Hyperfine splitting of hydrogenlike atoms based on relativistic mean field theory

We evaluate the hyperfine splitting of hydrogenlike Bi-209 and Pb-207 atoms based on a relativistic method for both the electron system and the nucleon system. The Bohr-Weisskopf (BW) effect is calculated with Lorentz covariant current. It is shown that the BW correction to the hyperfine splitting (HFS) is 0.58%-0.67% for Bi-209(82+) and 3.79%-4.00% for Pb-207(81+). It is also concluded that relativistic mean field theory reproduces the observed values of the HFS within the accuracy of 5% in Bi-209(82+) and 13% in Pb-207(81+).