Low-energy direct nuclear reactions

Abstract

The resonating group method is a successful method for treating nuclear many-body problems in an approximate way. Although the method uses the basic nucleon-nucleon interactions and treats the antisymmetrization of identical particles in an exact way, correction terms cannot be introduced without employing an overcomplete set of basis states for the wave function and the associated theoretical and numerical problems. We present an alternative derivation of the resonating group method, which incorporates bound state approximation for the resolvent operator corresponding to the two-body fragmentation channel appearing in an antisymmetrized version of the N-body Lippmann-Schwinger equation for the wave functions. Similar considerations when applied to the transition matrix Lippmann-Schwinger equation yield the transition matrix version of the resonating group method. Such derivation of the resonating group method allows us to introduce correction terms in a controlled way. The antisymmetrized N-body Lippmann-Schwinger equation for the transition matrix connecting specific two-body channels is reduced to a two-body Lippmann-Schwinger equation with an optical potential and a multiple scattering series for the optical potential, which unlike the usual multiple scattering series is expected to converge at low energy. The lowest order approximation to the optical potential is the resonating group method interaction. We show howmore » to introduce corrections to the optical potential due to excited discrete and certain continuous spectrum of the relevant resolvent operator. The present scheme is also applicable for the calculation of nuclear bound states.« less