Scattering length of a hard-core spherical square-well potential
= Scattering length of a hard-core spherical square-well potential
For outer radius $b=2a$ and zero-energy well wavenumber $\kappa_0=\sqrt{2mV_0}/\hbar$, matching the <S-wave scattering> logarithmic derivative gives
$$
a_s=2a-\frac{\tan(\kappa_0a)}{\kappa_0}.
$$
It diverges when $\kappa_0a=(n+\tfrac12)\pi$, where the well has a <zero-energy scattering resonance>.