Properties of the Pion-Pion Interaction Derived from the Analysis of Pion-Nucleon Scatterings
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概要
- 論文の詳細を見る
The properties of the pion-pion interaction are discussed by the use of dispersion relation techniques. New dispersion relations for the pion-nucleon scattering are obtained, by applying the reduction formula to the initial pion and final nucleon operators. In each of these dispersion relations the absorptive part is divided into two parts, one of which is written as an integral of the pion-pion scattering-amplitude multiplied by a certain matrix element similar to the pion-nucleon scattering-amplitude, while the other is written in terms of the phase shifts for the pion-nucleon scattering. Therefore, if the pion-pion scattering-amplitude is expressed in terms of unknown parameters, such as scattering lengths and effective ranges, their values can be determined by the use of these dispersion relations. Thus one can obtain some knowledge about the sign and the strength of the pion-pion interaction. In this way we are led to the conclusion that, in the isotopic spin state I=0 of the pion-pion system, the pion-pion interaction is attractive and its strength is such that the scattering length for the pion-pion scattering is of the same order of magnitude as that of the pion Compton wave length, and that, in the isotopic spin state I=1 of the pion-pion system, the interaction is also attractive and is of the strength at least comparable to that of the pion-nucleon interaction in the (3, 3) state.
- 理論物理学刊行会の論文
- 1959-11-25
著者
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Ueda Yoshiaki
Department Of Cardiovascular Medicine Sanda City Hospital
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Takahashi Atsushi
Department Of Cardiology Akita City General Hospital
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Sato Iwao
Department Of Anatomy School Of Dentistry At Tokyo Nippon Dental University
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Takahashi Atsushi
Departmant Of Surgery(i) Kanazawa University School Of Medicine
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SATO Iwao
Department of Physics, Tohoku University
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