Calculation of radial moments of charge distribution

The charge radius is one of the most fundamental quantities concerning nuclear structure. Recent advancements in high-precision spectroscopic measurements utilizing isotope shifts have provided accurate experimental data on the second-order moments of charge distribution, including isotopes in regions of proton and neutron excess. Although there is no precise theoretical calculation that can match these experimental values, its calculation has the potential to contribute to the search for new physics. In this study, we try to develop theoretical models with high accuracy. Our calculations take into account not only the contribution from proton distribution but also that from neutron distribution in determining the charge distribution of a nucleus. By comparing the calculated results with the experimental values, we investigate the systematic change among various isotopes. Calculations employing the Fayans type density functionals in the mean-field model successfully reproduce the changes in the second-order moments of charge distributions observed in Ca isotopes and other isotopes. We know, however, that there are unstable regions where experimental values cannot be reproduced. Therefore, we investigated the factor of non-reproducibility by examining various nuclei. We will discuss the current state of charge radius calculations and the necessity to construct theoretical models beyond the mean-field approximation.