Stark effect in hydrogen: High orders of perturbation theory for excited states

Abstract

The method proposed in refs. [3–5] for computation of high order terms of perturbation series (PS) is generalized to excited states with wave-functions having modes. The computation of the PS coefficients E k for the Stark shift in hydrogen is reduced to solving a system of recurrence relations. With these relations exact values of E k are calculated up to k = 12 for all states with the principal quantum number n = 2 as well as for the states with n 1 = n 2 = 0, | m| = n − 1 and n ⩽ 5. Numerical values of E k are obtained for k ⩽ 100. This makes it possible of investigate the approach of E k to their asymptotics ∼ K k and to determine power corrections to ∼ E k .