Calculations of Magnetic Moments for Three-Electron Atomic Systems

The first fully correlated calculations of the magnetic moment in lithium are presented. Relative to the free-electron value, the Zeeman $g_J$ factor for the ground state lithium $g_J{/g}_e-1\mathrm{}$ is calculated to a computational accuracy of 200 parts in ${10}^9$, including relativistic and radiative corrections of orders ${\alpha }^2$, ${\alpha }^{2}m/M$, and ${\alpha }^3$. The isotope shifts in $g_J$ are predicted precisely for various isotopes. The extensions to the first excited $S$ state of lithium and the ground state of ${\mathrm{Be}}^{+}$ are made.