QED nuclear recoil effect in helium isotope shift

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 in $m/M$, and perform its calculation for the $^3$He$-$$^4$He isotope shift, leading to an improved determination of the nuclear charge-radius difference.