Paschen-back effect

Splitting of the hydrogen levels under the influence of a magnetic field.

The Paschen-Back effect (after Friedrich Paschen and Ernst Back , who discovered it in 1921) describes the decoupling of spin and orbital angular momenta when a strong magnetic field is applied . An optical spectrum of atoms with an anomalous Zeeman effect thus merges into a spectrum with a normal Zeeman effect (i.e. with three equidistant lines). ${\displaystyle {\boldsymbol {B}}}$

Spin and orbital angular momentum of one or more electrons outside filled shells are coupled to a total angular momentum of the atomic shell in the absence of an external field and, depending on its quantum number, form states of different energies. The formation of the total angular momentum means that the magnetic quantum numbers of the individual spin and orbital angular momentum do not have a fixed value. When a "weak" magnetic field is applied, the quantum number of the total angular momentum is initially retained, but the level splits into equidistant "Zeeman levels" in proportion to the strength of the field . For two such levels with different levels , the split is generally different (depending on the Landé factor ): ${\displaystyle {\boldsymbol {J}}}$ ${\displaystyle J}$ ${\displaystyle J}$ ${\displaystyle 2J+1}$ ${\displaystyle J}$ ${\displaystyle g_{J}}$

${\displaystyle \Delta E=g_{J}\,m_{j}\,\hbar \,\gamma \,B}$.

As a result, the spectral lines of the transitions between them also split up into a number of equidistant lines (anomalous Zeeman effect). If the energy splitting comes close to the distance of the original levels with increasing field , then it becomes noticeable that spin and orbital angular momentum orientate themselves with different setting energies at the magnetic field. The further splitting is then no longer proportional to the field strength. In the “strong” magnetic field, the original coupling to the total angular momentum no longer plays a role at all. Spin and orbital angular momentum behave independently of one another and determine the energies of the split levels through their states with specific magnetic quantum numbers. This splitting is the same in all levels, which is why there is only a three-fold line splitting in the optical spectrum, which increases proportionally to the magnetic field. This corresponds to the normal Zeeman effect. ${\displaystyle J}$ ${\displaystyle J}$

${\displaystyle \Delta E=\left(g_{l}m_{l}+g_{s}m_{s}\right)\,\hbar \,\gamma \,B}$

In it is

• ${\displaystyle B}$ : magnetic flux density
• ${\displaystyle g_{\ell }=1}$or  : Landé factor for the orbital angular momentum or spin ${\displaystyle g_{s}=2}$
• ${\displaystyle m_{J},\ m_{\ell },\ m_{s}}$ : magnetic quantum number for total angular momentum or orbital angular momentum or spin.

Analogous to this, a Paschen-Back effect also occurs in the case of hyperfine structure splitting , which breaks the coupling between the shell angular momentum and the nuclear angular momentum to the total angular momentum of the entire atom. ${\displaystyle J}$ ${\displaystyle I}$ ${\displaystyle F}$

literature

• Hermann hook , Hans Christoph Wolf : atomic and quantum physics . Springer-Verlag , 8th edition, 2003, ISBN 3-540-02621-5 .