New decomposition of the S matrix for multichannel resonant collisions

Journal Article · Thu Oct 01 04:00:00 EDT 1987 · Phys. Rev. A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.36.3083· OSTI ID:5963736

Gazdy, B; Bowman, J M

The usual decomposition of the multichannel scattering matrix near an isolated, narrow resonance is given as a sum of a direct and resonant part. The direct part of the S matrix which describes the background scattering is regular and unitary. The resonant part features a pole at the complex resonance energy, and both its magnitude and phase change rapidly as the energy varies. Given the S matrix, it is often a cumbersome task to extract the resonance energy and partial widths from the usual decomposition. We propose a new decomposition (which is related to the usual one) that overcomes this difficulty. The new resonant part is a complete analog of the single-channel S matrix. Its magnitude is constant and its phase jumps by 2..pi.. as the energy passes through the resonance. The resonant time delays for each state-to-state transition are independent of the channel indices, and exhibit the same Lorentzian shape from which the resonance energy and total width are readily obtained. The square of the magnitude of the resonant S-matrix elements are the state-to-state transition probabilities of the resonant scattering and are expressed in terms of the channel partial widths. The applicability of the proposed decomposition is demonstrated in a coupled-channel study of multichannel resonances in H-CO collisions using a global ab initio potential-energy surface.

• Research Organization: Department of Chemistry, Emory University, Atlanta, Georgia 30322
• OSTI ID: 5963736
• Journal Information: Phys. Rev. A; (United States), Journal Name: Phys. Rev. A; (United States) Vol. 36:7; ISSN PLRAA
• Country of Publication: United States
• Language: English

Related Subjects

640304* -- Atomic
Molecular & Chemical Physics-- Collision Phenomena
74 ATOMIC AND MOLECULAR PHYSICS
AMPLITUDES
ARGAND DIAGRAMS
ATOM COLLISIONS
ATOM-MOLECULE COLLISIONS
CARBON COMPOUNDS
CARBON MONOXIDE
CARBON OXIDES
CHALCOGENIDES
COLLISIONS
COUPLED CHANNEL THEORY
DIAGRAMS
EINSTEIN COEFFICIENTS
ELEMENTS
HYDROGEN
MATRICES
MOLECULE COLLISIONS
NONMETALS
OXIDES
OXYGEN COMPOUNDS
RESONANCE
S MATRIX
SCATTERING
SCATTERING AMPLITUDES
SCATTERPLOTS