APPLICATION OF GENERAL UNITARITY TO PION-NUCLEON SCATTERING

Journal Article · Mon Jan 15 00:00:00 EST 1962 · Physical Review (U.S.) Superseded in part by Phys.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.125.714· OSTI ID:4806530

Meetz, K

The pi - pi -N intermediate state is included in the unitarity condition of pion-nucleon scattering. The general unitarity relations then couple the amplitudes for pi -N and pi - pi -N scattering, and one-pion production or absorption. The kinematical structure of these amplitudes is discussed and a formal decomposition into partial waves is outlined. The dynamical approach is based on a system of coupled partial wave dispersion relations. The dynamical singularities of pi -N scattering can be taken from the Mandelstam representation, whereas perturbation-theoretic approximations must be made for the other amplitudes. The dispersion relations can be solved by the generalized N/D method. As an example, a one-pion exchange approximation for the production and absorption amplitudes is considered. It is shown that amplitudes can be chosen which do not have any kinematical singularities. The N/D method here takes a more simple form by setting up integral equations for the N functions rather than for the D functions. Integrations over contours in the complex plane are then avoided. (auth)

• Research Organization: Princeton Univ., N.J.
• NSA Number: NSA-16-009383
• OSTI ID: 4806530
• Journal Information: Physical Review (U.S.) Superseded in part by Phys.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, Vol. Vol: 125; Other Information: Orig. Receipt Date: 31-DEC-62
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

PHYSICS
ABSORPTION
CONFIGURATION
DIFFERENTIAL EQUATIONS
DISPERSION RELATIONS
ENERGY LEVELS
FIELD THEORY
INTEGRAL EQUATIONS
INTEGRALS
INTERACTIONS
MANDELSTAM REPRESENTATION
MATHEMATICS
MOTION
N/D METHOD
NUCLEONS
NUMERICALS
OPE MODEL
PARTICLE MODELS
PERTURBATION THEORY
PIONS
PRODUCTION
REACTION KINETICS
SCATTERING