Determination of scattering amplitudes from differential cross-section data by using unitarity conditions

Abstract

Scattering amplitudes are extracted from (elastic scattering) differential cross sections under the constraint that the scattering function is unitary. A modification to the Newton iteration method has been used to solve the nonlinear equation that specifies the phase of the scattering amplitude in terms of the complete (0\ifmmode^\circ\else\textdegree\fi{} to 180\ifmmode^\circ\else\textdegree\fi{}) cross section. The approach is tested by using it to specify the scattering amplitude from simulated data and comparing the result with the amplitude found by using an exact iterated fixed point method of solution. The (modified) Newton method was then used to analyze the cross sections from neutron--\ensuremath{\alpha}-particle scattering at low nuclear energies (24 MeV) and from 1000-eV electron-water molecule scattering.