Measuring moving nuclear wave packets using laser Coulomb-explosion imaging

From exact non-Born-Oppenheimer simulations of dynamics of H2+ and D2+ in an intense (I>1015 W/cm2) ultrashort laser pulse (tp<5 fs), we show that it is possible to measure the time evolution of the probability distribution vertical bar ψ(R,t)|2 of a dissociating wave packet using laser Coulomb-explosion imaging (LCEI). In our numerical simulation, a pump-probe technique is used: first, a weaker laser (I<1014 W/cm2) photodissociates the molecule and next, with experimentally controlled time delay t0, a second intense (I>1015 W/cm2) ultrashort (tp<5 fs) laser pulse is applied. The latter, ionizes 'instantaneously' the dissociating molecule. Measurement of the kinetic-energy spectra of exploding nuclear fragments allows us, with the help of an inversion based on Coulomb's law and classical conservation of energy, to reconstruct the shape of the probability distribution vertical bar ψ(R,t)|2 at time t=t0. By repeating this experiment for many time delays t0, one can thus obtain detailed information about the time-dependent dynamics of the photoinduced dissociation. The theory of LCEI for moving nuclear wave packets and the limitations of the above classical inversion method are presented