possible important role of missing three-body terms in the Hamiltonian (see Sec. \[ScorrH\]), another source of our failure to describe nuclear collective states quantitatively can be the inadequacy of the RPA method to take into account residual long-range correlations.

The standard RPA is based on two assumptions which hint at possible remedies. First of all, only one-particle-one-hole excitations are taken into account. One can include higher-order configurations, starting with two-particle-two-hole within SRPA. Given that an extended model space is of great importance when using the $V_{\text{UCOM}}$, it is imperative to examine the effect; work along this line is in progress. The second assumption is that one can approximate the true RPA ground state by the HF ground state. One argument follows from the fact that the RPA is the theory of small-amplitude vibrations around the HF ground state, therefore correlations should be small anyway for the use of RPA to be justified. It is not obvious that this assumption holds when the UCOM Hamiltonian is used, given the large correction to the HF binding energies due to second-order [@RPP2006] and RPA [@BPR2006] correlations. Therefore, in this work we wish to examine the effect of explicit RPA ground-state correlations on our 