If $$\sigma $$ is the total cross-section and f(θ), θ being the angle of scattering, is the scattering amplitude for a quantum mechanical elastic scattering by a spherically symmetric potential, then which of the following is true? Note that k is the magnitude of the wave vector along the $${{\bf{\hat z}}}$$ direction.

A. $$\sigma = {\left| {f\left( \theta \right)} \right|^2}$$

B. $$\sigma = \frac{{4\pi }}{k}{\left| {f\left( {\theta = 0} \right)} \right|^2}$$

C. $$\sigma = \frac{{4\pi }}{k} \times {\text{Imaginary part of }}{\left| {f\left( {\theta = 0} \right)} \right|^2}$$

D. $$\sigma = \frac{{4\pi }}{k}{\left| {f\left( \theta \right)} \right|^2}$$

Answer: Option C