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Progress of Theoretical Physics
Article . 1960 . Peer-reviewed
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Pion-Pion Interaction and Pion-Nucleon Scattering

Pion-pion interaction and pion-nucleon scattering
Authors: Kin-ichi Ishida; Yoshiaki Ueda; Atsushi Takahashi;

Pion-Pion Interaction and Pion-Nucleon Scattering

Abstract

Pion-pion interaction is analyzed by using the dispersion relation for pion-nucleon scattering obtained by keeping the momentum transfer between an initial pion and a final nucleon constant. In order to take into account the singularity of two-pion threshold in the dispersion relation, the dispersion relation may be regarded as an integral equation for pion-nucleon scattering amplitude with the kernel of a pion-pion scattering amplitude. When this solution is compared with experiments on pion-nucleon scattering, it is found that the unknown quantity in the dispersion relation is only a pion-pion scattering amplitude. Therefore, if pion-pion amplitude is expressed in terms of an unknown parameter such as . scattering length, then this value can be determined via dispersion relation. Thus we are led to the following conclusion: In the isotopic spin state 1=0 (S-wave) of pion-pion system pion-pion interaction is attractive and the scattering length is of the order of one pion Compton wavelength, while in the isotopic spin state 1=1 (P-wave) of pion-pion state a definite conclusion could not be obtained. Finally the possibility of explaining the momentum dependence of pion-nucleon phase shift a 13 related to the pion-pion interaction is briefly discussed.

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quantum theory

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
6
Average
Top 10%
Top 10%
bronze