The response of an atomic hydrogen system in the presence of an intense ultrashort laser pulse is investigated by direct integration of the time-dependent Schr?dinger equation. The target wavefunctions are expanded in terms of an accurate and discrete L~2 basis, which is optimized for convergence, making the approach more realistic. We have studied the variation of probability of ionization with laser pulse parameters such as the intensity, frequency, chirp rate and pulsewidth. The need for ultrashort pulses is highlighted by the results and we also found that chirped pulses provide a more efficient way of population transfer when compared with a non-chirped pulse.
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