Discrete-state continuum scattering amplitude
= Discrete-state continuum scattering amplitude
{title2=$f_k=-A/(E-\widetilde\epsilon+iAk)$}
For a real point coupling $g$ between a three-dimensional continuum and one discrete state, $A=mg^2/(2\pi\hbar^2)$. After the short-distance level shift is absorbed, the isotropic amplitude has the displayed form. The imaginary part is fixed by the outgoing <boundary condition>, and $\operatorname{Im}(1/f_k)=-k$ supplies elastic <unitarity>.