Two-dimensional analogs of the ${\mathrm{H}}_2^{+}$ ion in stationary electric fields

We calculate energies and lifetimes for two two-dimensional analogs of the hydrogen molecular ion ${\mathrm{H}}_2^{+}$ in external static electric fields directed along the axis of the system. They are two positive Coulomb impurity centers with one electron in a narrow two-dimensional quantum well and the electron in a double quantum dot. For state $2p{\sigma }_u$ we obtain oscillating dependencies of the ionization rate $\Gamma$ on the electric-field strength F and the distance between centers R. We explain the oscillation picture by an interference of the electronic wave between two centers. The oscillations decrease faster for a pair of quantum dots with short-range attractive potentials than for a pair of Coulomb centers. The latter is due to the fact that long-range Coulomb potentials form a kind of channel preventing a dissipation of the electronic density sidewards from the axis of the system.