Sodium D-line Zeeman pattern

Neglect hyperfine structure and use a magnetic field weak compared with the spin-orbit interaction. The sodium D doublet has transitions $3p{}^2{P}_{1/2}\to 3s{}^2{S}_{1/2}$ and $3p{}^2{P}_{3/2}\to 3s{}^2{S}_{1/2}$. Their Landé g-factors are $2/3$, $4/3$ and $2$ respectively. With $m_u,m_l$ denoting upper and lower magnetic labels, the photon shift isThe first transition has four allowed shifts ${\mu }_{B}B\{\pm 2/3,\pm 4/3\}$; the second has six, ${\mu }_{B}B\{\pm 1/3,\pm 1,\pm 5/3\}$. The most blue-shifted component of the second is $m_u=1/2\to m_l=-1/2$, with shift $5{\mu }_{B}B/3$. The apparently larger shift $m_u=3/2\to m_l=-1/2$ is excluded by the electric-dipole selection rule. The $3p{}^2{P}_{3/2}$ level lies above $3p{}^2{P}_{1/2}$, so in this weak-field model the $5/3$ component also has the shortest wavelength of the whole doublet. ^[ref]

For weak-field sodium D lines neglecting hyperfine structure, the smallest adjacent spectral spacing in the full electronic pattern is $s_E=2{\mu }_{B}B/3$. A drawing without a labelled energy axis can still estimate $B$ if it includes both unsplit D lines with known wavelengths: their separation calibrates $hc(1/{\lambda }_2-1/{\lambda }_1)$. Divide the drawn split spacing by the drawn unsplit separation before using that energy scale. Graphical line thickness, unequal drawn spacings and uncalibrated rendering limit precision; they do not justify exact numerical field values.