|ΔE = gM µBB .||(6)|
The wavenumber shift Δσ corresponding to this energy shift is
|Δσ = gM (0.466 86 B cm-1) ,||(7)|
with B representing the numerical value of the magnetic flux density in teslas. The quantity in parentheses, the Lorentz unit, is of the order of 1 or 2 cm-1 for typical flux densities used to obtain Zeeman-effect data with classical spectroscopic methods. Accurate data can be obtained with much smaller fields, of course, by using higher-resolution techniques such as laser spectroscopy. Most of the g values now available for atomic energy levels were derived by application of the above formula (for each of the two combining levels) to measurements of optical Zeeman patterns. A single transverse-Zeeman-effect pattern (two polarizations, resolved components, and sufficiently complete) can yield the J value and the g value for each of the two levels involved.
Neglecting a number of higher-order effects, we can evaluate the g
value of a level βJ belonging to a pure LS-coupling term
using the formula
The usefulness of gSLJ values is enhanced by their relation
to the g values in intermediate coupling. In the notation used in
Eq. (4) for the wave function
of a level βJ in intermediate coupling, the corresponding g
value is given by
Formulas for magnetic splitting factors in the J1 J2 and J1 L2 coupling schemes are given in Refs.  and . Some higher-order effects that must be included in more accurate Zeeman-effect calculations are treated by Bethe and Salpeter  and by Wybourne , for example. High precision calculations for helium are given in Ref. .