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 atom–diatom interaction. The original atom–diatom Hamiltonian is transformed into a time-dependent 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 time-dependent 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.
The 1D collision between an atom and a diatomic molecule is investigated using an algebraic approach. Closed expressions for the quantum mechanical excitation transition probabilities are obtained. A Morse potential for the diatomic molecule is used. The classical trajectories are obtained in the united atom limit by taking an average over a finite number of states using the matrix density formalism, which allows the problem to be reformulated in terms of a time-dependent Hamiltonian. The system is studied in the interaction picture, which permits us to carry out an algebraic description through the approximation of the interaction potential in terms of a linear combination of the generators of the su(2) algebra. Comparisons with exact quantum mechanical results for transition probabilities in different systems are presented.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.