Is the Born approximation good for solving the inverse problem when the potential is small? (Q917823)

The author makes a few remarks concerning the Born approximation in the inverse scattering problem associated to the operator \(-\Delta +q(x)\) in \({\mathbb{R}}^ 3\). He notices that the scattering amplitude A equals its Born approximation \(A_ B\) only if \(q\equiv 0\), and that all the potentials obtained from the scattering amplitude by a suitable inverse Fourier formula, differ from q by a small quantity when \(A-A_ B\) is small.