HIGH ORDERS OF PERTURBATION-THEORY FOR THE STARK EFFECT IN HYDROGEN

An effective method is developed to calculate the high orders of the perturbation series (PS) for the Stark shift of the energy levels in the hydrogen atom. The method is based on the use of the Riccati equation instead of the Schrödinger equation. The PS coefficients αk (hyperpolarizabilities) are given by simple recurrence relations among integers. For the ground state αk are calculated exactly for k ≤ 14 and numerically up to k = 160. The asymptotic behaviour of αk when k → ∞ is discussed for the energy eigenvalues En, 1 ≤ n ≤ 5. With the results obtained the energy and the width of the ground state are determined for external fields ε {less-than or approximate} 0.1 au. © 1979.