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Prog. Theor. Phys. Vol. 24 No. 6 (1960) pp. 1262-1274

Pion-Nucleon Scattering and Pion-Pion Interaction

Shin Ishida

Department of Physics, Kyoto University, Kyoto

(Received July 27, 1960)

Abstract:

S-wave pion-nucleon scattering is investigated from the viewpoint that pion-pion interaction is important. Starting from the interaction Lagrangian L_I
-L_I = G² /(2M) \intρ_c(r)φ²(r)d³r + (G / 2M)²τ· \intρ_c(r)φ(r) ×\dotφ(r)d³r + V(0) \intρ_π(r)φ²(r)d³r,
(where the third term corresponds to the effective potential obtained from the original pion-pion interaction H_I^π-π = λ(φ·φ)²,) we solve directly the Klein-Gordon equation on the matrix-elements of the meson field operator between the nulceon state and the nucleon plus one-meson state. Choosing Yukawa type for the form factors ρ_i(r) = (4π r)^-1Λ_i² exp [-Λ_i r], we can obtain the best fit to the experimental behavior of the S-wave phase shifts for the following value of the parameters: Λ_c ≈5µ, Λ_π≈3.5µ, (2/4 π)(G²/2M+V(0)) = (2/4π)(G²/2M)(2/10) ∼0 = (0.4∼0)µ^-1. This choice of V(0) corresponds to the original pion-pion coupling constant λ/4π= 0.3 ∼0.5 and is consistent with the value |λ|/4π≈1 determined from the (π-2π) process at 1.4 Bev. On the basis as obtained above, the qualitative nature of the small P-wave phase shifts is discussed. And we obtain the results which coincide with the ones of analysis by Lomon and Chiu.

URL : http://ptp.ipap.jp/link?PTP/24/1262/
DOI : 10.1143/PTP.24.1262

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References:

1. For example, O. Hara, Prog. Theor. Phys. 24 (1960), 495, [PTP]and reference 16).
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Citing Article(s) :

1. Progress of Theoretical Physics Vol. 27 No. 1 (1962) pp. 33-50 :

   Pion-Pion Interaction

   Shin Ishida and Kazo Nakazawa

2. Progress of Theoretical Physics Vol. 27 No. 2 (1962) pp. 273-282 :

   Form Factor and Its Isoscalar Part of the Nucleons

   Shigeo Goto

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