Combining the Keldysh theory for a few cycle laser pulse with the theory of the inelastic tunneling (Kornev A S and Zon B A 2012 Phys. Rev. A 85 035402) agrees very well with the ab initio simulations performed by Rohringer and Santra (2009 Phys. Rev. A 79 053402) for the Ne atom. However, for the heavier Xe atom, agreement between analytical and numerical theories is not satisfactory. To eliminate this disagreement, we took into account the Stark shift of atomic level energies. As a result, the agreement between analytical and numerical theories significantly improved, but for Ne, it became worse. We discussed possible causes of these disagreements.

We show that the linear Stark effect due to a molecule permanent dipole moment does not influence the rate of molecule ionization by laser radiation in the multiphoton limit. However, it may influence the ionization rate in the tunnelling limit. A CO molecule is considered as an example. Its valence orbitals have σ symmetry. In this case, the tunnel effect rate is maximal if the permanent dipole moment (the molecule axis) is oriented along the direction of the laserwave electric field, and the role of the linear Stark effect is the most noticeable. This situation differs from that when the valence orbitals have π symmetry which we have considered previously (Kornev and Zon 2014 Laser Phys. 24 115302). In that case, the tunnel effect rate is maximal if the molecule axis is oriented perpendicularly to the electric field direction and the role of the linear Stark effect is less significant. We consider the tunnel effect in both dc and ac fields, accounting for perturbation of vibrational motion by an external field. We show that the influence of the permanent dipole moment does not vanish even after averaging the tunnelling rate over the molecule orientations.