Nuclear deformation effect on the binding energies in heavy ions

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Nuclear deformation effects on the binding energies in heavy ions are investigated. Approximate formulas for the nuclear-size correction and the isotope shift for deformed nuclei are derived. Combined with direct numerical evaluations, these formulas are employed to reanalyze experimental data on the nuclear-charge-distribution parameters in $^{238}\text{U}$ and to revise the nuclear-size corrections to the binding energies in H- and Li-like $^{238}\text{U}$. As a result, the theoretical uncertainties for the ground-state Lamb shift in ${^{238}\text{U}}^{91+}$ and for the $2{p}_{1/2}\ensuremath{-}2s$ transition energy in ${^{238}\text{U}}^{89+}$ are significantly reduced. The isotope shift of the $2{p}_{j}\ensuremath{-}2s$ transition energies for ${^{142}\text{N}\text{d}}^{57+}$ and ${^{150}\text{N}\text{d}}^{57+}$ is also evaluated including nuclear size and nuclear recoil effects within a full QED treatment.