Ground state hyperfine splitting in the Be${}^{+}$ ion

Relativistic and QED corrections are calculated for the hyperfine splitting (hfs) in the $2S_{1\mathrm{/}2}$ ground state of ${}^9$Be${}^{+}$ ions with an exact account for electronic correlations. The achieved accuracy is sufficient to determine the finite nuclear size effects from the comparison to the experimental hfs value. The obtained results establish the ground to determine the neutron halo in ${}^{11}$Be.