Kinematics of the CS method for the treatment of molecular collisions
This paper presents the kinematical part of a proposal for founding the CS method (for one definition, see V. Khare and D. J. Kouri (J. Chem. Phys. 72, 2017 (1980))) for the quantum treatment of molecular collisions on a certain testable physical approximation scheme. That is, let the molecules be rigid diatoms A/sub 1/A/sub 2/ and B/sub 1/B/sub 2/, with internal angular momentum j/sub a/ and j/sub b/, respectively; with relative position, momentum, and angular momentum r, p, and l = r x p; and with total angular momentum J = j/sub a/+j/sub b/+l. Then the motivating conjecture is that, in addition to commuting exactly with J, and as a result of dynamical properties not discussed here, the fully off-the-energy-shell T(E) operator approximately commutes with either r, r, or J x r = ..omega.. = ''the r-helicity.'' The principal results obtained in the paper are these: First, the definitions of, and transformations between, certain complete sets of system basis states in which the r-helicity ..omega.. or the p-helicity lambda = J x p is diagonal are established by methods similar to those of Jacob and Wick (Ann. Phys. (N.Y.) 7, 404 (1959)). Second, it is argued that in several papers in the literature of the CS method an explicitly or presumptively incorrect kinematical law was applied to derive the matrix elements of T(E) operators for atom--molecule collisions in a basis in which ..omega.. was said to be diagonal from the fully on-the-energy-shell matrix elements of a given T(E).
- Research Organization:
- Aircraft Aerodynamics Branch, NASA Ames Research Center, Moffett Field, California 94035
- OSTI ID:
- 6661252
- Journal Information:
- J. Math. Phys. (N.Y.); (United States), Vol. 25:8
- Country of Publication:
- United States
- Language:
- English
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ATOM-MOLECULE COLLISIONS
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640304* - Atomic
Molecular & Chemical Physics- Collision Phenomena