Extension of random-phase approximation preserving energy weighted sum rules: An application to a 3-

A limitation common to all extensions of random-phase approximation including only particle-hole configurations is that they violate to some extent the energy weighted sum rules. Considering one such extension, the improved RPA (IRPA), already used to study the electronic properties of metallic clusters, we show how it can be generalized in order to eliminate this drawback. This is achieved by enlarging the configuration space, including also elementary excitations corresponding to the annihilation of a particle (hole) and the creation of another particle (hole) on the correlated ground state. The approach is tested within a solvable 3-level model.