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Correlations and realistic interactions in doubly closed shell nuclei

We review the latest variational calculations of the ground state properties of doubly closed shell nuclei, from $^{12}$C to $^{208}$Pb, with semirealistic and realistic two- and three-nucleon interactions. The studies are carried on within the framework of the correlated basis function theory and integral equations technique, with state dependent correlations having central and tensor components. We report results for the ground state energy, one- and two-body densities and static structure functions. For $^{16}$O and $^{40}$Ca we use modern interactions and find that the accuracy of the method is comparable to that attained in nuclear matter with similar hamiltonians, giving nuclei underbound by $\sim$2 MeV/A. The computed Coulomb sums are in complete agreement with the latest analysis of the experimental data.