Some aspects of the convergence behaviour of the Brillouin-Wigner perturbation scheme

The notion of the radius of convergence in the context of Brillouin-Wigner perturbation theory is classified with special reference to finite-dimensional problems. A modified procedure is shown to be more useful for infinite-dimensional problems; in particular this demonstrates the role of scaling in assuring convergence for the ground state. Behaviour of the Brillouin-Wigner energy series for the ground state is illustrated by numerically studying the convergence of a model two-by-two matrix perturbation which is beset by the intruder-state problem