Zeeman effect

The Zeeman effect (Dutch: [ˈzeːmɑn]) is the splitting of a spectral line into several components in the presence of a static magnetic field.

The effect is named after the Dutch physicist Pieter Zeeman, who discovered it in 1896 and received a Nobel Prize in Physics for this discovery.

It is analogous to the Stark effect, the splitting of a spectral line into several components in the presence of an electric field.

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 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 for sodium light emission.

Energizing a 10-kilogauss magnet around the flame, he observed a slight broadening of the sodium images.

[1]: 76 When Zeeman switched to cadmium as the source, he observed the images split when the magnet was energized.

[2] Historically, one distinguishes between the normal and an anomalous Zeeman effect (discovered by Thomas Preston in Dublin, Ireland[3]).

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.

In the modern scientific literature, these terms are rarely used, with a tendency to use just the "Zeeman effect".

The magnetic moment consists of the electronic and nuclear parts; however, the latter is many orders of magnitude smaller and will be neglected here.

A more accurate approach is to take into account that the operator of the magnetic moment of an electron is a sum of the contributions of the orbital angular momentum

, in which case the atom can no longer exist in its normal meaning, and one talks about Landau levels instead.

Depicted on the right is the additional Zeeman splitting, which occurs in the presence of magnetic fields.

The Paschen–Back effect is the splitting of atomic energy levels in the presence of a strong magnetic field.

This occurs when an external magnetic field is sufficiently strong to disrupt the coupling between orbital (

The energies are simply The above may be read as implying that the LS-coupling is completely broken by the external field.

, each of these three components is actually a group of several transitions due to the residual spin–orbit coupling and relativistic corrections (which are of the same order, known as 'fine structure').

In the case of weak magnetic fields, the Zeeman interaction can be treated as a perturbation to the

To get the complete picture, including intermediate field strengths, we must consider eigenstates which are superpositions of the

, the Hamiltonian can be solved analytically, resulting in the Breit–Rabi formula (named after Gregory Breit and Isidor Isaac Rabi).

George Ellery Hale was the first to notice the Zeeman effect in the solar spectra, indicating the existence of strong magnetic fields in sunspots.

[12] Old high-precision frequency standards, i.e. hyperfine structure transition-based atomic clocks, may require periodic fine-tuning due to exposure to magnetic fields.

This is carried out by measuring the Zeeman effect on specific hyperfine structure transition levels of the source element (cesium) and applying a uniformly precise, low-strength magnetic field to said source, in a process known as degaussing.

[citation needed] A theory about the magnetic sense of birds assumes that a protein in the retina is changed due to the Zeeman effect.

[citation needed] The electron spin resonance spectroscopy is based on the Zeeman effect.

[16] However, the magnetic field also affects the flame, making the observation depend upon more than just the Zeeman effect.

[15] These issues also plagued Zeeman's original work; he devoted considerable effort to ensure his observations were truly an effect of magnetism on light emission.

[18][failed verification] When a magnetic field is applied, due to the Zeeman effect the spectral line of sodium gets split into several components.

The spectral lines of mercury vapor lamp at wavelength 546.1 nm, showing anomalous Zeeman effect. (A) Without magnetic field. (B) With magnetic field, spectral lines split as transverse Zeeman effect. (C) With magnetic field, split as longitudinal Zeeman effect. The spectral lines were obtained using a Fabry–Pérot interferometer .

Zeeman splitting of the 5s level of ⁸⁷ Rb , including fine structure and hyperfine structure splitting. Here F = J + I , where I is the nuclear spin (for ⁸⁷ Rb, I = 3 ⁄ 2 ).

This animation shows what happens as a sunspot (or starspot) forms and the magnetic field increases in strength. The light emerging from the spot starts to demonstrate the Zeeman effect. The dark spectra lines in the spectrum of the emitted light split into three components and the strength of the circular polarisation in parts of the spectrum increases significantly. This polarisation effect is a powerful tool for astronomers to detect and measure stellar magnetic fields.