[en] On classical scattering of high energy particles or waves by a nonspherical scatterer into small angles, the mapping of the impact parameter plane onto the transferred momenta plane is conformal, providing the scatterer is harmonic (the potential energy satisfies the Laplace equation). A consequence is that complex variables can be employed in both planes and the calculations are thus simplified considerably. The rainbow lines (singularities of the differential cross section) in this case degenerate into focal points. A result is that even after averaging over the directions of the scatterer, singularities of the step type are retained in the cross section (halo effect) and can be observed on scattering of protons by molecules or by the crystal surface. Rigorous inequalities for the effective scattering cross section of a system of coulomb centers follow, in the case of small or relatively large transferred momenta, from the extremal properties of the conformal mapping onto a circle. The approximation is also applicable to the problem of scattering of a charged particle by a magnetic scatterer and hence may be used not only in atomic and nuclear problems but also in electron optics