PX262 - G7b - strong-field zeeman effect

{\hat{H}}_{Z} = \frac{e}{2 m} B_{0} ({\hat{L}}_{z} + 2 {\hat{S}}_{z})

starting with a large external magnetic field, so, effects of LS-coupling can be neglected
here, simple products of the eigenfunctions of ${\hat{L}}_{z}$ and ${\hat{S}}_{z}$ are also eigenfunctions of ${\hat{H}}^{'}$
the energy eigen values are changed by:

Δ E = \frac{e ℏ B}{2 m} (m_{l} + 2 m_{s})

where, $l$ and $s$ subscripts distinguish the quantum numbers associated with the z components of the two angular momenta

if an electron in a state with a fixed $l$ is taken, the energy levels will split to $(2 l + 1) (2 s + 1)$ levels
they will all be equally spaced, but some might accidentally be degenerate