Scattering length of a hard-core spherical square-well potential

For outer radius $b=2a$ and zero-energy well wavenumber ${\kappa }_0=\sqrt{2m{V}_0}/\hslash$, matching the S-wave scattering logarithmic derivative givesIt diverges when ${\kappa }_{0}a=(n+\frac{1}{2})\pi$, where the well has a zero-energy scattering resonance.