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Using the Dirac equation, we study corrections to electron binding energiesand hyperfine splittings of atomic hydrogen and hydrogen-like ions due tofinite nuclear size (FNS) effects, relativistic QED radiative corrections andnuclear recoil corrections. Three models for the charge distribution and themagnetic moment distribution within the nucleus are considered. Calculationsare carried for light atoms (H, He and K) and heavy atoms (Rb, Cs, Pb, Bi, U).The FNS corrections to the ground-state energy are shown to be smaller than theelectron-nucleus reduced mass corrections, and comparable to the relativisticQED radiative corrections for the light nuclei, but much larger than both thesecorrections for heavy nuclei. Comparison is made with an experiment on the$1s$-$2s$ transition frequency for hydrogen. FNS corrections to the groundstate hyperfine splitting are comparable in size to the relativistic QEDradiative corrections for light nuclei, but are larger for heavy nuclei.

Hydrogen and hydrogen-like-ion bound states and hyperfine splittings: finite nuclear size effects}