The AC Stark Effect, Time-Dependent Born–Oppenheimer Approximation, and Franck–Condon Factors

We study the quantum mechanics of a simple molecular system that is subject to a laser pulse. We model the laser pulse by a classical oscillatory electric field, and we employ the Born–Oppenheimer approximation for the molecule. We compute transition amplitudes to leading order in the laser strength. These amplitudes contain Franck–Condon factors that we compute explicitly to leading order in the Born–Oppenheimer parameter.