There are two sources of spectral broadening that we considered. In order for the spectrum of the atoms in the lamp to be useful for laser locking we must be able to observe the individual spectral lines of each Yb isotope. Doppler broadening can be compensated for by using a technique called saturation spectroscopy. Pressure broadening cannot be compensated for, thus if the atoms have a large pressure broadened profile we will not be able to resolve individual isotopes.
Doppler broadening is due to the relative motion of the Yb atoms with respect to the observer. If we assume the Yb atoms have a thermal speed distribution the spectral width will be given by
Assuming the temperature of the Yb atoms is roughly 500K, the Doppler line width will be approximately 1GHz.
Pressure broadening is due to collisions between Yb atoms and the Neon buffer gas inside the tube. I derived the following equation for pressure broadening using the mean free path of the Yb atoms
where sigma is the collisional cross section of the Yb and Ne atoms, and P is the pressure inside the tube (roughly 5 Torr). I could not find an exact number for the collisional cross section, but I assumed that it was somewhere between 2 and 10 angstroms. m will be the mass of the Ne atoms. Since Yb is so much heavier than Ne the model assumes that the Yb is at rest while the Ne moves.
Depending on the pressure inside the lamp and the size of the collisional cross section, we can expect the pressure broadened line width to be between 20MHz – 100MHz.