Line width

Emission spectrum of a high pressure mercury vapor lamp
The numbers indicate the wavelength (in nm) of the spectral lines of the mercury . Other bands do not have numbers - these are the emissions of the phosphors that are stimulated by the UV radiation from the mercury plasma .

Spectrum of a low pressure mercury vapor lamp.
Upper image with a 256-pixel line sensor , lower image with a camera.

The line width is the width of the frequency or wavelength interval or which is covered by a spectral line in a spectrum. The phenomenon was discovered in optical spectra , but also occurs in all spectra of any other radiation type. ${\displaystyle \Delta \nu }$ ${\displaystyle \Delta \lambda }$

In quantum physics (e.g. in the case of unstable elementary particles ) the line width is also often expressed in terms of the energy uncertainty or the decay width : ${\displaystyle \Gamma }$

${\displaystyle \Gamma =h\cdot \Delta \nu \ (\equiv \hbar \cdot \Delta \omega )}$

With

• the Planck's quantum of action ${\displaystyle h\quad (\hbar =h/2\pi )}$
• the angular frequency . ${\displaystyle \omega =2\pi \cdot \nu }$

Usually the full width at half maximum is given , i.e. H. the interval over the profile of the line under consideration in which the spectral intensity is greater than half the maximum value.

If the observed radiation comes from many independent sources, one differentiates:

• the homogeneous line width that every single issuer already has,
• on the inhomogeneous line width , which could be reduced by a more precise selection of the emitters.

In addition to the fundamental energy uncertainty of all unstable systems, the causes of the line width include external disturbances such as collisions between the emitters and Doppler shifts due to their disordered movement.

Natural line width

According to quantum mechanics , if a physical system has a sharply defined energy, it cannot change over time. Conversely, systems that spontaneously disintegrate or generate radiation have a fundamental energy uncertainty and their radiation has a corresponding natural line width . The shape corresponds to a Cauchy distribution , which is also known in physics as the resonance curve or Lorentz curve . This is very general, equally z. B. for elementary particles, radioactive or excited nuclei , excited atoms , molecules .

The above-mentioned energy uncertainty is

${\displaystyle \Gamma =\hbar \lambda }$

with the decay constant (transition probability per unit of time). ${\displaystyle \lambda }$

In the shape

${\displaystyle \Leftrightarrow \Gamma \tau =\hbar }$

with the lifetime , d. H. the future mean length of stay of the system in the initial state, ${\displaystyle \tau =1/\lambda }$

the relationship is similar to Heisenberg's uncertainty relation and is therefore also referred to as the energy-time uncertainty relation .

In elementary particle physics , this relationship is used for the experimental determination of extremely short lifetimes. For example, in the case of the Z ⁰ boson , the decay width results in the lifetime - the shortest that has been found so far. ${\displaystyle \Gamma \!\!_{Z^{0}}=2{,}5\,\mathrm {GeV} }$ ${\displaystyle \tau _{Z^{0}}={\tfrac {\hbar }{\Gamma \!\!_{Z^{0}}}}=2{,}6\cdot 10^{-25}\,\mathrm {s} }$

In optics , the natural line width is directly related to the coherence length .

The natural line width can be modeled using a Lorentz oscillator .

Line broadening

→ Main article : Line broadening

Line broadening occurs due to certain effects such as Doppler broadening or pressure broadening.

See also

• Laser line width

Individual evidence

1. ↑ Demtröder, Experimentalphysik 3 Atome, Molecule and Solid Body, Volume 3, p. 246 ff, limited preview in the Google book search