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Physical Lineshape

Atomic collisions can reduce the life time of an excited state and thus enlarge this Lorentzian shape. This is called collisional or pressure broadening.

Due to the thermal movement of atomic light emitters the observed line width is altered from its natural (Lorentzian) shape. The light emitted by an atom moving towards the detectors will be seen blue shifted, light emitted by atoms moving away from the detector will appear red shifted. The shift is proportional to the speed of the atom.  The velocity distribution of the atoms is random and follows the normal Gauss distribution. The mean speed increases with the temperature of the atoms and for a given temperature decreases with the atomic mass. The Doppler shift in association with the random movement of the emitters leads therefore to a Gaussian spectral.

Gaus Profile
Doppler Profile (a minus is missing in the exponent)

Doppler width

The observed Doppler profile can therefore be described as a Gauss function. The Doppler width, FWHM, is given in the lower equation, with

  • Boltzmann constant: k= 1.380658 10-23 JK-1
  • atomic mass unit: u=1.660542 10-27 kg
  • speed of light: c= 2.99792458 108 ms-1

Choosing two examples, H (mass 1u) and Ar (mass 40 u) at a wavelength of 600 nm, both atoms have emission lines in that spectral region, we can calculate the expected line broadening as function of the gas temperature.

Width of Gauss profiles

Even for the high temperatures corresponding to an ICP plasma the broadening is less then 20 pm for the lightest atom Hydrogen. In order to observe the Gaussian profile the spectral resolution of the spectrometer needs to be significant higher then the width of the spectral feature to be observed. The spectrometer required for measuring the Doppler width must therefore provide a resolution in the low pico-meter range or even better fractions of a pico-meter. This corresponds to a resolving power of several hundred thousands.

Spectrometers operating in the visible region and providing a resolution in the "some-pico-meter range", are available, but can already be considered as high-end instruments, for higher resolving power considerable efforts must be made.

Other broadening mechanisms altering the physical lineshape are fine and hyperfinestructures, electric and magnetic fields. These effects will however, rather split the line into several components of slightly different wavelengths. A superposition of the original lineshape will therefore be observed.

As the natural line shape of one atom is Lorentzian and the population of the moving atoms generate a Gaussian lineshape the resulting physical lineshape is a convolution of the Lorentzian and Gaussian line shape.

The combination of Lorentzian and Gaussian profiles which results from random movement of atoms is called a Voigt profile.

Authors: Richard Payling and Thomas Nelis

First published on the web: 15 November 1999.