Reconstruction formula for a 3-d phaseless inverse scattering problem for the Schrodinger equation

The inverse scattering problem of the reconstruction of the unknown potential with compact support in the 3-d Schr\"odinger equation is considered. Only the modulus of the scattering complex valued wave field is known, whereas the phase is unknown. It is shown that the unknown potential can be reconstructed via the inverse Radon transform. Therefore, a long standing problem posed in 1977 by K. Chadan and P.C. Sabatier in their book "Inverse Problems in Quantum Scattering Theory" is solved.