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Title: Relativistic eikonal expansion. [Scalar-scalar theory]

Abstract

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.

Authors:
;
Publication Date:
Research Org.:
Univ. of Maryland, College Park, MD (United States). Dept. of Physics and Astronomy
OSTI Identifier:
5297417
Report Number(s):
ORO-5126-19
TRN: 78-002950
DOE Contract Number:  
EY-76-S-05-5126
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 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)

Citation Formats

Wallace, S. J., and McNeil, J. A. Relativistic eikonal expansion. [Scalar-scalar theory]. United States: N. p., 1977. Web. doi:10.2172/5297417.
Wallace, S. J., & McNeil, J. A. Relativistic eikonal expansion. [Scalar-scalar theory]. United States. https://doi.org/10.2172/5297417
Wallace, S. J., and McNeil, J. A. 1977. "Relativistic eikonal expansion. [Scalar-scalar theory]". United States. https://doi.org/10.2172/5297417. https://www.osti.gov/servlets/purl/5297417.
@article{osti_5297417,
title = {Relativistic eikonal expansion. [Scalar-scalar theory]},
author = {Wallace, S. J. and McNeil, J. A.},
abstractNote = {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.},
doi = {10.2172/5297417},
url = {https://www.osti.gov/biblio/5297417}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Mon Aug 01 00:00:00 EDT 1977},
month = {Mon Aug 01 00:00:00 EDT 1977}
}