Algebraic description of the inelastic collision between an atom and a Morse oscillator in one dimension

Abstract

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.