  A model based on the strong-field and Born-Oppenheimer approximations
qualitatively describes the distribution over vibrational states formed in a
diatomic molecular ion following ionization of the neutral molecule by intense
laser pulses. Good agreement is found with a recent experiment [X. Urbain et
al., Phys. Rev. Lett. 92, 163004 (2004)]. In particular, the observed deviation
from a Franck-Condon-like distribution is reproduced. Additionally, we
demonstrate control of the vibrational distribution by a variation of the peak
intensity or a change of frequency of the laser pulse.
