Spectral widths ofH2+multiphoton dissociation with short intense laser pulses

Photodissociation spectra of ${\mathrm{H}}_2^{+}$, obtained using ultrashort (a few femtoseconds), intense (within the range of ${10}^{12}$ to ${10}^{14}$ W/${\mathrm{cm}}^2$) laser pulses (with a peak frequency of 3.761 eV), and displaying well-separated proton kinetic-energy peaks corresponding to one-, two-, or three-photon absorptions are analyzed. Within some approximations, the validity range of which is related to the aforementioned assumptions on the laser and spectrum characteristics, a simple analytic formula is deduced. It gives the spectral widths of the observed peaks in terms of the total number of photons which are absorbed and/or emitted during the dissociation process. A quantitative support to some recent dynamical interpretations is provided. The successive absorption of three photons seems basically to be the initial step which, at intermediate intensities, leads to the three-photon peaks. A subsequent emission of one (or two) photons is responsible for the two- (or one-) photon peaks. Bond softening occurs at higher intensities by the lowering of potential-energy barriers. Dissociation proceeds through these barriers by reflection and tunneling. It involves at least three photons to end in a one-photon peak.