Zeeman Effect in Intermediate Coupling

A method is given for calculating $g$-values in intermediate coupling when the matrix of internal energy of the atom (spin-orbit plus electrostatic interaction) is known in $\mathrm{LS}$ coupling. The transformation from the states of $\mathrm{LS}$ coupling to the states of intermediate coupling, in which the internal energy matrix is diagonal, is then readily determined in terms of the parameters expressing the relative magnitudes of the interactions. The coupling parameters are ascertained from the measured energy levels. The transformation so determined is applied to the matrix of the energy due to an external magnetic field, as known for $\mathrm{LS}$ coupling. The diagonal terms of the transformed matrix contain the $g$-values of the states of the atom in intermediate coupling. Application of the method is made to the configurations $p^2$, $p^3$ and $d^2$. Agreement with the available experimental $g$-values is satisfactory, being as good as the agreement of energy levels to be had from a first order calculation.