DETERMINATION OF SCATTERING-AMPLITUDES FROM DIFFERENTIAL CROSS-SECTION DATA BY USING UNITARITY CONDITIONS

Scattering amplitudes are extracted from (elastic scattering) differen tial cross sections under the constraint that the scattering function is unitary. A modification to the Newton iteration method has been use d to solve the nonlinear equation that specifies the phase of the scat tering amplitude in terms of the complete (0 degrees to 180 degrees) c ross section. The approach is tested by using it to specify the scatte ring amplitude from simulated data and comparing the result with the a mplitude found by using an exact iterated fixed point method of soluti on. The (modified) Newton method was then used to analyze the cross se ctions from neutron-alpha-particle scattering at low nuclear energies (< 24 MeV) and from 1000 eV electron-water molecule scattering.