At low energy, \( k \rightarrow 0 \), S-waves are most important. In this region we can define the scattering length \( a \) and the effective range \( r \). The $S-$wave scattering amplitude is given by \[ f_l(\theta) = \frac{1}{k}\frac{1}{\cot \delta_l(k) - i}. \] Taking the limit \( k \rightarrow 0 \), gives us the expansion \[ k \cot \delta_0 = -\frac{1}{a} + \frac{1}{2}r_0 k^2 + \ldots \] Thus the low energy cross section is given by \[ \sigma = 4\pi a^2. \] If the system contains a bound state, the scattering length will become positive (neutron-proton in \( ^3S_1 \)). For the \( ^1S_0 \) wave, the scattering length is negative and large. This indicates that the wave function of the system is at the verge of turning over to get a node, but cannot create a bound state in this wave.