We investigate how various versions of the molecular strong-field approximation (MSFA) agree with the experiment by Grasbon et al. [Phys. Rev. A 63, 041402(R) (2001)], in which the suppression of the ionization yield in the low-energy spectrum of the O-2 molecule, compared to the spectrum of its companion atom Xe, was observed. In this experiment, it was also found that the spectrum of the N-2 molecule is comparable to the corresponding spectrum of its companion atom Ar. We show that the length-gauge version of the MSFA with the initial state dressed by the laser field gives the best agreement with the experimental data for both O-2 and N-2 molecules.
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