Scattering length from a partial-wave S-matrix
= Scattering length from a partial-wave S-matrix
= Scattering length
{synonym}
The $s$-wave scattering length is
$$
a_s=-\lim_{k\to0}\frac{\tan\delta_0(k)}k,
$$
and the low-energy total cross-section is $4\pi a_s^2$.