On the hyperfine structures of the ground state(s) in the $^6$Li and $^7$Li atoms

The hyperfine structure of the ground $2^2$ $S$-states of the three-electron atoms and ions is investigated. By using our recent numerical values for the doublet electron density at the atomic nucleus, we determine the hyperfine structure of the ground (doublet) $2^2$ $S$-state(s) in the $^6$Li and $^7$Li atoms. Our predicted values ($228.2058$ and $803.5581$ MHz, respectively) agree well with the experimental values $228.20528(8)$ MHz ($^6$Li) and $803.50404(48)$ MHz ($^7$Li [R.G. Schlecht and D.W. McColm, Phys. Rev. 142, 11 (1966)]). The hyperfine structures of a number of lithium isotopes with short lifetimes, including $^8$Li, $^9$Li, and $^{11}$Li atoms are also predicted. The same method is used to obtain the hyperfine structures of the three-electron $^7$Be$^+$ and $^9$Be$^+$ ions in their ground $2^2$ $S$-states. Finally, we conclude that our approach can be generalized to describe the hyperfine structure in the triplet $n^3$ $S$-states of the four-electron atoms and ions.