Solution
= Solution
The <scattering amplitude> is defined by
$$
\psi\sim e^{ikz}+f(\theta)\frac{e^{ikr}}r.
$$
For a central potential its <Partial-wave S-matrix>[partial-wave expansion] is
$$
f(\theta)=\frac1k\sum_{l=0}^\infty(2l+1)e^{i\delta_l}\sin\delta_lP_l(\cos\theta).
$$
Using orthogonality of the <Legendre polynomials> in $\sigma_T=\int|f|^2d\Omega$ gives
$$
\boxed{\sigma_T=\frac{4\pi}{k^2}\sum_{l=0}^\infty(2l+1)\sin^2\delta_l}.
$$