2.2: Anomalous Zeeman effect

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When an atom is placed in a magnetic field, each of its fine structure lines further splits into a series of equidistant lines with a spacing proportional to the magnetic field strength. Theoretically, this is explained by recognizing that the electron has an orbital magnetic moment

\[{\bf M} = {\mu_{\rm B} \over \hbar}{\bf L}\]

where \(L\) is the angular momentum operator, \(\mu_B\) is the Bohr magneton

\[\mu_{\rm B} = {e\hbar \over m_{\rm e}}\]

The orbital magnetic moment gives rise to an interaction with a magnetic field proportional to \({\bf M} \cdot {\bf B}\), where \({\bf B}\) is the magnetic field vector.

This interaction gives rise to the so called normal Zeeman effect. The normal Zeeman effect would predict a number of lines equal to \(2l+1\), the number of \(L_z\) eigenvalues. Note that, since \(l\) must be an integer, this number is always odd.

However, there is an anomalous Zeeman effect which shows up particularly for atoms with odd atomic number \(Z\) (hydrogen, for example). In such cases, it is found that the number of Zeeman sub-levels is actually even rather than odd. This cannot be explained within the normal Zeeman theory. However, it suggests the possible existence of an angular momentum like quantity that can take on half-integer values.