Inatomic physics,Doppler broadening is broadening ofspectral lines due to theDoppler effect caused by a distribution of velocities ofatoms ormolecules. Different velocities of theemitting (orabsorbing) particles result in different Doppler shifts, the cumulative effect of which is the emission (absorption) line broadening.^[1]This resulting line profile is known as aDoppler profile.

A particular case is thethermal Doppler broadening due to thethermal motion of the particles. Then, the broadening depends only on thefrequency of the spectral line, themass of the emitting particles, and theirtemperature, and therefore can be used for inferring the temperature of an emitting (or absorbing) body being spectroscopically investigated.

When a particle moves (e.g., due to the thermal motion) towards the observer, the emitted radiation is shifted to a higher frequency. Likewise, when the emitter moves away, the frequency is lowered. In the non-relativistic limit, theDoppler shift is

${\displaystyle f=f_0\left(1+\frac{v}{c}\right),}$

where${\displaystyle f}$ is the observed frequency,${\displaystyle f_0}$ is the frequency in the rest frame,${\displaystyle v}$ is the velocity of the emitter towards the observer, and${\displaystyle c}$ is thespeed of light.

Since there is a distribution of speeds both toward and away from the observer in any volume element of the radiating body, the net effect will be to broaden the observed line. If${\displaystyle P_v(v)dv}$ is the fraction of particles with velocity component${\displaystyle v}$ to${\displaystyle v+dv}$ along a line of sight, then the corresponding distribution of the frequencies is

${\displaystyle P_f(f)df=P_v(v_f)\frac{dv}{df}df,}$

where${\displaystyle v_f=c\left(\frac{f}{f_0}-1\right)}$ is the velocity towards the observer corresponding to the shift of the rest frequency${\displaystyle f_0}$ to${\displaystyle f}$. Therefore,

We can also express the broadening in terms of thewavelength${\displaystyle \lambda }$. Since${\displaystyle v/c\ll 1}$,${\displaystyle \left|f/f_0-1\right|\ll 1}$, and so${\displaystyle \frac{\lambda -{\lambda }_0}{{\lambda }_0}\approx -\frac{f-f_0}{f_0}}$. Therefore,

In the case of the thermal Doppler broadening, the velocity distribution is given by theMaxwell distribution

${\displaystyle P_v(v)dv=\sqrt{\frac{m}{2\pi kT}}\exp \left(-\frac{m{v}^2}{2kT}\right)dv,}$

where${\displaystyle m}$ is the mass of the emitting particle,${\displaystyle T}$ is the temperature, and${\displaystyle k}$ is theBoltzmann constant.

Then

${\displaystyle P_f(f)df=\frac{c}{f_0}\sqrt{\frac{m}{2\pi kT}}\exp \left(-\frac{m{\left[c\left(\frac{f}{f_0}-1\right)\right]}^2}{2kT}\right)df.}$

We can simplify this expression as

${\displaystyle P_f(f)df=\sqrt{\frac{m{c}^2}{2\pi kT{f}_0^2}}\exp \left(-\frac{m{c}^2{\left(f-f_0\right)}^2}{2kT{f}_0^2}\right)df,}$

which we immediately recognize as aGaussian profile with thestandard deviation

${\displaystyle {\sigma }_f=\sqrt{\frac{kT}{m{c}^2}}{f}_0}$

andfull width at half maximum (FWHM)

Inastronomy andplasma physics, the thermal Doppler broadening is one of the explanations for the broadening of spectral lines, and as such gives an indication for the temperature of observed material. Other causes of velocity distributions may exist, though, for example, due toturbulent motion. For a fully developed turbulence, the resulting line profile is generally very difficult to distinguish from the thermal one.^[2]Another cause could be a large range ofmacroscopic velocities resulting, e.g., from the receding and approaching portions of a rapidly spinningaccretion disk. Finally, there are many other factors that can also broaden the lines. For example, a sufficiently high particlenumber density may lead to significantStark broadening.

Doppler broadening can also be used to determine the velocity distribution of a gas given its absorption spectrum. In particular, this has been used to determine the velocity distribution of interstellar gas clouds.^[3]

This articleneeds attention from an expert in physics. The specific problem is:This appears to conflate two different meanings of "absorption," describing a causal relationship that doesn't make sense.. See thetalk page for details.WikiProject Physics may be able to help recruit an expert.(August 2025)

Doppler broadening, the physical phenomenon driving thefuel temperature coefficient of reactivity also been used as a design consideration in high-temperaturenuclear reactors^{[citation needed]}. In principle, as the reactor fuel heats up, the neutron absorption spectrum will broaden due to the relative thermal motion of the fuel nuclei with respect to the neutrons. Given the shape of the neutron absorption spectrum, this has the result of reducingneutron absorption cross section, reducing the likelihood of absorption and fission. The end result is that reactors designed to take advantage of Doppler broadening will decrease their reactivity as temperature increases, creating apassive safety measure. This tends to be more relevant togas-cooled reactors, as other mechanisms are dominant inwater cooled reactors.

Saturated absorption spectroscopy, also known as Doppler-free spectroscopy, can be used to find the true frequency of an atomic transition without cooling a sample down to temperatures at which the Doppler broadening is negligible.

• Mössbauer effect
• Dicke effect

• Doppler effects
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