Coulomb effects on strong-field ionization of stretched $H_2{}^{+}$

We numerically and analytically study ionization of $H_2{}^{+}$ with large internuclear distances $R$ in strong elliptically polarized laser fields. Numerical simulations show that the offset angle in the photoelectron momentum distribution (PMD) is larger for cases of large $R$ than for cases of $H_2{}^{+}$ with small $R$ and model atoms with similar ionization potentials. In addition, the PMDs for cases of large $R$ show clear interference patterns which disappear for cases of small $R$. By developing a strong-field model which includes the contributions of the first excited state and the Coulomb potential, we reproduce the phenomena for large $R$. Tunneling ionization of $H_2{}^{+}$ with large $R$ involves a complex four-body interaction between the laser, the electron, and the two nuclei. Our model can approximate the four-body interaction as the three-body one and clearly identify the effects of charge resonance and different nuclei on tunneling ionization. Our work suggests a manner for probing complex interactions in strong-field ionization of stretched molecules with high time resolution.