Local representation of the exchange nonlocality in n-16O scattering.

Abstract

The nonlocal Schr\odinger equation is solved rigorously in a microscopic folding model, incorporating both direct and knock-on exchange potentials, for n${\mathrm{\ensuremath{-}}}^{16}$O scattering at laboratory energies of 20 and 50 MeV. The model uses the complex and density dependent n-n interaction of N. Yamaguchi et al. uses harmonic oscillator wave functions for the bound nucleons, and calculates the scattering wave function for this nonlocal problem using a Bessel-Sturmian expansion method incorporating correct boundary conditions. All spins are neglected. The local phase-equivalent potential is obtained from the scattering matrix elements at a given energy by using the iterative perturbative inversion method. This representation allows comparison between the microscopic model and a phenomenological potential, showing good agreement for the local real part of the potential at 20 MeV. From the ratio of the wave functions for the nonlocal potential and for the potential calculated by inversion, a Perey damping factor (PDF) is obtained which is of similar form to the well-known Perey-Buck prescription for the PDF for a Gaussian nonlocality of the conventional range of 0.85 fm. The significance of these results for distorted wave Born approximation calculations is discussed.