 Normal Zeeman effect

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 $\Delta E={\mu }_B{m}_{J}B$. Define $q=m_u-m_l$, rather than the final-minus-initial change of the emitting atom. The electric-dipole selection rule allows $q=0,\pm 1$, henceMany 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 $q=\pm 1$ components ${\sigma }^{\pm }$ with this stated convention. During emission the atom changes its magnetic quantum number by $-q$.

For an original numerical example choose $B=0.50\mathrm{T}$ and a zero-field vacuum wavelength ${\lambda }_0=500\mathrm{nm}$. Using ${\mu }_B\simeq 9.27401\times 10^{-24}\mathrm{J}{\mathrm{T}}^{-1}$ and $h=6.62607015\times 10^{-34}\mathrm{J}\mathrm{s}$ gives $\delta {\nu }_B\simeq 7.00\mathrm{GHz}$. The two outer components are separated by $2\delta {\nu }_B\simeq 14.0\mathrm{GHz}$. Differentiating the vacuum relation $\lambda =c/\nu$, with $c$ the speed of light, givesEach 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.