DopplerBreite

DopplerBreite, or Doppler broadening, is the broadening of spectral lines caused by the distribution of radial velocities of emitting or absorbing particles along the line of sight. In a gas at thermal equilibrium, particle velocities follow the Maxwell–Boltzmann distribution, which spreads the frequencies of photons produced by different particles.

The width of a Doppler-broadened line depends on temperature and particle mass. For a line with rest wavelength λ0 (or rest frequency ν0) and a gas temperature T, the one-dimensional velocity dispersion is σv = sqrt(kB T / m), where kB is the Boltzmann constant and m is the mass of the emitting particle. The resulting line profile is often modeled as Gaussian. The Doppler-broadened full width at half maximum in velocity units is ΔvFWHM = 2 sqrt(2 ln 2) σv ≈ 2.3548 sqrt(kB T / m). In wavelength units, the corresponding FWHM is ΔλFWHM = (λ0 / c) ΔvFWHM, with c the speed of light. A commonly used parameter in spectroscopy is the Doppler parameter b = sqrt(2kB T / m), giving ΔvFWHM = 2 sqrt(ln 2) b.

DopplerBreite is most evident in hot, low-density gases and in astronomical spectra. It can be altered by non-thermal motions such as turbulence, and it is often convolved with instrumental broadening. In practice, observed line widths combine Doppler broadening with other broadening mechanisms, requiring careful analysis to disentangle temperature, turbulence, and instrumental effects.