Soluble model test of the multi-valued G-matrix effective interaction

The recently proposed multi-valued G-matrix effective interaction is tested in a soluble multi-level monopole-pairing interaction model. To mimic the no-core shell model approach, different effective interactions including the multi-valued G-matrix are calculated in a two-particle space and subsequently applied for the many-particle calculation. The multi-valued G-matrix effective interaction, both starting energy dependent and starting energy independent, is shown to be superior to the single-valued G-matrix. The formalism is extended to effective operators, where a similar conclusion is found.