J/sub z/-conserving coupled states approximation: Magnetic transitions and angular distributions in rotating and fixed frames. [T matrix, helicity, integrals, scattering amplitude, cross sections]

Journal Article · Fri Jul 01 04:00:00 EDT 1977 · J. Chem. Phys.; (United States)

OSTI ID:7215116

Kouri, D J; Shimoni, Y

Recently Shimoni and Kouri have pointed out that a careful treatment of j/sub z/-conserving coupled states (CS) approximation results in a body frame T-matrix T/sup J/(jlambdavertical-barj/sub 0/lambda/sub 0/) which is not diagonal in lambda,lambda/sub 0/. In addition they have shown that previous investigations of the CS did not optimally identify body frame T-matrix. In this paper, we explore the consequences of these observations. The exact T-matrix is obtained in the R- and P-helicity frames, as well as in an uncoupled spaceframe (USF) representation. The resulting exact expressions for these T-matrices are in terms of certain integrals, I/sup J//sub l/(jlambdavertical-barj/sub 0/lambda/sub 0/), introduced earlier by Shimoni and Kouri. By obtaining CS approximation to these integrals, we are able to derive the preferred CS approximation in the R- and P-helicity and USF representations. We then employ the resulting CS T-matrices to derive the differential scattering amplitude and cross section in the various possible reference frames. The result is a unified treatment of these quantities. We are then able to demonstrate the equivalence of the CS approximation to the R- and P-helicity amplitudes. In addition, we show explicitly that the CS approximate degeneracy averaged differential cross section is frame independent. The CS approximation to the USF equation provides a rigorous basis for the original derivation of the CS method as given by McGuire and Kouri. In particular, our treatment shows that when the L/sup 2/ operator is approximated by an eigenvalue form l (l+1) h/sup 2/ (as was suggested first by McGuire and Kouri), there is no longer any difference between the BF and USF in the dynamical equations (for the wavefunction or amplitude density). Any differences are strictly kinematic in origin, and are the source of the lambda transitions which occur in the BF CS approximation. In the USF, there are no magnetic transitions in the CS approximation.

• Research Organization: Departments of Chemistry and Physics, University of Houston, Houston, Texas 77004
• OSTI ID: 7215116
• Journal Information: J. Chem. Phys.; (United States), Journal Name: J. Chem. Phys.; (United States) Vol. 67:1; ISSN JCPSA
• Country of Publication: United States
• Language: English

Related Subjects

640304* -- Atomic
Molecular & Chemical Physics-- Collision Phenomena
74 ATOMIC AND MOLECULAR PHYSICS
ANGULAR MOMENTUM
COLLISIONS
CONSERVATION LAWS
HELICITY
MATRICES
MOLECULE COLLISIONS
PARTICLE PROPERTIES
S MATRIX
SCATTERING