a harmonic-oscillator basis are the input to such calculations. The harmonic-oscillator basis is typically restricted to $13$ major shells, which warrants complete convergence of the HF results. Calculations with larger basis sizes are possible but increasingly time-consuming. The optimal value of the harmonic oscillator parameter is determined from an explicit energy minimization for different regions in the nuclide chart.

The ERPA method {#Serpa}
===============

The method used in this work is a first-order RPA. The excited nuclear states are described as linear combinations of particle-hole ($ph$) and hole-particle ($hp$) configurations and created by a set of vibration creation operators. The RPA ground state (reference state) is the vacuum of the corresponding annihilation operators and contains induced long-range correlations. As mentioned in Sec. \[Sintro\], in order to facilitate the actual solution of the RPA equations, one usually approximates the reference state by the uncorrelated HF ground state when calculating the RPA matrix elements and the transition matrix elements. Here we use a renormalized formulation of the RPA that avoids this approximation and allows us not only to assess the effect of ground-state correlations on the excitation spectra, but also to evaluate some properties of the correlated RPA ground state. Following Ref. 