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PION-PION INTERACTION AND PION-NUCLEON SCATTERING

Journal Article · · Progr. Theoret. Phys. (Kyoto)
DOI:https://doi.org/10.1143/PTP.23.731· OSTI ID:4169639
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Pion-pion interactions are 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 the following conclusion is reached: In the Isotopic spin state I = 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 I 1 (P-wave) of plon-pion state a definite conclusion could not be obtained. Finally, the possibility of explaining the momentum dependence of pion-nucleon phase shift han the 800 deg / sub 13/ related to tbe pion-pion interaction is briefly discussed. (auth)
Research Organization:
Yamagata Univ., Japan; Tohoku Univ., Sendai
Sponsoring Organization:
USDOE
NSA Number:
NSA-14-020859
OSTI ID:
4169639
Journal Information:
Progr. Theoret. Phys. (Kyoto), Journal Name: Progr. Theoret. Phys. (Kyoto) Vol. Vol: 23
Country of Publication:
Country unknown/Code not available
Language:
English

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Related Subjects

DIFFERENTIAL EQUATIONS
DISPERSION RELATIONS
ELEMENTARY PARTICLES
FIELD THEORY
INTERACTIONS
ISOSPIN
MOMENTUM
NUCLEONS
PARTICLE MODELS
PHYSICS
PIONS
SCATTERING
SPECTRAL SHIFT