= Normal Zeeman effect
{title2=$\Delta\nu=0,\pm\mu_BB/h$}
The normal Zeeman effect is the simple three-<frequency> pattern obtained in the orbital limit. Assume negligible net <spin>, negligible <hyperfine structure> and quadratic shifts, and an allowed <electric-dipole interaction> between levels with orbital splitting factor one. A level with $J=0$ has only $m_J=0$ and no first-order shift. For the other levels, $g_J=1$ gives $\Delta E=\mu_Bm_JB$. Define $q=m_u-m_l$, rather than the final-minus-initial change of the emitting atom. The <electric-dipole selection rule> allows $q=0,\pm1$, hence
$$
\nu_{ul}=\nu_0+q\delta\nu_B,\qquad
\delta\nu_B=\frac{\mu_BB}{h}.
$$
Many allowed transitions can share one <frequency>; a triplet need not mean exactly three transitions. The cleanest illustrative example is $J_u=1\to J_l=0$, with three upper <quantum states> and one unshifted lower <quantum state>. The $q=0$ component is called $\pi$, and $q=\pm1$ components $\sigma^\pm$ with this stated convention. During emission the atom changes its <magnetic quantum number> by $-q$.
\Image[/zeeman-normal-triplet-photon-transitions.png]
{title=Normal Zeeman triplet from three photon transitions}
{description=Original schematic of the ideal $J_u=1\to J_l=0$ orbital model. The upper splitting factor is one and the lower level has zero first-order shift. Downward arrows show photon emission; the spectrum uses frequency increasing to the right. Equal stick heights are schematic and do not predict observed intensities.}
For an original numerical example choose $B=0.50\ \mathrm T$ and a zero-field vacuum <wavelength> $\lambda_0=500\ \mathrm{nm}$. Using $\mu_B\simeq9.27401\times10^{-24}\ \mathrm{J\,T^{-1}}$ and $h=6.62607015\times10^{-34}\ \mathrm{J\,s}$ gives $\delta\nu_B\simeq7.00\ \mathrm{GHz}$. The two outer components are separated by $2\delta\nu_B\simeq14.0\ \mathrm{GHz}$. Differentiating the vacuum relation $\lambda=c/\nu$, with $c$ the <speed of light>, gives
$$
\Delta\lambda_q\simeq-\frac{\lambda_0^2}{c}q\delta\nu_B.
$$
Each outer component lies about $0.00584\ \mathrm{nm}$ from the centre. Positive $q$ means higher <frequency> and shorter <wavelength>. Equal spacing in <frequency> is only approximately equal spacing in <wavelength>. These are calculated values for a chosen model, not historical measurements.
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