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We study revival and fractional revival phenomena of wave packets in a one-dimensional Rydberg atom irradiated by two time-delayed half-cycle pulses using an autocorrelation function characterized by electronic transition probabilities as weighting factors rather than modeling them by a Gaussian or Lorentzian distribution. If the momentum (q_2) delivered to the atom by the second kick is much smaller than that (q_1) imparted by the first one, the times of revival and fractional revival coincide with those of the single kicked atom. For q_2 ≥ q_{1}/4 appearance of revival and fractional revival depends on both the values of q_2 and time delay t_1 between the pulses but more sensitively on t_1. The number of fractional revivals tends to become numerous as the value of t_1 increases.
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