Discrete sudden perturbation theory for inelastic scattering. I. Quantum and semiclassical treatment

Journal Article · Sun Dec 01 04:00:00 EST 1985 · J. Chem. Phys.; (United States)

DOI:https://doi.org/10.1063/1.449676· OSTI ID:6336803

Cross, R J

A double perturbation theory is constructed to treat rotationally and vibrationally inelastic scattering. It uses both the elastic scattering from the spherically averaged potential and the infinite-order sudden (IOS) approximation as the unperturbed solutions. First, a standard perturbation expansion is done to express the radial wave functions in terms of the elastic wave functions. The resulting coupled equations are transformed to the discrete-variable representation where the IOS equations are diagonal. Then, the IOS solutions are removed from the equations which are solved by an exponential perturbation approximation. The results for Ar+N/sub 2/ are very much more accurate than the IOS and somewhat more accurate than a straight first-order exponential perturbation theory. The theory is then converted into a semiclassical, time-dependent form by using the WKB approximation. The result is an integral of the potential times a slowly oscillating factor over the classical trajectory. A method of interpolating the result is given so that the calculation is done at the average velocity for a given transition. With this procedure, the semiclassical version of the theory is more accurate than the quantum version and very much faster. Calculations on Ar+N/sub 2/ show the theory to be much more accurate than the infinite-order sudden (IOS) approximation and the exponential time-dependent perturbation theory.

• Research Organization: Department of Chemistry, Yale University, New Haven, Connecticut 06511
• OSTI ID: 6336803
• Journal Information: J. Chem. Phys.; (United States), Journal Name: J. Chem. Phys.; (United States) Vol. 83:11; ISSN JCPSA
• Country of Publication: United States
• Language: English

Related Subjects

640304* -- Atomic
Molecular & Chemical Physics-- Collision Phenomena
74 ATOMIC AND MOLECULAR PHYSICS
ARGON
ATOM COLLISIONS
ATOM-MOLECULE COLLISIONS
COLLISIONS
ELEMENTS
ENERGY LEVELS
ENERGY-LEVEL TRANSITIONS
EXCITED STATES
FLUIDS
GASES
MOLECULE COLLISIONS
NITROGEN
NONMETALS
PERTURBATION THEORY
RARE GASES
ROTATIONAL STATES
SUDDEN APPROXIMATION
VIBRATIONAL STATES