PaschenBack

The Paschen-Back effect is the regime of atomic energy level splitting in a strong external magnetic field in which the coupling between the electron's orbital angular momentum L and its spin S is broken by the magnetic interaction, so that L and S precess independently. This decoupling changes the Zeeman splitting pattern from the anomalous Zeeman effect seen in weak fields to a linear pattern determined by the separate magnetic quantum numbers m_l and m_s.

In atoms with fine structure, the Zeeman effect in weak fields is described using LS coupling and total angular momentum J. When the magnetic field becomes large enough that the Zeeman splitting exceeds the spin–orbit coupling energy, J is no longer a good quantum number and the energy shifts approach ΔE ≈ μ_B B (m_l + 2 m_s). The result is a simplification of line spectra, with energy spacings that are nearly proportional to B and determined by m_l and m_s rather than m_J.

The effect is named after Friedrich Paschen and Walther Back, who studied hydrogen spectra in strong magnetic fields and demonstrated deviations from the normal Zeeman pattern in 1921.

There is a gradual transition from the LS-coupled regime to the Paschen-Back regime; the intermediate region may show mixed characteristics, but at very strong fields the linear splitting becomes evident and well described by m_l and m_s. The Paschen-Back concept also extends to hyperfine interactions in atoms with nuclear spin, where the hyperfine coupling decouples from the electron in very strong fields, an effect called the hyperfine Paschen-Back regime.

Applications include laboratory spectroscopy in strong magnetic fields and astrophysical plasmas, as well as magnetic field diagnostics in certain devices. The effect is a foundational concept in atomic spectroscopy and quantum mechanics of angular momentum in fields.

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