The microscopic feshbach optical potential for a schematic coupled channel example

Abstract

By means of a method of expanding the solutions of a system of coupled equations into a set of positive-energy sturmian basis functions, a separable approximation to the microscopic (Feshbach) elastic optical potential is obtained. The properties of this nonlocal potential are analysed in terms of the moments of the potential and of the wronskian of two independent solutions of the single-channel nonlocal Schroedinger equation. A numerical application is given for a schematic coupled channel example, representing a 60 MeV neutron incident on a schematic nucleus with up to 10 channels, coupled by phenomenological surface-peaked potentials. The nature of the nonlocality of this schematic potential is very different from the nonlocality due to exchange effects in that the wronskian is strongly angular momentum dependent and can be larger as well as smaller than unity. The range of the nonlocality is found to be larger than the wavelength of the elastic projectile.