SOME ASPECTS OF THE COVARIANT TWO-BODY PROBLEM. II. THE SCATTERING PROBLEM

Journal Article · Fri Jan 01 04:00:00 EST 1960 · Physical Review (U.S.) Superseded in part by Phys.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.117.292· OSTI ID:4202099

Okubo, S; Feldman, D

By way of extension of a previous study of the boundstate problem witain the framework of the covariant Bethe-Salpeter formalism, the scattering of nucleons was investigated in the ladder approximation, assuming scalar nucleons and zero-mass scalar mesons. The solution of the scattering problem can be effected by using an integraltransform method which is similar to that developed for the bound-state problem, subject to the assumption that the nucleon mass is large compared to the kinetic energy in the center-of-mass system. An essential complication which is now encountered is the appearance of an infrared divergence. Two methods of circumventing this difficulty are discussed. The cross section can be calculated from the Green's function by a limiting process; the usual Smatrix formalism leads to incorrect results in this case, and an amplitude renormalization is required. In this comertion, it is instructive to re-examine, in detail, the Coulomb-scattering problem in momentum space, since this is very closely related to the Bethe-Salpeter scattering problem. The Green's-function method turns out to be unsuitable for the calculation of higher-order corrections to the nucleon-nucleon scattering cross section, so that here a cutoff procedure must be used. (auth)

• Research Organization: Univ. of Rochester, N.Y.; Brown Univ., Providence
• NSA Number: NSA-14-011028
• OSTI ID: 4202099
• Journal Information: Physical Review (U.S.) Superseded in part by Phys.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 D, Journal Name: Physical Review (U.S.) Superseded in part by Phys.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: 117; ISSN PHRVA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

BETHE-SALPETER EQUATION
BOUND STATE
CROSS SECTIONS
ELECTRIC CHARGES
FIELD THEORY
GREEN FUNCTION
INTERACTIONS
MANY BODY PROBLEM
MATRICES
MESONS
NUCLEONS
PHYSICS
QUANTUM MECHANICS
RELATIVITY THEORY
S-MATRIX
SCATTERING