Scattering Theory of Absorption-Line Profiles and Refractivity

Attenuation processes are examined from the viewpoint of collision theory, and the optical theorem is used to connect attenuation cross section $\sigma$ and refractive index $n$ with diagonal elements of the $T$ matrix. This approach provides resonance profiles (for "natural" lines shapes) of the form $\sigma \left(\omega \right)=C+\frac{\left(\frac{\Gamma }{2}\right)B+(\omega -{\omega }_0)A}{{(\omega -{\omega }_0)}^2+{\left(\frac{\Gamma }{2}\right)}^2},$ $n\left(\omega \right)-1=\frac{\mathrm{Nc}}{2\omega }\left[\frac{\left(\frac{\Gamma }{2}\right)A-(\omega -{\omega }_0)B}{{(\omega -{\omega }_0)}^2+{\left(\frac{\Gamma }{2}\right)}^2}-D\right],$ where the profile parameters $A$, $B$, $C$, $D$, $\Gamma$, ${\omega }_0$ are given in terms of atomic matrix elements.