Hidden crossings and excitation of hydrogen by a slow electric pulse

The complex eigenenergy surfaces of quasistationary states for the hydrogenic Stark problem as a function of complex field strength have been calculated. It is shown that the location of `hidden crossings' of energy surfaces connected with different states can be obtained from a semiclassical quantization of `top of the barrier' motion. A numerical calculation of the excitation of hydrogenic states by an electric field pulse shows an unexpected threshold-like behaviour in the adiabatic regime. In addition, the lower the peak-field strength, the higher is the state populated maximally. It is found that these effects are correlated to the position of the `top of the barrier' hidden crossings as a function of field strength.