The systematics are investigated for the charge radii of the even-$Z$ nuclei with $8⩽Z⩽120$ calculated by the deformed relativistic Hartree-Bogoliubov theory in continuum with the functional PC-PK1, and their deformation correlation is explored. The available data of the charge radius are reproduced with a root-mean-square deviation $\sigma =0.033$ fm. In particular, for the nuclei between the closed shells, the descriptions of the charge radii are remarkably improved by including the deformation. Taking molybdenum isotopes as examples, both the evolutions of the charge radius and deformation are well reproduced. It is found that while the charge radius typically increases with the deformation, there also exist different cases. For example, in ${}^{346}\mathrm{Sg}$, the charge radius of the deformed ground state is smaller than the one of the spherical state, and the largest binding energy does not necessarily correspond to the smallest charge radius. The increase or decrease of the charge radii with deformation is related to specific shell structures, particularly the key single-particle levels near the Fermi energy.

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• Nuclear density functional theory
• Nuclear radii
• Nuclear shapes and moments