  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.
