Improved Theory of the Zeeman Effect of Atomic Oxygen

The previous calculations of Abragam and Van Vleck on the $g$ factors of the $2p^4{}_{}{}^3{}_{}{}^{}P$ terms of atomic oxygen are refined by including exchange, using better wave functions, and not assuming that the charge distribution in which a $2p$ electron moves is spherically symmetric. In Sec. 2, a general technique is developed for calculating the relativistic and diamagnetic corrections to the $g$ factors of complex atoms (Breit-Margenau and Lamb terms, etc.) by an expansion in spherical harmonics which is an extension of the well-known Slater procedure for computing the angular dependence of electrostatic energy. The integrals encountered are usually either of the Condon and Shortley $F$, $G$ type, or variants thereof. The most important members are computed by means of the wave functions of Hartree, Hartree, and Swirles, based on a Fock self-consistent field, but some of the minor contributions are estimated with Slater wave functions improved by introducing slightly different screening constants for the $2s$ and $2p$ terms. When all corrections are comprised, including also the Schwinger electrodynamic shift, motion of nucleus, and deviations from Russell-Saunders coupling, the calculated values of the $g$ factors for the ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ terms are, respectively, 1.500974, 1.500913, in excellent agreement with Rawson and Beringer's experimental determinations 1.500971, 1.500905.