 Bethe-Peierls boundary condition

This zero-range boundary condition replaces a short-range interaction by its S-wave scattering length. If $\psi =A/r+B+O(r)$, it requires $B=-A/a$. An outgoing spherical wave also has a constant $ik$ term; retaining that term gives the unitary scattering-length amplitude $f_0=-a/(1+ika)$. The model neglects effective-range corrections and is applied outside the microscopic range, not literally inside a finite potential.