DETERMINATION OF PION-PION SCATTERING AMPLITUDES SATISFYING DISPERSION RELATIONS AND UNITARITY

Journal Article · Wed Feb 01 04:00:00 EST 1961 · Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D

DOI:https://doi.org/10.1103/PhysRev.121.926· OSTI ID:4087566

Moffat, J W

A method was developed for determining the partialwave scattering amplitude in terms of the unitarity condition and the known branch cuts and poles of the inverse amplitude. The method was applied to the problem of pionpion scattering and an implicit solution to the pion-pion partial-wave amplitude was derived for any angular momentum state and for both elastic and inelastic scattering. With the aid of this solution the low-energy resonance behavior of the pion-pion scattering system was studied by neglecting all inelastic processes and concentrating on s and p waves. It was found that a p-wave resonance with a position and width required by nucleon electromagnetic structure can be determined in terms of two parameters. An iteration procedure is described that is applicable when the p wave dominates the equations, and this proce dure determines the contribution of the unphysical cut. The first iteration of the unphysical cut was numerically in- tegrated on the IBM 709, and the results showed that the shift of the resonance position due to the unphysical branch cut can be neglected. (auth)

• Research Organization: RIAS, Baltimore
• NSA Number: NSA-15-009718
• OSTI ID: 4087566
• Journal Information: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D, Journal Name: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D Vol. Vol: 121; ISSN PHRVA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

DIGITAL SYSTEMS
DISPERSION THEORY
FIELD THEORY
IBM 709
MATHEMATICS
NUMERICALS
P-WAVE
PHYSICS
PIONS
QUANTUM MECHANICS
RESONANCE
SCATTERING
SCATTERING AMPLITUDE
UNITARITY