Doppler broadening

The Doppler spread is caused by the Doppler effect caused broadening of spectral lines . In the optical spectral range it is observable or disturbing in the spectroscopy of small molecules (including atoms ) at high temperature and low gas pressure , and in the range of gamma radiation for atomic nuclei .

In nuclear reactions comparable Doppler broadening occurs resonances on.

root cause

In relation to a certain spectral line, particles are oscillators that can oscillate with a characteristic frequency . An observer sees this frequency when he is at rest opposite the particle. ${\ displaystyle f_ {0}}$

Due to the thermal movement, several particles do not have a common rest system , but move relative to each other and to the observer. Due to the Doppler effect, he sees different oscillation frequencies. The Maxwell-Boltzmann distribution for the speed of the particles is converted into a distribution for the frequencies (or wavelengths ). In the center of gravity system of the particles, the mean value of the distribution is unchanged , while the width ( standard deviation ) of the frequency distribution depends on the temperature and the particle mass : ${\ displaystyle f_ {0}}$ ${\ displaystyle \ sigma _ {f}}$ ${\ displaystyle T}$ ${\ displaystyle m}$

{\ displaystyle \ sigma _ {f} = {\ frac {f_ {0}} {c}} {\ sqrt {\ frac {k _ {\ mathrm {B}} \, T} {m}}}}

With

the speed of light ${\ displaystyle c}$
the Boltzmann constant . ${\ displaystyle k _ {\ mathrm {B}}}$

The line broadening is usually described by the half-width of the distribution. This is calculated for the Gaussian distribution by: ${\ displaystyle \ delta f}$

{\ displaystyle \ delta f = 2 {\ sqrt {2 \ ln {2}}} \ cdot \ sigma _ {f}}

Hence the line broadening is:

{\ displaystyle \ Rightarrow \ delta f = {\ frac {f_ {0}} {c}} {\ sqrt {\ frac {8 \, k _ {\ mathrm {B}} \, T \ ln {2}} { m}}}}

If one looks at the wavelength scale instead of the frequency, the following applies:

{\ displaystyle \ delta \ lambda = {\ frac {\ lambda _ {0}} {c}} {\ sqrt {\ frac {8 \, k _ {\ mathrm {B}} \, T \ ln {2}} {m}}}}

Examples

Relative line width as a function of the temperature

The diagram opposite shows the relative line width (i.e. the ratio of the standard deviation of the Doppler profile to the central wavelength) as a function of temperature: ${\ displaystyle {\ frac {\ sigma _ {\ lambda}} {\ lambda _ {0}}} = {\ frac {1} {c}} {\ sqrt {\ frac {k _ {\ mathrm {B}} \, T} {m}}}}$

at room temperature it is only about 10 ⁻⁶ , so the Doppler width in the optical is only about 0.001 nm.
In the atmospheres of hot stars, a relative latitude of up to about 10 ^{−4 is} reached, which corresponds to an absolute latitude of about 0.1 nm in the visible.

Oxygen is sixteen times as heavy as hydrogen, so its relative Doppler latitude at the same temperature is only a quarter of that of hydrogen.

In fact, spectral lines are often much wider because collisions with other particles during an absorption or emission process also cause the pressure to broaden.

Effects

Since the Doppler broadening at atomic transitions is usually several orders of magnitude larger than the natural line width , it makes high-resolution spectroscopy more difficult . It prevents, for example, the dissolution of the hyperfine structure . However, there are modern spectroscopic methods such as Doppler- free saturation spectroscopy , which switch off Doppler broadening by clever arrangements.

Nuclear and Neutron Physics

In nuclear reactions, a higher temperature of the target material causes a broadening of the resonances in the excitation function , because when colliding with free particles, the impact energy also depends on the thermal movement of the atoms or molecules of a material. As the temperature rises, it becomes more likely that the absorption of a projectile of a given energy will lead to one of the possible energy levels of the compound core in question .

This widening is particularly important for nuclear reactors . As the temperature rises, it leads to a loss of neutrons through increased trapping in uranium-238 atomic nuclei. The effect, often simply called the Doppler effect in technical terms, is described by the Doppler coefficient of reactivity . This indicates the reactivity contribution per degree of temperature increase and is always negative, i.e. stabilizing the reactor performance.

Individual evidence

↑ G. Lindström, W. Langkau, G. Scobel: Physics compact 3 . 2nd edition, Springer 2002, ISBN 978-3-540-43139-8 , page 76.
↑ B. Welz, M. Sperlimg: Atomic absorption spectroscopy . 4th edition, Wiley 1999, ISBN 3-527-28305-6 , pages 1-55, 1-59.
↑ ^a ^b A. Ziegler, H.-J. Allelein (Hrsg.): Reaktortechnik : Physical-technical basics . 2nd edition, Springer-Vieweg, Berlin, Heidelberg 2013, ISBN 978-3-642-33845-8 , page 87.
^ G. Kessler: Sustainable and Safe Nuclear Fission Energy . Springer, 2012, ISBN 978-3-642-11989-7 , page 131 ff.

[1] G. Lindström, W. Langkau, G. Scobel: Physics compact 3 . 2nd edition, Springer 2002, ISBN 978-3-540-43139-8 , page 76.

[2] B. Welz, M. Sperlimg: Atomic absorption spectroscopy . 4th edition, Wiley 1999, ISBN 3-527-28305-6 , pages 1-55, 1-59.

[ZiAl-3] A. Ziegler, H.-J. Allelein (Hrsg.): Reaktortechnik : Physical-technical basics . 2nd edition, Springer-Vieweg, Berlin, Heidelberg 2013, ISBN 978-3-642-33845-8 , page 87.

[4] G. Kessler: Sustainable and Safe Nuclear Fission Energy . Springer, 2012, ISBN 978-3-642-11989-7 , page 131 ff.