Nonperturbative approximation schemes for the effective interaction in nuclei

Several methods are investigated to deal with the singularities of the effective interaction which cause the perturbation series to diverge. Some of these methods, which are found to be quite useful, are based upon a semiphenomenological treatment of the "intruder" states. One method, based upon the use of Padé approximants, seems to be free of such semiphenomenological input data and appears to yield a particular effective interaction which has as eigenvalues those levels of the system for which the corresponding eigenfunctions have maximum overlap with the model space. The methods are investigated with the help of simple examples. Those methods which are found to be useful are applied to the 0⁺ and 2⁺ levels of ¹⁸O.