Neutral atoms have been observed to survive intense laser pulses in high Rydberg states with surprisingly large probability. Only with this Rydberg-state excitation (RSE) included is the picture of intense-laser-atom interaction complete. Various mechanisms have been proposed to explain the underlying physics. However, neither one can explain all the features observed in experiments and in time-dependent Schr{o}dinger equation (TDSE) simulations. Here we propose a fully quantum-mechanical model based on the strong-field approximation (SFA). It well reproduces the intensity dependence of RSE obtained by the TDSE, which exhibits a series of modulated peaks. They are due to recapture of the liberated electron and the fact that the pertinent probability strongly depends on the position and the parity of the Rydberg state. We also present measurements of RSE in xenon at 800 nm, which display the peak structure consistent with the calculations.
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