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.
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 10^{8} 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.
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 picometer range or even
better fractions of a picometer. This corresponds to a resolving power
of several hundred thousands. Spectrometers operating in the
visible region and providing a resolution in the "somepicometer
range", are available, but can already be considered as highend
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.
