Perturbation theory for projected states in the pairing force model: (II). The problem of convergence

In a previous paper second-order calculations were carried out on the two-level pairing force model using perturbation theory for projected states and the results were compared with those of BCS or ordinary perturbation theory. In the present paper criteria for convergence are applied to two different forms of the perturbation series for both the projected and ordinary perturbation theories. It is found that the superior results obtained for the convergence rates in the projected theory tally neatly with the results of the second-order calculations, and give further support to the use of the projected perturbation theory.