BEHAVIOR OF SCATTERING AMPLITUDES AT HIGH ENERGIES, BOUND STATES, AND RESONANCES

Journal Article · Sun Apr 15 04:00:00 EST 1962 · Physical Review (U.S.) Superseded in part by Phys.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.126.766· OSTI ID:4830906

Blankenbecler, R; Goldberger, M L

An exact Fourier-Bessel representation of the scattering amplitude is introduced and discussed for potential scattering and field theory. It is shown to contain the Mandelstam representation as a special case. The representation automatically satisfies unitarity exactly in the high-energy limit, even in the many-channel situation. The behavior of the scattering amplitude for large momentum transfers is discussed and it is demonstrated that this limit is directly connected with the formation of bound states and resonances. A selection rule governing the ordering of resonances is derived. A variational principle for calculating the asymptotic dependence on momentum transfer in potential scattering is formulated. Some relations between the asymptotic behaviors of pi - pi , pi -N, and N-N are developed, and related to the single- particle poles and low-energy resonances. (auth)

• Research Organization: Princeton Univ., N.J.
• NSA Number: NSA-16-018603
• OSTI ID: 4830906
• Journal Information: Physical Review (U.S.) Superseded in part by Phys.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 D, Journal Name: Physical Review (U.S.) Superseded in part by Phys.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: 126; ISSN PHRVA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

BESSEL FUNCTIONS
BOUND STATE
ENERGY
ENERGY RANGE
FIELD THEORY
FOURIER TRANSFORMATIONS
HOLES
MANDELSTAM REPRESENTATION
MATHEMATICS
MOMENTUM
NUCLEONS
PHYSICS
PIONS
QUANTUM MECHANICS
RESONANCE
SCATTERING
SCATTERING AMPLITUDE
SELECTION RULES
TRANSIENTS
UNITARITY
VARIATIONAL METHOD
VARIATIONAL PRINCIPLE
VARIATIONS