Nuclear recoil effects with a realistic nuclear charge form factor

We introduce a novel two-parameter Gamma model of the nuclear charge distribution as an alternative to the widely used Fermi distribution. The model yields simple analytical formulas for all moments of the charge distribution and closed-form expressions for the electrostatic potential and momentum-space form factor, the latter satisfying the correct analyticity requirements for a physical charged particle. We apply the model to calculate the nuclear recoil correction to the Lamb shift in electronic and muonic atoms and analyze its nuclear-model dependence. We find that the nuclear-size recoil corrections to energy levels of heavy muonic atoms are strongly sensitive to higher moments of the nuclear charge distribution, highlighting the importance of realistic nuclear modeling. To facilitate further calculations, we also provide the Fortran code RECFNS, designed for computing the nuclear recoil correction within the QED framework. The present work establishes a basis for future extensions to higher orders in the electron-to-nucleus mass ratio, hyperfine splitting, and radiative corrections.