The dynamics of multiphoton processes in H{sub 2}{sup +} ions interacting with strong femtosecond fields is investigated by solving the time-dependent Schroedinger equation in the Born-Oppenheimer approximation. We use a spectral method with prolate spheroidal coordinates to represent the electronic wave functions. The theoretical approach is of spectral type in which the electronic and vibrational wave functions are represented with L{sup 2} basis functions. In order to check the accuracy of these wave functions we have investigated the cases of the multiphoton ionization and dissociation of H{sub 2}{sup +} at long wavelengths. First, we calculate the ionization probabilities and the electron spectra at 228 nm and 400 nm, and we compare our results with other calculations when available. The effect of the initial dispersion of the internuclear distance R in the equilibrium region is discussed in the context of short pulses. Then, we study the dissociation of H{sub 2}{sup +} at 350 nm and we compare our results with other recent calculations. Finally, the case of two-photon ionization of H{sub 2}{sup +} at short wavelength is investigated, and we examine the electronic and vibrational spectra that have been obtained.

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