Relativistic Contributions to the Magnetic Moment ofn-Electron Atoms

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 α² terms in the resulting Hamiltonian contain corresponding α²μ₀H and α²Ry (fine structure) parts. The α²μ₀H 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 ²S1/2 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.