This animation shows the variation of the spectral function in the quasi-bound state region as the atomic well separation parameter a varies. The dashed line represents the spectral function without an electric field. In this F=0 case, for a=0 there is one bound state for this free case, but as a increases another state comes out of the continuum and becomes a second bound state. As a becomes very large these two bound states merge together, becoming degenerate, since the tunneling mixing is highly suppressed when a becomes very large. The behavior in the presence of an electric field [the solid line] is rather different. The would-be second quasi-bound state comes out of the continuum but is Stark shifted back up again, and so does not merge with the other quasi-bound state, which is Stark-shifted in the opposite direction.