Hamiltonian dynamics of atom-diatomic molecule complexes and collisions

Pages: 655 - 666, Issue Special, September 2007

Abstract
Full Text (212.3K)

F. J. Lin - University of Southern California, Department of Mathematics, KAP 108, 3620 Vermont Avenue, Los Angeles, CA 90089-2532, United States (email)

Abstract:
For a polyatomic molecule at zero *total* angular momentum, this paper shows that an *internal* motion with nonzero internal angular momentum within a (generalized) Eckart frame will produce a net rotation of the (generalized) Eckart frame in the center-of-mass frame. For a polyatomic molecule at nonzero total angular momentum, an internal motion within a generalized Eckart frame with nonzero *orbital* angular momentum will produce a net rotation of the generalized Eckart frame in the center-of-mass frame. Specifically, at zero total angular momentum, an internal rotation of a diatomic molecule within an atom-diatomic molecule system has nonzero internal rotational angular momentum and produces a counter-rotary net rotation of the orientation of the system (and of its generalized Eckart frame) in the center-of mass frame. Beyond a net overall rotation of an atom-diatomic molecule complex in the center-of-mass frame, a net rotation of the scattering angle of an atom colliding with a rotating diatomic molecule is obtained. A rotation in the recoil angle of an atom departing from a dissociating triatomic molecule has been observed.

Keywords: Three-body problem, N-body problem, Hamiltonian dynamical system, classical geometric phase, symplectic reduction, molecular dynamics, Eckart frame.

Mathematics Subject Classification: Primary: 70F07, 70H05; Secondary: 70H33, 53D20.

Received: September 2006;
Revised:
February 2007;
Published: September 2007.