Normal Zeeman Splitting

The normal Zeeman effect describes the splitting of a spectral line into multiple components in the presence of a static magnetic field. For a spinless orbital level with quantum number l, the magnetic field lifts the degeneracy, splitting the level into 2l+1 sublevels.

Predict the sublevel shift

Consider an orbital level with l = 1 in a magnetic field B = 1 T. We track the sublevel with magnetic quantum number m = 1.

Identify the constants: the Bohr magneton in educational units is approximately µ_B = 57.88381806 µeV/T, and the Landé g-factor g_L = 1.
Calculate the shift for the selected sublevel: ΔE = m · µ_B · B = 1 · 57.88381806 · 1 = 57.88381806 µeV.
Find the total number of sublevels: 2l + 1 = 2(1) + 1 = 3 sublevels, corresponding to m = -1, 0, 1.
Calculate the total energy span across all sublevels: 2l · µ_B · |B| = 2(1) · 57.88381806 · 1 = 115.76763612 µeV.

Track shifts across fields

Open the Normal Zeeman Splitting module and follow these steps to see how the magnetic field affects energy levels.

Set Field B to 1 T, Orbital l to 1, and Selected m to 1. The visual panel will show 3 sublevels splitting from the central unperturbed state, with the selected m=1 level highlighted. The Shift micro-eV reads 57.88381806.
Change Field B to -1 T. The selected m=1 sublevel is now shifted down instead of up. The shift becomes -57.88381806 µeV.
Set Field B back to 1 T, change Orbital l to 3, and Selected m to -3. The energy span increases to 347.30290836 µeV and the number of sublevels increases to 7.
Set Field B to 0. The 7 sublevels remain degenerate and coincide at 0 shift.

Model boundaries and assumptions

This module models the normal weak-field orbital effect, which applies to spinless states or transitions where the net spin effect is zero. It does not depict anomalous spin splitting, where electron spin and orbital angular momentum couple, nor the strong-field Paschen–Back regime, where the external field breaks the internal coupling.

Additionally, this visualization shows the static energy levels of a single orbital manifold (a fixed l), rather than plotting allowed electric-dipole emission lines between different levels. Selecting an m value with magnitude greater than l is rejected by the model, as such states do not exist in the manifold.

Primary reference

For comprehensive details on atomic spectra in magnetic fields and standard constants, see theNIST Atomic Spectroscopy Compendium on the Zeeman Effect. It covers both normal and anomalous effects, including derivations of the energy shifts.

Normal Zeeman Splitting