The Fayans energy density functional (EDF), and in particular its pairing sector, has been claimed to be able to reproduce the experimental data of charge radii in many instances. A particularly intriguing case is that of the $\mathrm{Ca}$ isotopes between $A=40$ and 48, where charge radii exhibit a “bell shape.” In our work, we examine the microscopic origin of this behavior. The pairing part of the Fayans EDF contains three essential parameters: the overall strength $f$ and the density-dependent and density-gradient terms, ${\tilde{h}}_0$ and ${\tilde{h}}_{\text{D}}$. We select a number of parametrizations, fixing the overall strength $f$ to reproduce the pairing gap of ${}^{44}\mathrm{Ca}$. We find that some parameter sets enhance the charge radii in open-shell nuclei and reproduce the bell shape of the charge radii of $\mathrm{Ca}$ isotopes. It is found that this effect originates from the repulsive nature of the rearrangement potential, and cannot be mocked up by a refit of the pairing strength. On the other hand, none of the parametrizations that we have considered can reproduce satisfactorily the experimental charge radii of $\mathrm{Ca}, \mathrm{Sn}$, and $\mathrm{Pb}$ isotopes at the same time.

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• Nuclear charge radii
• Nuclear forces
• Nuclear density functional theory