Magnetic moment of atomic lithium

Abstract

Bound-state relativistic contributions to the $g_J$ factor of ground-state atomic lithium are calculated and compared with the experimental value $\frac{g_J\left(\mathrm{Li}\right)}{g_e}=1-(8.9\mathrm{}\pm 0.4)\times {10}^{-6\mathrm{}}$, where $g_e$ is the free-electron $g$ factor. This comparison is taken as the basis for judging the accuracy of several different Li wave functions taken from the literature. Most of these wave functions give agreement with the experimental value within the experimental uncertainty. A more precise experimental measurement would be desirable in order to provide a more stringent test. A wave function of the restricted Hartree-Fock type, however, leads to a value which is in disagreement with the experimental value. This is attributed to the inability of the restricted Hartree-Fock function to account for the exchange polarization of the $1s^2$ core electrons; the latter are found to contribute about -1.2 × ${10}^{-6\mathrm{}}$ to $\frac{g_J\left(\mathrm{Li}\right)}{g_e}$, or about 13% of the total relativistic correction. In addition to the dominant relativistic corrections of order ${\alpha }^2$, radiative corrections (order ${\alpha }^3$), and nuclear-mass corrections (order $\frac{{\alpha }^{2}m}{M}$) are also calculated. An isotopic shift $\frac{g_J\left({}_{}{}^6{}_{}{}^{}\mathrm{Li}\right)}{g_J\left({}_{}{}^7{}_{}{}^{}\mathrm{Li}\right)}=1+3.0\mathrm{}\times {10}^{-11\mathrm{}}$ is predicted. The experimental measurements for Li are not yet precise enough to test these higher-order corrections.