Multidimensional WKB approach to high-energy elastic scattering at fixed angle
We discuss here the application of a multidimensional WKB method to the Schroedinger equation and the Klein-Gordon equation. This method enables us to calculate scattering amplitudes in the limit of large incident momentum p and fixed scattering angle theta. As an application, we calculate the scattering amplitude for the Klein-Gordon equation with the potential ..cap alpha..e/sup -lambdar//r, and find that in the limit of large p and fixed theta, it is equal to the scattering amplitude for a Coulomb potential multiplied by (lambdae/sup ..gamma..//2p)/sup 2ialpha/, where ..gamma.. = 0.57721... . Our result differs from the eikonal formula, in the high-energy fixed-angle region. We also show that our formula agrees with the eikonal formula for small scattering angles satisfying 1>>theta>>lambda/p. Thus our formula, together with the eikonal formula, give complete information on the high-energy amplitude for all angles. A side result of the application of the WKB method is a generalized eikonal formula for the case of the Klein-Gordon equation with a four-potential A/sub ..mu../(x) which depends not only on space but also on time. This formula holds for the scattering amplitude in the region p..-->..infinity with the momentum transfer fixed.
- Research Organization:
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
- OSTI ID:
- 6702398
- Journal Information:
- Phys. Rev. D; (United States), Vol. 26:4
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
ELASTIC SCATTERING
WKB APPROXIMATION
SCATTERING AMPLITUDES
SCHROEDINGER EQUATION
EIKONAL APPROXIMATION
KLEIN-GORDON EQUATION
QUANTUM FIELD THEORY
AMPLITUDES
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD THEORIES
PARTIAL DIFFERENTIAL EQUATIONS
SCATTERING
WAVE EQUATIONS
645500* - High Energy Physics- Scattering Theory- (-1987)