Energy dependent potentials determined by inversion: The p+ alpha potential up to 65 MeV.

Abstract

The iterative perturbative inversion method is extended to determine explicitly energy and parity dependent potentials from S matrices specified at a series of discrete energies. The energy dependence is inserted only in the potential magnitude, although enhanced ``energy bite'' techniques allow this approximation to be tested. With a linear energy dependence in both real and imaginary components, S-matrix data for p+\ensuremath{\alpha} scattering is fitted with a single potential for a wide range of energies above the inelastic threshold. The imaginary potential is shown to be parity dependent. The real potential is consistent, in both the potential shape and the parity and energy dependence, with potentials established for subthreshold energies. The method is also applied to resonating group model (RGM) phase shifts for n${+}^{16}$O and p+\ensuremath{\alpha} scattering to give energy and parity dependent potentials in both cases. For p+\ensuremath{\alpha}, a close correspondence is obtained between the RGM and the empirical potentials in both the energy and parity dependence up to about 65 MeV. For n${+}^{16}$O, potentials are determined for positive and negative energies. \textcopyright{} 1996 The American Physical Society.