The Zeeman effect (Dutch: [ˈzeːmɑn]) is the splitting of a spectral line into several components in the presence of a static magnetic field. It is caused by the interaction of the magnetic field with the magnetic moments of the atomic electrons associated with their orbital motion and spin; this interaction shifts some orbital energies more than others, resulting in the split spectrum. The effect is named after the Dutch physicist Pieter Zeeman, who discovered it in 1896 and received the Nobel Prize in Physics for it in 1902. It is analogous to the Stark effect, the splitting of a spectral line into several components in the presence of an electric field. Also, similar to the Stark effect, transitions between different components have, in general, different intensities, with some being entirely forbidden (in the dipole approximation), as governed by the selection rules. Since the distance between the Zeeman sub-levels is a function of magnetic field strength, this effect can be used to measure magnetic field strength, e.g. that of the Sun and other stars or in laboratory plasmas.
Discovery In 1896, Zeeman learned that his laboratory had one of Henry Augustus Rowland's highest resolving diffraction gratings. Zeeman had read James Clerk Maxwell's article in Encyclopædia Britannica describing Michael Faraday's failed attempts to influence light with magnetism. Zeeman wondered if the new spectrographic techniques could succeed where early efforts had not. When illuminated by a slit-shaped source, the grating produces a long array of slit images corresponding to different wavelengths. Zeeman placed a piece of asbestos soaked in salt water into a Bunsen burner flame at the source of the grating: he could easily see two lines in the sodium light emission spectrum. Switching on a strong (about one tesla) electromagnet around the flame, he observed a slight broadening of the lines. When Zeeman switched to cadmium as the source, he observed the spectral lines split when the magnetic field was applied. These splittings could be analyzed with Hendrik Lorentz's then-new electron theory. It is now known that the magnetic effects on sodium require quantum-mechanical treatment. Zeeman and Lorentz were awarded the 1902 Nobel Prize; in his acceptance speech Zeeman explained his apparatus and showed slides of the spectrographic images.
Nomenclature Historically, one distinguishes between the normal and an anomalous Zeeman effect (discovered by Thomas Preston in Dublin, Ireland). The anomalous effect appears on transitions where the net spin of the electrons is non-zero. It was called "anomalous" because the electron spin had not yet been discovered, and so there was no good explanation for it at the time that Zeeman observed the effect. Wolfgang Pauli recalled that when asked by a colleague as to why he looked unhappy, he replied: "How can one look happy when he is thinking about the anomalous Zeeman effect?" At higher magnetic field strength the effect ceases to be linear. At even higher field strengths, comparable to the strength of the atom's internal field, the electron coupling is disturbed and the spectral lines rearrange. This is called the Paschen–Back effect. In modern scientific literature, these terms are rarely used, with a tendency to use just the "Zeeman effect". Another rarely used obscure term is inverse Zeeman effect, referring to the Zeeman effect in an absorption spectral line. A similar effect, splitting of the nuclear energy levels in the presence of a magnetic field, is referred to as the nuclear Zeeman effect.
Theoretical presentation The total Hamiltonian of an atom in a magnetic field is
H = H 0 + V M , {\displaystyle H=H_{0}+V_{\text{M}},}
where H 0 {\displaystyle H_{0}} is the unperturbed Hamiltonian of the atom, and V M {\displaystyle V_{\text{M}}} is the perturbation due to the magnetic field:
V M = − μ → ⋅ B → , {\displaystyle V_{\text{M}}=-{\vec {\mu }}\cdot {\vec {B}},}
where μ → {\displaystyle {\vec {\mu }}} is the magnetic moment of the atom. The magnetic moment consists of the electronic and nuclear parts; however, the latter is many orders of magnitude smaller and will be neglected here. Therefore,
μ → ≈ − μ B g J → ℏ , {\displaystyle {\vec {\mu }}\approx -{\frac {\mu _{\text{B}}g{\vec {J}}}{\hbar }},}
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