= Bethe-Peierls boundary condition
{c}
{title2=$\lim_{r\to0}\partial_r(r\psi)/(r\psi)=-1/a$}
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.
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