Lorentzian line shape ($L(\nu )={\gamma }^2/[(\nu -{\nu }_0{)}^2+{\gamma }^2]$)

A spectral line profile with the shape of a Cauchy distribution. In the displayed peak-normalized convention, $\nu$ is frequency, ${\nu }_0$ is the line centre, and $\gamma >0$ is the half width at half maximum: $L({\nu }_0\pm \gamma )=1/2$, so the full width is $2\gamma$. The normalization used for a probability density function differs from this unit-peak convention.