Analyticity and unitarity as constraints to obtain scattering phase shifts and an application to e-He scattering

The requirements that the scattering functions for quantal scattering at energies below the first inelastic threshold be unitary and analytic have been used to establish a process that gives the complex scattering amplitudes from differential cross sections. From those amplitudes, scattering phase shifts have been deduced by Legendre integration. The effects of the natural ambiguity of the phase of the scattering amplitude, under conditions for which uniqueness and (numerical) stability of solutions are not assured, also have been studied to show that the process we have developed to specify the scattering phase shifts can give stable nonspurious results. The scattering of electrons from He atoms for incident energies ranging from 1.5 to 19 eV are considered as an example of this procedure. Phase-shift analyses of those data have been made with a variety of other techniques to allow a comparative study of our results and of sets with which are associated fits to cross sections that are statistically significant.