Weak-field asymptotic theory of tunneling ionization of the hydrogen molecule including core polarization, spectator nucleus, and internuclear motion effects

We present a state-of-the-art theory of tunneling ionization of the hydrogen molecule in a static electric field. The theory is based on the leading-order many-electron weak-field asymptotic theory and successively incorporates core polarization, spectator nucleus, and internuclear motion effects. The predictions of the theory are compared with ab initio calculations of the ionization rate of ${\mathrm{H}}_{2}$ with frozen nuclei and experimental results on the anisotropy of strong-field ionization of ${\mathrm{H}}_{2}$ and ${\mathrm{D}}_{2}$. The comparison reveals the relative role of the different effects. We show that all the effects should be taken into account in order to achieve good agreement with the ab initio and experimental results.