Study of the convergence radius of the Rayleigh–Schrödinger perturbation series for the delta-function model of H

The convergence radius of the series expansion for the energy of H₂⁺ in the δ-function model (in terms of the perturbation parameter μ/λ, where μ is the charge of the perturbing nucleus and λ the fixed charge of the other nucleus) is investigated. A lower bound of this convergence radius (possibly equal to it) previously defined by Robinson 5] is studied analytically as a function of the internuclear distance R and computed numerically. The results differ strikingly from those previously obtained by Robinson who used a simplified but poorer lower bound: in contrast with this poorer bound, the one studied in the present paper is larger than for I every R, from which fact it may be concluded that, contrary to Robinson's previous result, the series expansion of the energy, in the δ-function model under consideration, still converges when μ = λ for every R.