Abstract
The authors present a detailed analysis of the connection between perturbation and variation theory applied to the Stark effect. They consider the continuous spectrum of the Stark Hamiltonian as a limit of the discrete spectrum of a model Hamiltonian matrix, when the order of this matrix increases indefinitely. For a given basis set, they study the convergence properties of the variation-perturbation series, by investigating the analytical properties of the eigenvalues as functions of the field strength. As a particular example, they use the 1s resonance of the perturbed hydrogen atom, and then consider the applicability of their conclusions to excited states and more complicated systems. The convergence properties of the perturbation expansion can be established by performing variational calculations with the same basis set. These calculations indicate the field strength up to which no convergence properties will appear. The model does not hold when there is near-degeneracy of the zeroth-order eigenvalues, but the analysis of this case is shown not to be difficult.