Date of Original Version
Using the K-matrix formalism, we give a simplified reformulation of the S-wave rank-one inverse scattering problem. The resulting Cauchy integral equation, obtained differently by Gourdin and Martin in their first paper, is tailored to rational representations of F(k)=k cot(δ0). Use of such F(k) permits a simple but general solution without integration, giving analytic form factors having a pole structure like the S matrix that are reducible to rational expressions using Padé approximants. Finally, we show a bound state pole condition is necessary, and makes the form factor unique.
K. Hartt. (1983). "Rank-one inverse scattering problem: Reformulation and analytic solutions." Physical Review C, 29(3), 695. Available at: http://dx.doi.org/10.1103/PhysRevC.29.695