Relativistic eikonal expansion. [Scalar-scalar theory]
The generalized ladder series of Feynman diagrams for scattering of two particles by scalar meson exchange is expanded, using functional methods, to obtain the relativistic eikonal approximation and the next two terms of an expansion about the eikonal limit. The established similarity between nonrelativistic and relativistic eikonal approximations is shown to persist, in part, to the higher order terms in the relativistic eikonal expansion. The leading order correction to the eikonal limit differs only kinematically from its nonrelativistic counterpart. In second order, there is again much similarity with nonrelativistic results, however a part of the second order eikonal correction explicitly depends on the relative time coordinate of the scattering particles. An approximate relativistic Schroedinger equation is found to reproduce the leading corrections to the eikonal limit by means of a simple kinematic generalization of the nonrelativistic potential theory results, however the relative time effect cannot be readily incorporated into a three-dimensional wave equation.
- Research Organization:
- Univ. of Maryland, College Park, MD (United States). Dept. of Physics and Astronomy
- DOE Contract Number:
- EY-76-S-05-5126
- OSTI ID:
- 5297417
- Report Number(s):
- ORO-5126-19; TRN: 78-002950
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
EIKONAL APPROXIMATION
SERIES EXPANSION
TWO-BODY PROBLEM
SCATTERING AMPLITUDES
COORDINATES
CORRECTIONS
FEYNMAN DIAGRAM
FUNCTIONALS
LADDER APPROXIMATION
LIMITING VALUES
OBE MODEL
PARTICLE INTERACTIONS
POTENTIAL SCATTERING
QUANTUM FIELD THEORY
RELATIVISTIC RANGE
SCALAR MESONS
SCHROEDINGER EQUATION
THREE-DIMENSIONAL CALCULATIONS
TIME DEPENDENCE
WAVE FUNCTIONS
AMPLITUDES
BOSON-EXCHANGE MODELS
BOSONS
DIAGRAMS
DIFFERENTIAL EQUATIONS
ELASTIC SCATTERING
ELEMENTARY PARTICLES
ENERGY RANGE
EQUATIONS
FIELD THEORIES
FUNCTIONS
HADRONS
INTERACTIONS
MANY-BODY PROBLEM
MATHEMATICAL MODELS
MESONS
PARTICLE MODELS
PERIPHERAL MODELS
SCATTERING
WAVE EQUATIONS
645500* - High Energy Physics- Scattering Theory- (-1987)