Hanle effect

The Hanle effect is a phenomenon that occurs when magnetic fields interact with matter. The Hanle effect was discovered in 1924 by the physicist Wilhelm Hanle . He provided a semi-classic explanation for the effect. In the 1930s, the physicist Breit presented a quantum mechanical theory, the so-called level crossing , which could explain the Hanle effect quantum mechanically. The level crossing was experimentally observed in 1959 by the physicists Colegrave, Franken, Lewis and Sands and the Hanle effect experienced a small renaissance.

Observation / experiment

Let there be a light mercury lamp in emitting direction and in the polarized direction. This light then hits a glass bulb filled with a residual gas (also mercury ). The residual gas is then excited to fluorescence ( resonance fluorescence ) by the light (primary photons) . An observer who observes the residual gas from the direction cannot initially detect any light. Now a magnetic field is applied perpendicular to the polarization plane of the light (e.g. in the direction) over the residual gas. With a magnetic field around zero, the observer (in the direction) will notice an intensity minimum and with increasing magnetic field strength (positive as well as negative) an increase in intensity. This phenomenon is called the Hanle effect. ${\displaystyle x}$ ${\displaystyle y}$ ${\displaystyle y}$ ${\displaystyle z}$ ${\displaystyle y}$

Of course, this effect doesn't only work with mercury. It is suitable e.g. B. for measuring the lifetime of atomic and molecular states.

Semi-classic explanation

The electrons in the residual gas are excited by the primary beam and can be viewed as small, dampened, oscillating dipoles. If the dipoles are only excited in -direction, no light is emitted due to the radiation characteristics of dipoles in -direction. However, a magnetic field applied perpendicular to the direction of oscillation of the electrons leads to a rotational movement of the direction of oscillation around the magnetic field axis with the Larmor frequency : ${\displaystyle y}$ ${\displaystyle y}$

${\displaystyle \omega _{\mathrm {L} }={\frac {g_{j}\mu _{0}H}{\hslash }}}$

The oscillation of the electrons is dampened with . Then one can calculate the intensity of the emitted light through the distribution of the dipole radiation: ${\displaystyle e^{-{\frac {t}{\tau }}}}$

${\displaystyle I=C\cdot \int _{0}^{\infty }e^{-{\frac {t}{\tau }}}\sin ^{2}\left(\omega _{\mathrm {L} }\cdot t\right)dt}$

When evaluated, this results in a Lorentz curve with the asymptotic value

${\displaystyle I={\frac {C}{2}}\tau }$

The half-width is with the Landé factor and the Bohr magneton . ${\displaystyle {\frac {\hslash }{g_{j}\mu _{0}\tau }}}$ ${\displaystyle g_{j}}$ ${\displaystyle \mu _{0}}$

If the field strength is to reach half the intensity, then it follows for the lifetime of the excited atomic state: ${\displaystyle H_{\frac {1}{2}}}$

${\displaystyle \tau ={\frac {\hslash }{2g_{j}\mu _{0}H_{\frac {1}{2}}}}}$

Quantum mechanical explanation

The Hanle effect is a special case of level crossing , in which the lines of fine structure splitting are crossed by superimposing a magnetic field. Gregory Breit provided the theoretical explanation for this as early as 1933, but experimental observation only followed later.

Breit developed a formula for the rate at which photons of polarization f are re- emitted with polarization g :

${\displaystyle R(f,g)=c\cdot \sum _{m,m',\mu ,\mu '}{\frac {f_{\mu m}f_{m\mu '}g_{\mu 'm'}g_{m'\mu }}{1-2\pi i\tau \nu (\mu ,\mu ')}}}$

(to be completed)

literature

• Wolf-Dieter Hasenclever: Construction of an apparatus for measuring the lifetimes of excited atomic states with the help of the Hanle effect. Freiburg, 1970 (approval thesis, PDF file ; 3.69 MB).
• Wilhelm Hanle: About magnetic influence on the polarization of the resonance fluorescence . In: Journal of Physics . tape 30 , no. 1 , December 1924, p. 93-105 , doi : 10.1007 / BF01331827 .
• G. Breit: Quantum Theory of Dispersion . In: Reviews of Modern Physics . tape 4 , no. 3 , 1932, p. 504-576 , doi : 10.1103 / RevModPhys.4.504 .
• FD Colegrove, PA Franken, RR Lewis, RH Sands: Novel Method of Spectroscopy With Applications to Precision Fine Structure Measurements . In: Physical Review Letters . tape 3 , no. 9 , 1959, pp. 420-422 , doi : 10.1103 / PhysRevLett.3.420 .
• Giovanni Moruzzi, F. Strumia (eds.): The Hanle effect and level-crossing spectroscopy . Plenum Press, New York 1991, ISBN 0-306-43630-2 .

Individual evidence

1. ^ ^{A b} F. D. Colegrove, PA Franken, RR Lewis, RH Sands: Novel Method of Spectroscopy With Applications to Precision Fine Structure Measurements . In: Physical Review Letters . tape 3 , no. 9 , 1959, pp. 420-422 , doi : 10.1103 / PhysRevLett.3.420 .
2. ^ Wilhelm Hanle: About magnetic influence on the polarization of the resonance fluorescence . In: Journal of Physics . tape 30 , no. 1 , December 1924, p. 93-105 , doi : 10.1007 / BF01331827 .