Calculation of the Magnetic Moment of Atomic Fluorine

Abstract

The atomic $g_J$ factors for the two levels composing the lowest term of atomic fluorine have been calculated utilizing the theory of Kambe and Van Vleck and wave functions resulting from Hartree-Fock treatments of varying accuracy. For the high-accuracy wave functions, the results of our calculation are in exact agreement with the measured $\frac{g_J({\mathrm{F}}^{19}; {}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{})}{g_J({\mathrm{H}}^1; {}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{})}=\frac{2}{3}-(497\mathrm{}\pm 1)\times {10}^{-6\mathrm{}}$, to within the experimental error. The contribution to $g_J({\mathrm{F}}^{19}; {}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{})$ arising from the Breit interaction is found to amount to 49×${10}^{-6\mathrm{}}$. This sizeable contribution, and the excellent agreement obtained, substantiate the validity of the theory and, in particular, of the Breit interaction to the order of ${\alpha }^2$. For the upper level, the value $g_J({\mathrm{F}}^{19}; {}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{})=\frac{2}{3}-(1072\mathrm{}\pm 2)\times {10}^{-6\mathrm{}}$ is obtained. For this, no experimental test of adequate sensitivity has been made.