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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.

It may also be utilized to improve accuracy in atomic absorption spectroscopy. A theory about the magnetic sense of birds assumes that a protein in the retina is changed due to the Zeeman effect.

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

At higher magnetic field strength the effect ceases to be linear. At even-higher field strength, when the strength of the external field is comparable to the strength of the atom's internal field, electron coupling is disturbed and the spectral lines rearrange.

This is called the Paschen-Back effect. In the modern scientific literature, these terms are rarely used, with a tendency to use just the "Zeeman effect". The total Hamiltonian of an atom in a magnetic field is. The magnetic moment consists of the electronic and nuclear parts; however, the latter is many orders of magnitude smaller and will be neglected here.

In the case of the LS coupling , one can sum over all electrons in the atom:. There are intermediate cases which are more complex than these limit cases. The Lyman-alpha transition in hydrogen in the presence of the spin—orbit interaction involves the transitions.

Note in particular that the size of the energy splitting is different for the different orbitals, because the g J values are different. On the left, fine structure splitting is depicted. This splitting occurs even in the absence of a magnetic field, as it is due to spin-orbit coupling.

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 effect is the strong-field limit of the Zeeman effect. The energies are simply. The above may be read as implying that the LS-coupling is completely broken by the external field. Together with the selection rules for an electric dipole transition , i.

In general, one must now add spin-orbit coupling and relativistic corrections which are of the same order, known as 'fine structure' as a perturbation to these 'unperturbed' levels. First order perturbation theory with these fine-structure corrections yields the following formula for the hydrogen atom in the Paschen—Back limit: [4].

In the magnetic dipole approximation, the Hamiltonian which includes both the hyperfine and Zeeman interactions is. This pair of states is a Two-level quantum mechanical system. Now we can determine the matrix elements of the Hamiltonian:. Solving for the eigenvalues of this matrix, as can be done by hand - see Two-level quantum mechanical system , or more easily, with a computer algebra system we arrive at the energy shifts:.

George Ellery Hale was the first to notice the Zeeman effect in the solar spectra, indicating the existence of strong magnetic fields in sunspots. Such fields can be quite high, on the order of 0.

Today, the Zeeman effect is used to produce magnetograms showing the variation of magnetic field on the sun. The Zeeman effect is utilized in many laser cooling applications such as a magneto-optical trap and the Zeeman slower. From Wikipedia, the free encyclopedia. Play media. Journal of the Royal Society Interface. Physica in German. Introduction to Quantum Mechanics 2nd ed. Prentice Hall. Elementary Atomic Structure 2nd ed. Oxford, England: Oxford University Press.

Physical Review. Bibcode : PhRv Pekar and E. Rashba, Combined resonance in crystals in inhomogeneous magnetic fields, Sov. Tokura, W. Obata, and S. Tarucha, Coherent single electron spin control in a slanting Zeeman field, Phys. CS1 maint: uses authors parameter link. Categories : Spectroscopy Quantum magnetism Foundational quantum physics Magneto-optic effects. Namespaces Article Talk. Views Read Edit View history. Contribute Help Community portal Recent changes Upload file.

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