Dirac Coulomb Green's function and its application to relativistic Rayleigh scattering

Journal Article · Mon Jul 01 00:00:00 EDT 1985 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.526882· OSTI ID:5547073

Wong, M K.F.; Yeh, E H.Y.

The Dirac Coulomb Green's function is obtained in both coordinate and momentum space. The Green's function in coordinate space is obtained by the eigenfunction expansion method in terms of the wave functions obtained by Wong and Yeh. The result is simpler than those obtained previously by other authors, in that the radial part for each component contains one term only instead of four terms. Our Green's function reduces to the Schroedinger Green's function upon some simple conditions, chiefly by neglecting the spin and replacing lambda by l. The Green's function in momentum space is obtained as the Fourier transform of the coordinate space Green's function, and is expressed in terms of basically three types of functions: (1) F/sub A/ (..cap alpha..; ..beta../sub 1/ ..beta../sub 2/ ..beta../sub 3/; ..gamma../sub 1/ ..gamma../sub 2/ ..gamma../sub 3/; z/sub 1/ z/sub 2/ z/sub 3/), (2) the hypergeometric function, and (3) spherical harmonics. The matrix element for Rayleigh scattering, or elastic Compton scattering, from relativistically bound electrons is then obtained in analytically closed form. The matrix element is written basically in terms of the coordinate space Dirac Coulomb Green's function. The technique used in the evaluation of the matrix element is based on the calculation of the momentum space Dirac Coulomb Green's function. Finally the relativistic result is compared with the nonrelativistic result.

• Research Organization: Fairfield University, Fairfield, Connecticut 06430
• OSTI ID: 5547073
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 26:7; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

645500* -- High Energy Physics-- Scattering Theory-- (-1987)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANALYTICAL SOLUTION
BASIC INTERACTIONS
COHERENT SCATTERING
COULOMB FIELD
COULOMB SCATTERING
EIGENFUNCTIONS
ELASTIC SCATTERING
ELECTRIC FIELDS
ELECTROMAGNETIC INTERACTIONS
ELECTRONS
ELEMENTARY PARTICLES
FERMIONS
FIELD THEORIES
FOURIER TRANSFORMATION
FUNCTIONS
GENERAL RELATIVITY THEORY
GREEN FUNCTION
HYPERGEOMETRIC FUNCTIONS
INTEGRAL TRANSFORMATIONS
INTEGRALS
INTERACTIONS
LEPTONS
MATRIX ELEMENTS
RAYLEIGH SCATTERING
RELATIVITY THEORY
SCATTERING
SPHERICAL HARMONICS
TRANSFORMATIONS
WAVE FUNCTIONS