Exact treatment of the dwba by analytic means for particle transfer between heavy ions

Abstract

The Fourier-Bessel expansion is utilized for the exact evaluation of the DWBA amplitude in transfer reactions. The partial wave radial components of the elastic scattering wave function in the outgoing channel and one of the bound-state wave functions of the transferred particle are expanded in terms of a complete set of spherical Bessel functions over a finite interval. For a radial wave function of a given angular momentum, the basis is chosen to be a complete set of spherical Bessel functions of the same angular momentum, so that the addition theorem for the product of spherical Bessel function and spherical harmonic can be utilized. It is shown that the method proposed has the distinct advantage that the recoil angular momentum appears as a natural expansion parameter, and that the various approximate methods can be retrieved as simple limits of the exact expression. The method is applied to the transfer of a single nucleon or a cluster, and to the transfer of several nucleons.