Extended renormalized random phase approximation

The random phase approximation (RPA) is fully renormalized to take into account the ground-state correlations (g.s.c.) beyond the RPA, which arise due to the fermion structure of the collective RPA operators. As compared to the conventional renormalized RPA (RRPA), the novelty of the present extended renormalized RPA (ERRPA) is the inclusion of the particle-particle (pp) and hole-hole (hh) g.s.c. beyond the RPA along with the ph ones in the complete set of ERRPA equations. The formalism is illustrated by numerical calculations within a schematic four-level model. The results show that the effects of g.s.c. beyond the RPA due to pp (and $hh)$ transitions can cause a partial or complete compensation of the ones due to ph transitions. This reduces the deviation from the RPA energy-weighted sum of strength within the ERRPA as compared to the one within the conventional RRPA.