Relativistic Contributions to the Magnetic Moment ofn-Electron Atoms

Abstract

A Schr\"odinger-Pauli approximation wave equation for an $n$-electron atom in an external magnetic field $H$ is derived from a Dirac equation by straightforward extension of the procedure for $n=2$. The order ${\ensuremath{\alpha}}^{2}$ terms in the resulting Hamiltonian contain corresponding ${\ensuremath{\alpha}}^{2}{\ensuremath{\mu}}_{0}H$ and ${\ensuremath{\alpha}}^{2}\mathrm{Ry}$ (fine structure) parts. The ${\ensuremath{\alpha}}^{2}{\ensuremath{\mu}}_{0}H$ terms can be arranged as a sum of the existing relativistic bound state contributions due to Breit, Margenau, and Lamb, and an additional contribution. The additional contribution is analogous to the spin-orbit contribution to fine structure. In the $^{2}S_{\frac{1}{2}}$ ground state of the heavier alkalies it is estimated to yield a positive contribution to the atomic $g$ value of the order of ten times the aforementioned (negative) contributions, which may help to account for some experimental results.