Theory of scattering by complex potentials

Journal Article · Sat Oct 15 00:00:00 EDT 1983 · Ann. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1016/0003-4916(83)90020-9· OSTI ID:5170005

Thylwe, K; Froeman, N

The scattering problem for a non-relativistic spinless particle under the influence of a complex effective potential, which is spherically symmetric and tends to zero faster than 1/r at infinity, is considered. Certain general relations, which illuminate the influence of the imaginary part of the potential on the scattering process, are derived with the use of the expression for the probability current density. The rigorous phase-integral method developed by N. Froeman and P. O. Froeman is used for obtaining an exact, general formula for the scattering matrix, or equivalently, for the phase shift. The formula is expressed in terms of phase-integral approximations of an arbitrary order and certain quantities defined by convergent series. Estimating the latter quantities and omitting small corrections, an approximate formula is derived for the phase shift, valid for the case that only one complex turning point contributes essentially to the phase shift. Criteria for classifying a scattering problem as such a one-turning-point problem are given. The treatment is made general enough to also cover situations of interest in Regge-pole or complex angular momentum theory.

• Research Organization: Fachbereich Physik der Universitaet Kaiserslautern, 6750 Kaiserslautern, Erwin-Schroedinger Str., Germany
• OSTI ID: 5170005
• Journal Information: Ann. Phys. (N.Y.); (United States), Vol. 150:2
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
POTENTIAL SCATTERING
FEYNMAN PATH INTEGRAL
PHASE SHIFT
S MATRIX
SCHROEDINGER EQUATION
DIFFERENTIAL EQUATIONS
ELASTIC SCATTERING
EQUATIONS
INTEGRALS
MATRICES
PARTIAL DIFFERENTIAL EQUATIONS
SCATTERING
WAVE EQUATIONS
645500* - High Energy Physics- Scattering Theory- (-1987)