Vibrational transitions in the non-linearly driven oscillator: role of a time-varying frequency

Abstract

An operator-algebraic approach is used to study the role of time-varying frequency in vibrational transitions in molecular collisions. The time-evolution operator is constructed in terms of the number, one-quantum, and direct two-quantum operators. The evolution of vibrational states in a homonuclear diatomic molecule forced by an incident particle of the same mass is presented. The effect of the time-dependent frequency on 0 → 1, O → 2, and 0 → 3 is found to be important over a wide range of collision energies. Two-quantum processes interfere destructively with one-quantum processes at lower energies but constructively at higher energies.