Coulomb sum rule ofA=2, 3, and 4 nuclei

The ${\omega }^2$-weighted sums $W_L^{\mathrm{}\left(2\right)\mathrm{}}$(k) of the longitudinal response of two-, three-, and four-body nuclei are calculated with realistic nuclear forces, and exact (A=2) and variational (A=3 and 4) wave functions. These and the ω-weighted sums $W_L$(k) are used to estimate the unmeasured longitudinal response at ω>$E_{\max }$. The Coulomb sums obtained by integrating the measured response up to ω=$E_{\max }$ and the estimated response at ω>$E_{\max }$, are in good agreement with the theoretical predictions in light nuclei. The ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ data show the presence of proton-proton correlations, although they are not accurate enough to allow for a quantitative determination of the size of the repulsive core in the nucleon-nucleon interaction.