Collective multipole excitations based on correlated realistic nucleon-nucleon interactions

Abstract

We investigate collective multipole excitations for closed-shell nuclei from $^{16}\mathrm{O}$ to $^{208}\mathrm{Pb}$ by using correlated realistic nucleon-nucleon interactions in the framework of the random phase approximation (RPA). The dominant short-range central and tensor correlations are treated explicitly within the unitary correlation operator method (UCOM), which provides a phase-shift-equivalent correlated interaction ${V}_{\mathrm{UCOM}}$ adapted to simple uncorrelated Hilbert spaces. The same unitary transformation that defines the correlated interaction is used to derive correlated transition operators. Using ${V}_{\mathrm{UCOM}}$, we solve the Hartree-Fock (HF) problem and employ the single-particle states as a starting point for the RPA. By construction, the UCOM-RPA is fully self-consistent, i.e., the same correlated nucleon-nucleon interaction is used in calculations of the HF ground state and in the residual RPA interaction. Consequently, the spurious state associated with the center-of-mass motion is properly removed, and the sum rules are exhausted within $\ifmmode\pm\else\textpm\fi{}3%$. The UCOM-RPA scheme results in a collective character of giant monopole, dipole, and quadrupole resonances in closed-shell nuclei across the nuclear chart. For the isoscalar giant monopole resonance, the resonance energies are in agreement with experiment, hinting at a reasonable compressibility. However, in the ${1}^{\ensuremath{-}}$ and ${2}^{+}$ channels the resonance energies are overestimated because of missing long-range correlations and three-body contributions.