Relativistic few-body problem. I. Two-body equations

Journal Article · Mon Nov 01 04:00:00 EST 1982 · Phys. Rev. C; (United States)

DOI:https://doi.org/10.1103/PhysRevC.26.2203· OSTI ID:6524478

Gross, F

This paper begins with an explanation of the implications of the requirement that a two-body relativistic equation should approach a one-body equation when one of the masses becomes very large. It is found that the Bethe-Salpeter equation does not satisfy this requirement. A infinite family of three-dimensional equations depending on a parameter -1< or =..nu..< or =1 is constructed, all of which do satisfy this limit. When Vertical Bar..nu..Vertical Bar = 1 one of the particles is on its mass shell; when ..nu.. = 0 both particles are equally off mass shell. The fourth order irreducible kernel for this family is studied in the expanded static limit for all ..nu... It is found, both for scalar theories and for a realistic chiral theory of spin (1/2) nucleons interacting with isovector pions, that the leading order terms in the static limit cancel for any ..nu.., and that the nonleading terms are independent of energy only for the Vertical Bar..nu..Vertical Bar = 1 equation. Other criteria for the selection of a relativistic two-body equation and implications for the form of the two-pion exchange potential are briefly discussed.

• Research Organization: Department of Physics, Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213
• OSTI ID: 6524478
• Journal Information: Phys. Rev. C; (United States), Journal Name: Phys. Rev. C; (United States) Vol. 26:5; ISSN PRVCA
• Country of Publication: United States
• Language: English

Related Subjects

645500* -- High Energy Physics-- Scattering Theory-- (-1987)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANGULAR MOMENTUM
BETHE-SALPETER EQUATION
CHIRAL SYMMETRY
ENERGY RANGE
EQUATIONS
FUNCTIONS
GREEN FUNCTION
ISOSPIN
KERNELS
MANY-BODY PROBLEM
MATHEMATICAL MODELS
NUCLEAR MODELS
PARTICLE PROPERTIES
RELATIVISTIC RANGE
SHELL MODELS
SPIN
SYMMETRY
TWO-BODY PROBLEM