NUCLEON-ALPHA-PARTICLE INTERACTIONS FROM INVERSION OF SCATTERING PHASE-SHIFTS

Scattering amplitudes have been extracted from (elastic scattering) ne utron-alpha (n-alpha) differential cross sections below threshold usin g the constraint that the scattering function is unitary. Real phase s hifts have been obtained therefrom. A modification to the Newton itera tion method has been used to solve the nonlinear equation that specifi es the phase of the scattering amplitude in terms of the complete (0 t o 180 degrees) cross section since the condition for a unique and conv ergent solution by an exact iterated fixed point method, the ''Martin' ' condition, is not satisfied. The results compare well with those fou nd using standard optical model search procedures. Those optical model phase shifts, from both n-alpha and p-alpha (proton-alpha) calculatio ns 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 invers ion potentials (both central and spin orbit) for nucleon energies in t he range 1 to 24 MeV. The inversion interactions differ noticeably fro m the Woods-Saxon forms used to give the input phase shifts. Not only do those inversion potentials when used in Schrodinger equations repro duce the starting phase shifts but they are also very smooth, decay ra pidly, and are as feasible as the optical model potentials of others t o be the local form for interactions deduced by folding realistic two- nucleon g matrices with the density matrix elements of the ct particle .