Stark effect in intense field. Perturbation theory and 1/n-expansion

The problem of the Stark effect in a hydrogen atom is considered. The computation results of higher orders of perturbation series (PS) are briefly described. Stark shifts and widths of the grouns and excited states of the hydrogen atom in the intense electric field ε are computed by two independent methods: PS summation and 1/n-expansion. The first method works well at n ∼ 1, while the second fastly converges in the case of Rydberg states, n >> 1