Multidimensional WKB approach to high-energy elastic scattering at fixed angle

Journal Article · Sun Aug 15 04:00:00 EDT 1982 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.26.896· OSTI ID:6702398

Cheng, H; Coon, D D; Zhu, X

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), Journal Name: Phys. Rev. D; (United States) Vol. 26:4; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645500* -- High Energy Physics-- Scattering Theory-- (-1987)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AMPLITUDES
DIFFERENTIAL EQUATIONS
EIKONAL APPROXIMATION
ELASTIC SCATTERING
EQUATIONS
FIELD THEORIES
KLEIN-GORDON EQUATION
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM FIELD THEORY
SCATTERING
SCATTERING AMPLITUDES
SCHROEDINGER EQUATION
WAVE EQUATIONS
WKB APPROXIMATION