Linewidth (redirected from Spectral linewidth)

Linewidth

A measure of the width of the band of frequencies of radiation emitted or absorbed in an atomic or molecular transition. One of the dominant sources of electromagnetic radiation of all frequencies is transitions between two energy levels of an atomic or molecular system. The frequency of the radiation is related to the difference in the energy of the two levels by the Bohr relation (1),

(1) 

where ν₀ is the frequency of the radiation, h is Planck's constant, and E₁ and E₂ are the energies of the levels. This radiation is not monochromatic, but consists of a band of frequencies centered about ν₀ whose intensity I(ν) can be characterized by the linewidth. The linewidth is the full width at half height of the distribution function I(ν). The simplest case is for a transition from an excited state to the ground state for an atom or molecule at rest. For this case, the normalized distribution function is the lorentzian line profile given by Eq. (2).

(2) 

Here Δν is the full width at half maximum (FWHM). The FWHM is related to the lifetime τ of the excited level through Eq. (3).

(3) 

This is a manifestation of the quantum-mechanical uncertainty principle, and the linewidth Δν is referred to as the natural linewidth. See Energy level (quantum mechanics), Quantum mechanics, Uncertainty principle

Another major source of line broadening for atomic and molecular transitions is the Doppler shift due to thermal motion. For most situations the Doppler width is greater than the natural linewidth. See Doppler effect

A third major source of line broadening is collisions of the radiating molecule with other molecules. This broadens the line, shifts the center of the line, and shortens the lifetime of the radiating state.

For radiating atoms in a liquid or solid the width is usually dominated by the strong interaction of the radiator with the surrounding molecules. The net result is a broad line profile with a complex structure. See Band theory of solids