Determination of Pion-Nucleon <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi></math></span>-Wave Scattering Lengths by the <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mfrac><mrow><mi>N</mi></mrow><mrow><mi>D</mi></mrow></mfrac></math></span> Method

S. K. Bose; S. N. Biswas

doi:10.1103/PhysRev.134.B635

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Determination of Pion-Nucleon $S$ -Wave Scattering Lengths by the $\frac{N}{D}$ Method

S. K. Bose and S. N. Biswas

Tata Institute of Fundamental Research, Bombay, India

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Phys. Rev. 134, B635 – Published 11 May, 1964

DOI: https://doi.org/10.1103/PhysRev.134.B635

Abstract

The pion-nucleon $S$ -wave scattering lengths are calculated using the method originally developed by Balázs, wherein an effective-range two-pole approximation is made for the numerator function. The residues of the effective-range poles are determined by matching the amplitude and its derivative with those calculated with a fixed energy dispersion relation. In calculating the latter the contribution of only the $N^{*}$ and $ρ$ , together with those of appropriate nucleon-pole terms, are retained. The calculated scattering length in the $T = \frac{3}{2}$ state is in excellent agreement with experimental result, while for the $T = \frac{1}{2}$ state, the calculated value, though of the right sign, is about twice the experimental scattering length.

References (13)

L. A. P. Balázs, Phys. Rev. 126, 1220 (1962)
F. Zachariasen and C. Zemach, Phys. Rev. 128, 849 (1962)
E. S. Abers and C. Zemach, Phys. Rev. 131, 2305 (1963)
J. S. Ball and D. Wong, La Jolla preprint, 1963 (unpublished)
V. Singh and B. M. Udgaonkar, Phys. Rev. 130, 1177 (1963)
S. C. Frautschi and J. D. Walecka, Phys. Rev. 120, 1486 (1960)
[5] [B. M. Udgaonkar (private communication)]
V. Singh and B. M. Udgaonkar, Phys. Rev. 128, 1820 (1962)
W. S. Woolcock, Proceedings of the Aix-en-Provence International Conference on Elementary Particles, 1961 (Centre d'Etudes Nucléaires de Saclay, Seine et Oise, 1961), p. 459
[5] L. A. P. Balázs, Phys. Rev. 132, 867 (1963)
J. L. Uretsky, Phys. Rev. 123, 1459 (1961)
J. J. Sakurai, Proceedings of International School of Physics, Varenna, 1963 (unpublished)
J. Bowcock, W. N. Cottingham, and D. Lurie, Nuovo Cimento 16, 918 (1960)

[c1] L. A. P. Balázs, Phys. Rev. 126, 1220 (1962)

[c2] F. Zachariasen and C. Zemach, Phys. Rev. 128, 849 (1962)

[c3] E. S. Abers and C. Zemach, Phys. Rev. 131, 2305 (1963)

[c4] J. S. Ball and D. Wong, La Jolla preprint, 1963 (unpublished)

[c5] V. Singh and B. M. Udgaonkar, Phys. Rev. 130, 1177 (1963)

[c6] S. C. Frautschi and J. D. Walecka, Phys. Rev. 120, 1486 (1960)

[c7] [5] [B. M. Udgaonkar (private communication)]

[c8] V. Singh and B. M. Udgaonkar, Phys. Rev. 128, 1820 (1962)

[c9] W. S. Woolcock, Proceedings of the Aix-en-Provence International Conference on Elementary Particles, 1961 (Centre d'Etudes Nucléaires de Saclay, Seine et Oise, 1961), p. 459

[c10] [5] L. A. P. Balázs, Phys. Rev. 132, 867 (1963)

[c11] J. L. Uretsky, Phys. Rev. 123, 1459 (1961)

[c12] J. J. Sakurai, Proceedings of International School of Physics, Varenna, 1963 (unpublished)

[c13] J. Bowcock, W. N. Cottingham, and D. Lurie, Nuovo Cimento 16, 918 (1960)

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Determination of Pion-Nucleon $S$ -Wave Scattering Lengths by the $\frac{N}{D}$ Method

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Determination of Pion-Nucleon S-Wave Scattering Lengths by the ND Method

Abstract

References (13)

Determination of Pion-Nucleon $S$ -Wave Scattering Lengths by the $\frac{N}{D}$ Method