Hyperfine splitting in ${}^{6,7}$Li${}^{+}$

We present a detailed derivation of the QED effects of order ${\alpha }^{7}m$ to the hyperfine structure (hfs) of the ${}^{3}S$ states of helium-like ions and perform numerical calculations for ${}^6$Li${}^{+}$ and ${}^7$Li${}^{+}$. By comparing the theoretical point-nucleus results with the measured hfs of Li${}^{+}$, we determine the nuclear-structure contribution parameterized in terms of the effective Zemach radius. Using the experimental hfs results for Li${}^{+}$, we obtain accurate predictions for the hfs of ${}^6$Li${}^{2+}$ and ${}^7$Li${}^{2+}$, for which no experimental data is available so far. By examining the normalized differences of the hfs of Li${}^{+}$ and Li and of the corresponding isotope-shift differences, we test the consistency of the hfs measurements in ${}^{6,7}$Li${}^{+}$ and ${}^{6,7}$Li.