Solution
= Solution
Here $k\cot\delta_0=-K$, so the s-wave amplitude is
$$
f_0(k)=\frac1{-K-ik}.
$$
It has a pole at $k=iK$, corresponding to the bound-state energy
$$
\boxed{E=-\frac{\hbar^2K^2}{2m}}.
$$
Moreover,
$$
\boxed{\sigma_T\simeq4\pi|f_0|^2=\frac{4\pi}{K^2+k^2}}.
$$