We present a detailed investigation of the leading-order $m{\alpha }^5$ QED correction with inclusion of the finite-nuclear-mass effects. Previously, this correction had been calculated within an expansion in the electron-nucleus mass ratio $m/M$ up to the first order. In this work, we derive formulas for the $m{\alpha }^5$ QED contribution that are valid up to the second order, and perform its calculation for the ${}^3\mathrm{He}\text{−}{}^4\mathrm{He}$ isotope shift, leading to an improved determination of the nuclear-charge-radius difference.

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• Atomic spectra
• Relativistic & quantum electrodynamic effects in atoms, molecules,& ions
• Atomic systems
• Atomic Properties