Resonant s-wave unitarity check
= Resonant s-wave unitarity check
{title2=$\operatorname{Im}f=k|f|^2$}
For an isotropic elastic amplitude normalized by an incident unit <plane wave> and outgoing $fe^{ikr}/r$, total cross section is $4\pi|f|^2$. The <optical theorem> gives the displayed identity. At a <resonance> where the real part of $1/f$ vanishes, $f=i/k$ and the cross section is $4\pi/k^2$.