From exact non-Born-Oppenheimer simulations of dynamics of H-2(+) and D-2(+) in an intense (I >10(15) W/cm(2)) ultrashort laser pulse (t(p)<5 fs), we show that it is Possible to measure the time evolution of the probability distribution vertical bar psi(R,t)vertical bar(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<10(14) W/cm(2)) photodissociates the molecule and next, with experimentally controlled time delay t(0), a second intense (I >10(15) W/cm(2)) ultrashort (t(p)<5 fs) laser pulse is applied. The latter, ionizes "instantaneously" the dissociating molecule, Measurement of the kinetic-energy spectra of exploding nuclear fragments allow, us, With the help of all inversion based on Coulomb's law and classical conservation of energy, to reconstruct the shape of the probability distribution vertical bar psi(R,t)vertical bar(2) at time t =t(0). By repeating this experiment for many time delays t(0), 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.
