An algebraic model to describe atom diatom inelastic collisions in the semiclassical approximation
Abstract
An algebraic model to describe inelastic collisions between an atom and a diatomic molecule within the semiclassical approximation framework is presented. For the interaction in the diatomic system a Morse potential is considered, while an exponential function is taken for the atomdiatom interaction. The original atomdiatom Hamiltonian is transformed into a timedependent Hamiltonian for the diatomic system. In the interaction picture framework the interaction potential is approximated by a linear expansion in terms of the generators of the SU(2) group, the dynamical algebra for the Morse potential bound states. A minimization procedure to determine the timedependent coefficients is proposed. The transition intensities are given in terms of matrix elements of the product of exponentials of the Morse potential dynamical group generators. A comparison of the algebraically obtained transition probabilities with the exact semiclassical results is presented.
 Publication:

Journal of Physics B Atomic Molecular Physics
 Pub Date:
 December 2007
 DOI:
 10.1088/09534075/40/23/011
 Bibcode:
 2007JPhB...40.4513A