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 analyti c have been used to establish a process that gives the complex scatter ing amplitudes from differential cross sections. From those amplitudes , scattering phase shifts have been deduced by Legendre integration. T he effects of the natural ambiguity of the phase of the scattering amp litude, under conditions for which uniqueness and (numerical) stabilit y of solutions are not assured, also have been studied to show that th e 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 a s an example of this procedure. Phase-shift analyses of those data hav e 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 cro ss sections that are statistically significant.