DopplerBreitung

DopplerBreitung, often referred to in English as Doppler broadening, is the widening of spectral lines caused by the distribution of radial velocities of emitting or absorbing particles along the observer’s line of sight due to thermal motion. Each particle shifts the frequency of emitted or absorbed radiation by an amount proportional to its velocity, and the collective effect of many particles produces a broadened line rather than a sharp transition.

In non-relativistic regimes, the DopplerBreitung is well described by a Gaussian line profile. The standard deviation of the frequency distribution is σ_ν = (ν0/c) sqrt(k_B T / m), where ν0 is the line center frequency, c is the speed of light, k_B is Boltzmann’s constant, T is the temperature, and m is the particle mass. The full width at half maximum (FWHM) of the Doppler-broadened line is Δν_D = 2 sqrt(2 ln 2) σ_ν = (ν0/c) sqrt(8 ln 2 · k_B T / m). Equivalent expressions can be written for angular frequency or wavelength.

Thus DopplerBreitung increases with temperature and decreases with particle mass; lighter species and higher temperatures produce broader lines. In practice, observed spectra may exhibit a Voigt profile, a convolution of Doppler broadening (Gaussian) with natural (Lorentzian) broadening due to finite excited-state lifetimes and collisional (pressure) broadening. Instrumental resolution can also contribute to the observed width.

Applications of DopplerBreitung are widespread in spectroscopy, astrophysics, and plasma physics. It is used to infer temperatures, kinetic motions, and turbulent velocities in stars, interstellar and intergalactic gas, and laboratory plasmas. Techniques that mitigate or exploit Doppler broadening, such as Doppler-free spectroscopy, are important in achieving high-precision measurements.