Nucleon-alpha-particle interactions from inversion of scattering phase shifts

Scattering amplitudes have been extracted from (elastic scattering) neutron-alpha (n-alpha) differential cross sections below threshold using the constraint that the scattering function is unitary. Real phase shifts have been obtained therefrom. 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 to 180 degrees) cross section since the condition for a unique and convergent solution by an exact iterated fixed point method, the ''Martin'' condition, is not satisfied. The results compare well with those found using standard optical model search procedures. Those optical model phase shifts, from both n-alpha and p-alpha (proton-alpha) calculations in which spin-orbit effects were included, were used in the second phase of this study, namely to determine the scattering potentials by inversion of that phase shift data. A modified Newton-Sabatier scheme to solve the inverse scattering problem has been used to obtain inversion potentials (both central and spin orbit) for nucleon energies in the range 1 to 24 MeV. The inversion interactions differ noticeably from the Woods-Saxon forms used to give the input phase shifts. Not only do those inversion potentials when used in Schrodinger equations reproduce the starting phase shifts but they are also very smooth, decay rapidly, and are as feasible as the optical model potentials of others to be the local form for interactions deduced by folding realistic two-nucleon g matrices with the density matrix elements of the ct particle.