DETERMINATION OF THE PION-NUCLEON SCATTERING AMPLITUDE FROM DISPERSION RELATIONS AND UNITARITY. GENERAL THEORY

Journal Article · Sat Nov 15 04:00:00 EST 1958 · Physical Review (U.S.) Superseded in part by Phys.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.112.1344· OSTI ID:4272597

Mandelstam, S

ABS>A method is proposed for using relativistic dispersion relations, together with unitarity. to determine the pion nucleon scattering amplitude. The usual dispersion relations by themselves are not sufficient, and a representation is assumed which exhibits the analytic properties of the scattering amplitude as a function of the energy snd the momentum transfer. Unitarity conditions for the two reactions pi + N yields pi + N and N + N bar yields 2 pi will be required, and they will be approximated by neglecting states with more than two particles. The method makes use of an iteration procedure analogous to that used by Chew and Low for the corresponding problem in ihe static theory. One has to introduce two coupling constants; the pion-pion coupling constant can be found by fitting the sum of the threshold scattering lengths with experiment. It is hoped that this method avoids some of the formal difficulties of the TammDancoff and Bethe-Salpeter methods and. in particular. the existence of ghost states. The assumptions introduced are justified in perturbation theory. As an incidental result, we find the precise limits of the region for which the absorptive part of the scattering amplitude is an analytic function of the momentum transfer, and hence the boundaries of the region in which the partial-wave expansion is valid. (auth)

• Research Organization: Columbia Univ., New York
• NSA Number: NSA-13-008071
• OSTI ID: 4272597
• Journal Information: Physical Review (U.S.) Superseded in part by Phys.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 D, Journal Name: Physical Review (U.S.) Superseded in part by Phys.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: 112; ISSN PHRVA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

ABSORPTION
ANTINUCLEONS
COUPLING
CROSS SECTIONS
DISPERSION RELATIONS
ENERGY
FIELD THEORY
INTERACTIONS
MOMENTUM
NUCLEONS
PERTURBATION THEORY
PHYSICS AND MATHEMATICS
PIONS
QUANTITATIVE ANALYSIS
RELATIVITY THEORY
SCATTERING