Resonance Broadening of Spectral Lines

A general treatment of the collision of an excited atom with an unexcited one shows that the three principal methods of calculating collision broadening are all justified as approximations to the complete treatment. When the fine structure of the lines is taken into account it follows that all members of a Russell-Saunders multiplet are broadened to the same extent. The calculated broadening turns out to be $\Delta \nu =\frac{{\left(\frac{3}{2}\right)}^{\frac{1}{2}}NS(J, J^{\prime })}{\hslash \mathrm{}(2J+1)(2\mathrm{}{J}^{\prime }+1)}$, which is less by a factor of five than that observed in the work of Hughes and Lloyd.