An incident plane wave with wavenumber k is scattered by a spherically symmetric soft potential. The scattering occurs only in S- and P- waves. The approximate scattering amplitude at angles \(\theta=\frac{\pi}{3} \) and \(\theta=\frac{\pi}{2} \) are

\(f\left(\theta=\frac{\pi}{3}\right) \simeq \frac{1}{2 k}\left(\frac{5}{2}+3 i\right) \text { and } f\left(\theta=\frac{\pi}{2}\right) \simeq \frac{1}{2 k}\left(1+\frac{3 i}{2}\right) \text {. } \)

Then the total scattering cross-section is closest to