Higher-order nuclear-size corrections in atomic hydrogen

Nuclear-size corrections of order $(Z\alpha {)}^5$ and $(Z\alpha {)}^6$ to the $S$-state levels of hydrogenic atoms are considered. These nuclear-elastic contributions are somewhat smaller than the polarizability (nuclear-inelastic) corrections for deuterium, but are of comparable or larger size for the hydrogen case. For deuterium the (attractive) nonrelativistic $(Z\alpha {)}^5$ correction to the $2S$-$1S$ transition is 0.49 kHz, while the (repulsive) relativistic $(Z\alpha {)}^6$ contribution is $-$3.40 kHz. For the proton the corresponding corrections are 0.03 kHz and $-$0.61 kHz, respectively. The $(Z\alpha {)}^5$ contribution largely cancels the Coulomb-retardation part of the nuclear-polarization correction.