Theory of molecular tunneling ionization X. M. Tong,* Z. X. Zhao, and C. D. Lin Physics Department, Kansas State University, Manhattan, Kansas 66506 Received 10 June 2002; published 20 September 2002 We have extended the tunneling ionization model of Ammosov-Delone-Krainov ADK for atoms to di- atomic molecules by considering the symmetry property and the asymptotic behavior of the molecular elec- tronic wave function. The structure parameters of several molecules needed for calculating the ionization rates using this molecular ADK model have been obtained. The theory is applied to calculate the ratios of ionization signals for diatomic molecules with their companion atoms that have nearly identical binding energies. The origin of ionization suppression for some molecules has been identified. The predicted ratios for pairs with suppression (D 2 :Ar, O 2 :Xe) and pairs without suppression (N 2 :Ar, CO:Kr are in good agreement with the measurements. However, the theory predicts suppression for F 2 :Ar, which is in disagreement with the experi- ment. The ionization signals of NO, S 2 , and of SO have also been derived from the experimental data, and the results are also shown to be in agreement with the prediction of the present molecular ADK theory. DOI: 10.1103/PhysRevA.66.033402 PACS numbers: 33.80.Rv, 42.50.Hz I. INTRODUCTION The ionization of an atom in an intense laser field has been investigated extensively in the last decades, both theo- retically and experimentally. While direct solution of the Schro ¨ dinger equation in a time-dependent laser field has been widely used by theorists, simpler models are often pref- erable to experimentalists. One of the commonly used mod- els for calculating the ionization rate is the so-called ADK Ammosov-Delone-Krainov model 1. This model is based on the ionization rate of a hydrogenlike atom in a static electric field, with modifications introduced for the real many-electron atoms. A key element of the ADK theory is that the ionization rate depends critically on the ionization potential of the atom. Subsequent experimental studies of ionization of molecules have found that ionization rates for molecules, in general, are very similar to atoms if they have nearly identical binding energies. Further investigations have found exceptions 2–6. These latter experiments showed that ionization is strongly suppressed for D 2 and O 2 , in com- parison with their companion atoms Ar and Xe, but ioniza- tion for N 2 and F 2 are comparable to their companion Ar atom under the same laser pulses. While ab initio calcula- tions for the ionization rates of atoms are readily available, at least within the single-electron approximation, this is not the case for molecules. Based on the KFR or Keldysh-Faisal- Reiss model 7, the ionization rates for molecules have been calculated 8 in terms of ionization rates of atoms modified by the interference from the atomic centers. For ionization from an antibonding valence orbital, the interfer- ence is destructive and thus ionization is suppressed. For ionization from molecules in a bonding orbital, no suppres- sion was expected. The ionization of molecules including many-electron effect has been studied based on the time- dependent density-functional theory by Chu and co-workers 9, but the complicated nature of these calculations sheds little light so far on the general issues of ionization suppres- sion for molecules. When considering the ionization of molecules versus at- oms, effects due to the additional degrees of freedom in mol- ecules should be evaluated. To begin with, the electronic cloud of an atom is spherically symmetric while for mol- ecules it is not. The ionization rate of molecules can further be affected by the rotational and vibrational motion. While the exponential growth of ionization rates with field strength before reaching saturation is determined primarily by the ionization potential, the absolute ionization rates are deter- mined by other properties of atoms and molecules. Thus in studying the ionization suppression of molecules, it is pref- erable to compare the ratio of ionization rates of molecules with respect to their companion atoms that have nearly iden- tical binding energies. This is true also for experiments. As pointed out by DeWitt et al. 5 it is important to measure ionization signals of the companion atoms and molecules at the same time to reduce errors from variations of laser pulses in different shots. Since the observation of ionization suppression of some molecules, different theoretical interpretations have been proposed. To explain the ionization suppression of D 2 in comparison to Ar ionization energies of 15.4 eV and 15.8 eV, respectively, Talebpour et al. 3 attributed the suppres- sion to the alignment of molecules. Such a claim is not sup- ported by other studies 10. For the simple H 2 + molecular ions, quantum calculation 11 has shown that tunneling ion- ization rate does not depend strongly on the alignment of molecules. Saenz 10 has considered the possible effect on ionization suppression from the vibrational motion of mol- ecules, but the effect was found to be too small. To explain the ionization suppression of O 2 in comparison to Xe ion- ization energies at 12.06 and 12.13 eV, respectively, Guo 12 argued for a larger ‘‘effective’’ ionization potential for O 2 , invoking that the open-shell nature of this molecule would result in the valence electron experiences a larger ef- fective charge and a larger effective ionization potential 16.9 eV. The proposed larger ionization potential cannot be obtained theoretically, nor empirically from other experi- *Email address: xmtong@phys.ksu.edu PHYSICAL REVIEW A, 66, 033402 2002 1050-2947/2002/663/03340211/$20.00 ©2002 The American Physical Society 66 033402-1