Wave vector modification of the infinite order sudden approximation

Journal Article · Wed Oct 15 00:00:00 EDT 1980 · J. Chem. Phys.; (United States)

DOI:https://doi.org/10.1063/1.440742· OSTI ID:5071210

Sachs, J G; Bowman, J M

A simple method is proposed to modify the infinite order sudden approximation (IOS) in order to extend its region of quantitative validity. The method involves modifying the phase of the IOS scattering matrix to include a part calculated at the outgoing relative kinetic energy as well as a part calculated at the incoming kinetic energy. An immediate advantage of this modification is that the resulting S matrix is symmetric. We also present a closely related method in which the relative kinetic energies used in the calculation of the phase are determined from quasiclassical trajectory calculations. A set of trajectories is run with the initial state being the incoming state, and another set is run with the initial state being the outgoing state, and the average final relative kinetic energy of each set is obtained. One part of the S-operator phase is then calculated at each of these kinetic energies. We apply these methods to vibrationally inelastic collinear collisions of an atom and a harmonic oscillator, and calculate transition probabilities P/sub n/1..-->..nf for three model systems. For systems which are sudden, or nearly so, the agreement with exact quantum close-coupling calculations is substantially improved over standard IOS ones when ..delta..n=such thatub f/-n/sub i/ is large, and the corresponding transition probability is small, i.e., less than 0.1. However, the modifications we propose will not improve the accuracy of the IOS transition probabilities for any collisional system unless the standard form of IOS already gives at least qualitative agreement with exact quantal calculations. We also suggest comparisons between some classical quantities and sudden predictions which should help in determining the validity of the sudden approximation. This is useful when exact quantal data is not available for comparison.

• Research Organization: Department of Chemistry, Illinois Institute of Technology, Chicago, Illinois 60616
• OSTI ID: 5071210
• Journal Information: J. Chem. Phys.; (United States), Vol. 73:8
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
ATOM-MOLECULE COLLISIONS
SUDDEN APPROXIMATION
S MATRIX
ENERGY-LEVEL TRANSITIONS
KINETIC ENERGY
VIBRATIONAL STATES
ATOM COLLISIONS
COLLISIONS
ENERGY
ENERGY LEVELS
EXCITED STATES
MATRICES
MOLECULE COLLISIONS
640304* - Atomic
Molecular & Chemical Physics- Collision Phenomena