Accuracy of analytic semiclassical T-matrix elements

Journal Article · Mon Jun 01 04:00:00 EDT 1981 · Phys. Rev. A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.23.2826· OSTI ID:6442870

Bieniek, R J

The accuracy of two different semiclassical methods of evaluating T-matrix elements by stationary-phase techniques are reported. Their predictions are compared to quantal results for the far-red-wing emission spectrum of Rb collisionally broadened by Xe perturbers. One method is based on the direct use of uniform semiclassical wave functions in the overlap integral of the T-matrix elements. It is shown to give very accurate results (generally to within 3% of quantal values) for both classically allowed and classically forbidden transitions, whether they are near to or far from the classical singularity associated with the collisional turning points. The other semiclassical method is based on a cubic expansion of the phases of the semiclassical wave functions. If simple semiclassical amplitudes and phases are used in the resulting expression, individual T-matrix elements can have significant errors. However, the sum over angular momenta tends to compensate for the individual discrepancies so that the final differential intensity is generally within 10% of quantal values, except for narrow spikes due to the turning-point singularities. The use of uniform semiclassical amplitudes and phases removes these spikes and reduces the error in the total differential intensity given by the cubic expression to only a few percent.

• Research Organization: Department of Astronomy, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
• OSTI ID: 6442870
• Journal Information: Phys. Rev. A; (United States), Journal Name: Phys. Rev. A; (United States) Vol. 23:6; ISSN PLRAA
• Country of Publication: United States
• Language: English

Related Subjects

640304* -- Atomic
Molecular & Chemical Physics-- Collision Phenomena
74 ATOMIC AND MOLECULAR PHYSICS
ACCURACY
ALKALI METALS
ATOM COLLISIONS
ATOM-ATOM COLLISIONS
COLLISIONS
ELEMENTS
EMISSION SPECTRA
ENERGY-LEVEL TRANSITIONS
FLUIDS
FORBIDDEN TRANSITIONS
GASES
LINE BROADENING
MATRICES
MATRIX ELEMENTS
METALS
NONMETALS
RARE GASES
RUBIDIUM
S MATRIX
SEMICLASSICAL APPROXIMATION
SPECTRA
WKB APPROXIMATION
XENON