Recoil corrections with finite nuclear size in hydrogenic systems

Formulas for the combined nuclear-recoil and finite-nuclear-size effects of orders ${(Z\ensuremath{\alpha})}^{5}$ and ${(Z\ensuremath{\alpha})}^{6}$ are derived without any expansion in the nuclear-charge radius ${r}_{C}$, making them applicable to both electronic and muonic atoms. The obtained results are particularly relevant for high-precision determinations of root-mean-square charge radii from muonic atom spectroscopy. We demonstrate that calculations of the atomic isotope shift based on the widely used Breit approximation give rise to an unphysical nuclear-size contribution that is linear in the nuclear-charge radius ${r}_{C}$ at order ${(Z\ensuremath{\alpha})}^{5}$. This spurious term vanishes in a full QED treatment, leaving the correct contribution quadratic in ${r}_{C}$. For electronic atoms, this quadratic term is significantly smaller than the spurious linear contribution.