Evolving model-free scattering matrix via evolutionary algorithm: $^{16}$O-$^{16}$O elastic scattering at 350 MeV

We present a new procedure which enables to extract a scattering matrix $S(l)$ as a complex function of angular momentum directly from the scattering data, without any a priori model assumptions implied. The key ingredient of the procedure is the evolutionary algorithm with diffused mutation which evolves the population of the scattering matrices, via their smooth deformations, from the primary arbitrary analytical $S(l)$ shapes to the final ones giving high quality fits to the data. Due to the automatic monitoring of the scattering matrix derivatives, the final $S(l)$ shapes are monotonic and do not have any distortions. For the $^{16}$O-$^{16}$O elastic scattering data at 350 MeV, we show the independence of the final results of the primary $S(l)$ shapes. Contrary to the other approaches, our procedure provides an excellent fit by the $S(l)$ shapes which support the ``rainbow'' interpretation of the data under analysis.