c14] Omitted endnote

[c15] Omitted endnote

[c16] D. Atkinson, P. Menotti, G. C. Oades, and L. L. J. Vick (private communication)

[c17] F. G. Tricomi, Integral Equations (Interscience Publishers, Inc., New York, 1957), Chapter 4 N. I. Muskheliskvili, Singular Integral Equations (P. Noordhoff Ltd., Groningen, the Netherlands, 1953), Chapter 4

[c18] Omitted endnote

[c19] H. Lehmann, Hamburg University (1961) (to be published)

[c20] Omitted endnote

[c21] Omitted endnote

[c22] Omitted endnote

[c23] B. M. Udgaonkar, Phys. Rev. Letters 8, 142 (1962)

[c24] R. Cool, O. Piccioni, and D. Clarke, Phys. Rev. 103, 1082 (1956)

[c25] R. G. Thomas. Phys. Rev. 120, 1015 (1960)

[c26] Proceedings of the International Conference on High-Energy Nuclear Physics, Geneva, 1962 (CERN Scientific Information Service, Geneva, Switzerland, 1962), edited by J. Prentk and A. Taylor

[c27] reference 26

[c28] Omitted endnote

[c29] J. W. Cronin, Phys. Rev. 118, 824 (1960)

[c30] I.Ia Pomeranchuk, Soviet Phys.—JETP 7, 499 (1958)

[c31] I. Ia. Pomeranchuk, Soviet Phys.—JETP 3, 306, 307 (1956) S. Z. Belenki, 6, 960 (1958)

[c32] G. F. Chew and S. C. Frautschi, Phys. Rev. 7, 394 (1961) ibid.8, 41 (1962) B. M. Udgaonkar Phys. Rev. Letters 8, 142 (1962)

[c33] J. Hamilton and T. D. Spearman, Ann. Phys. 12, 172 (1961)

[c34] Omitted endnote

[c35] D. Amati, M. Fiertz, and V. Glaser, Phys. Rev. Letters 4, 59 (1960)

[c36] Omitted endnote

[c37] Omitted endnote

[c38] G. H. Hardy and D. E. Littlewood, Proc. Math. Soc. (London) 30, 23 (1930)

[c39] Omitted endnote

[c40] Omitted endnote

[c41] Omitted endnote

[c42] Omitted endnote

[c43] S. Weinberg, Phys. Rev. 124, 2049 (1961)

[c44] M. L. Goldberger, H. Miyazawa, and R. Oehme, Phys. Rev. 99, 986 (1955)

[c45] J. Hamilton and W. S. Woolcock, Phys. Rev. 118, 291 (1960)

[c46] T. D. Spearman, Nucl. Phys. 16, 402 (1960)

[c47] G. von Dardel, D. Dekkers, R. Mermod, M. Vivargent, G. Weber, and K. Winter, Phys. Rev. Letters 8, 173 (1962)

[c48] J. Hamilton, Proceedings of the International Conference on Very High-Energy Physics, Geneva, 1961 (CERN Scientific Information Service, Geneva, Switzerland, 1961), p. 151

[c49] Omitted endnote

[c50] Omitted endnote

[c51] A. C. Finn, Phys. Rev. 119, 1786 (1960)

[c52] V. Singh and B. M. Udgaonkar, Phys. Rev. 123, 1487 (1961)

[c53] A. C. Finn (reference 50)

[c54] Omitted endnote

[c55] Omitted endnote

[c56] S. C. Frautschi, M. Gell-Mann, and F. Zachariasen [Phys. Rev. 126, 2204 (1962)]

[c57] C. Lovelace, Nuovo Cimento 25, 730 (1962)

[c58] G. Cocconi in Proceedings of the International Conference on High-Energy Physics, Geneva, 1962 (CERN Scientific Information Service, Geneva, Switzerland, 1962)

[c59] S. C. Frautschi, M. Gell-Mann, and F. Zachariasen, Phys. Rev. 126, 2204 (1962)

[c60] Omitted endnote

[c61] H. Lehmann, Nuovo Cimento 10, 579 (1958)

[c62] Omitted endnote

[c63] Omitted endnote

[c64] Omitted endnote

[c65] W. R. Frazer and J. R. Fulco, Phys. Rev. 117, 1063 (1960)

[c66] A. R. Irwin, R. H. March, W. D. Walker, and E. West, Proceedings of the International Conference on Elementary Particles, Aix-en-Provence, 1961 (C.E.N. Saclay, France, 1961), Vol. I, p. 249 G. Puppi, in Proceedings of the International Conference on High-Energy Physics, Geneva, 1962, edited by J. Prentke and A. Taylor (CERN Scientific Information Service, Geneva, Switzerland, 1962)

[c67] Omitted endnote

[c68] J. H. Foote, O. Chamberlain, E. H. Rogers, and H. M. Steiner, Phys. Rev. 122, 959 (1961)

[c69] Omitted endnote

[c70] A. C. Finn, Plays. Rev. 119, 1786 (1960)

[c71] J. Hamilton, T. D. Spearman, and W. S. Woodcock, Ann. Phys. 17, 1 (1962) J. Hamilton, P. Menotti, G. C. Oades, and L. L. J. Vick, Phys. Rev. 128, 1881 (1962)

[c72] J. Hamilton and W. S. Woolcock, Phys. Rev. 118, 291 (1960)

[c73] Omitted endnote

[c74] W. S. Woolcock, Ph.D. thesis, University of Cambridge, 1961 (unpublished)

