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The finite-nuclear-size (FNS) effect has a large contribution to the atomicspectral properties especially for heavy nuclei. By adopting the microscopicnuclear charge density distributions obtained from the relativistic continuumHartree-Bogoliubov (RCHB) theory, we systematically investigate the FNScorrections to atomic energy levels and bound-electron $g$ factors ofhydrogen-like ions with nuclear charge up to $118$. The comparison of thepresent numerical calculations with the predictions from empirical nuclearcharge models, the non-relativistic Skyrme-Hartree-Fock calculations, and theresults based on experimental charge densities indicate that both the nuclearcharge radius and the detailed shape of charge density distribution playimportant roles in determining the FNS corrections. The variation of FNScorrections to energy levels and $g$ factors with respect to the nuclear chargeare investigated for the lowest several bound states of hydrogen-like ions. Itis shown that they both increase by orders of magnitude with increasing thenuclear charge, while the ratio between them has a relatively weak dependenceon the nuclear charge. The FNS corrections to the $s_{1/2}$ and $p_{1/2}$ boundstate energies from the RCHB calculations are generally in good agreement withthe analytical estimations by Shabaev [J. Phys. B, 26, 1103 (1993)] based onthe homogeneously charged sphere nuclear model, with the discrepancy indicatingthe distinct contribution of microscopic nuclear structure to the FNS effects.

Finite-nuclear-size effect in hydrogen-like ions with relativistic nuclear structure