Partial-wave expansion of a scattering amplitude

For a central potential and the convention $S_l=1+2i{f}_l=e^{2i{\delta }_l}$, the scattering amplitude isThe identity $|S_l|=1$ is equivalent to $\mathrm{Im}{f}_l=|f_l{|}^2$.

For elastic scattering by a central potential,At low momentum, the S-wave normally supplies the leading term.