[c75] W. S. Woolcock, in Proceedings of the Tenth International Conference on High-Energy Physics, Rochester, edited by E. C. G. Sudarshan, J. H. Tinlot, and A. C. Melissinos (Interscience Publishers, Inc., New York, 1960), p. 302

[c76] J. Hamilton and W. S. Woolcock, Phys. Rev. 118, 291 (1960) J. H. Foote et al. (reference 67)

[c77] S. W. Barnes, B. Rose, G. Giacomelli, J. Ring, R. Miyake, and K. Kinsey, Phys. Rev. 117, 116 and 238 (1960)

[c78] D. N. Edwards and T. Massam (private communication)

[c79] J. H. Foote et al. (reference 67)

[c80] Omitted endnote

[c81] Omitted endnote

[c82] H. P. Noyes and D. N. Edwards, Phys. Rev. 118, 1409 (1960)

[c83] V. G. Zinov, S. M. Korenchenko, N. L. Polumordvinova, and G. N. Tentyukova, Soviet Phys.-JETP 11, 1016 (1960)

[c84] J. Hamilton and W. S. Woolcock, Phys. Rev. 118, 291 (1960)

[c85] J. Deahl, M. Derrick, J. Fetkovich, T. Fields, and G. B. Yodh, Phys. Rev. 124, 1987 (1961)

[c86] J. C. Brisson, R. Omnes, and G. Valladas, Nuovo Cimento 19, 210 (1961) Proceedings of the International Conference on Elementary Particles, Aix-en-Provence, 1961 (C.E.N. Saclay, France, 1961), Vol. I, p. 467

[c87] J. Hamilton, Phys. Rev. 110, 1134 (1958)

[c88] Omitted endnote

[c89] W. J. Willis, Phys. Rev. 116, 753 (1959)

[c90] M. E. Blevins, M. M. Block, and J. Leitner, Phys. Rev. 112, 1287 (1958) W. D. Walker, 118, 1612 (1960)

[c91] Omitted endnote

[c92] Omitted endnote

[c93] N. P. Klepikov, Dubna preprint (1960) W. N. Wong and M. Ross, Phys. Rev. Letters 3, 398 (1959)

[c94] R. Blanckenbeckler and M. L. Goldberger, Phys. Rev. 126, 766 (1962) W. M. Layson, CERN preprint (1961)

[c95] R. Omnes and G. Valladas (reference 85)

[c96] Omitted endnote

[c97] B. Udgaonkar, Phys. Rev. Letters 8, 142 (1962)

[c98] Omitted endnote

[c99] Omitted endnote

[c100] Omitted endnote

[c101] Omitted endnote

[c102] reference 74

[c103] M. Cini, R. Gatto, E. L. Goldwasser, and M. Ruderman, Nuovo Cimento 10, 242 (1958)

[c104] reference 73 [J. Hamilton and W. S. Woolcock, Phys. Rev. 118, 291 (1960)]

[c105] Omitted endnote

[c106] J. Hamilton, P. Menotti, G. C. Oades, and L. L. J. Vick, Phys. Rev. 128, 1881 (1962)

[c107] reference 75

[c108] Omitted endnote

[c109] G. F. Chew and S. C. Frautschi, Phys. Rev. Letters 7, 394 (1961) ibid.8, 41

[c110] reference 85)

[c111] S. W. Barnes et al. (cf. reference 76)

[c112] D. E. Knapp and K. F. Kinsev, Bull. Am. Phys. Soc. 6, 435 (1961)

[c113] Omitted endnote

[c114] Omitted endnote

[c115] D. N. Edwards, S. G. F. Frank, and J. R. Holt, Proc. Phys. Soc. (London) 73, 856 (1959) D. N. Edwards and T. Massam, private communications

[c116] W. S. Woolcock, Proceedings of the International Conference on High-Energy Physics, Aix-en-Provence, 1961 (C.E.N. Saclay, France, 1961), Vol. I, pp. 459 and 461

[c117] reference 75

[c118] J. Hamilton and W. S. Woolcock. Phys. Rev. 118, 29 (1960)

[c119] J. Hamilton, P. Menotti, G. C. Oades, and L. L. J. Vick, Phys. Rev. 128, 1881 (1962)

[c120] Sec. 3(xi) of reference (118)

[c121] Omitted endnote

[c122] Omitted endnote

[c123] Omitted endnote

[c124] Omitted endnote

[c125] J. H. Foote et al. (reference 67)

[c126] Omitted endnote

[c127] V. G. Zinov et al. (reference 82)

[c128] A. Loria et al., Nuovo Cimento 22, 820 (1961)

[c129] references 73 and 115

[c130] G. Höhler and K. Dietz, Z. Physik 160, 453 (1960)

[c131] J. Deahl et al. (reference 84)

[c132] Omitted endnote

[c133] Omitted endnote

[c134] Hamilton and T. D. Spearman, Ann. Phys. 12, 172 (1961)

[c135] D. Atkinson, Phys. Rev. 128, 1908 (1962)

[c136] Omitted endnote

[c137] Omitted endnote

[c138] Omitted endnote

[c139] Sec. 15.4 of E. T. Whittaker and G. N. Watson, Modern Analysis (Cambridge University Press, New York, 1952) Sec. 11.3 of E. T. Copson, Theory of Functions of a Complex Variable (Oxford University Press, New York, 1952)

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Determination of Pion-Nucleon Parameters and Phase Shifts by Dispersion Relations

References (139)

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