Multiphonon states in even-even spherical nuclei I. Calculation of the overlap matrix

The multiphonon method, previously developed for deformed nuclei is extended to the case of even-even spherical nuclei. Recursion formulae, well suited for numerical calculations are given for the overlap matrix elements. The method is illustrated for a single j-shell, where S-, D-, G-, … phonons are introduced. In such an approach, the Pauli principle is fully and properly taken into account.