Nuclear rearrangement scattering. II scattering of composite projectiles with application to deuteron elastic scattering, the deuteron optical model, and deuteron stripping

Abstract

Methods developed for the description of scattering from correlated nuclei and applied previously to the elastic scattering of nucleons, and to quasifree ( p, 2 p) reactions, are extended to include the possibility of describing composite nuclear projectiles. These methods are then applied to obtain a unified description of deuteron scattering. We consider the elastic and the stripping final channels explicitly. The correlated structure of the deuteron and of the target nucleus and the influence of these correlations on the off-shell character of the appropriate channel interactions are taken fully into account. So too are the Pauli and exchange effects due to the identity of the nucleons of the deuteron and the target nucleus. Our methods, however, do not contain any treatment of target recoil effects. The theory leads to a two-potential formulation for the optical potential for deuteron elastic scattering. The first potential describes the deuteron breakup and scattering resulting from the Pauli principle as it applies to the constituents of the target and is expressed entirely in terms of well-behaved quantities, even in the case of singular nucleon-nucleon interactions. The second potential contains the remaining deuteron-nucleus interaction and is evaluated in terms of a fully renormalized perturbation expansion. While this expansion involves the usual Brueckner reaction matrices and occupation probabilities for the bound orbitals it cannot in general be expressed solely in terms of such quantities. It requires the introduction of more complicated two-body interaction matrices as well. These are quite distinct from the reaction matrix because they involve the entire two-body Hamiltonian and because the projction operator accompanying the intermediate state propogator cannot be factorized into a product of one-body projection operators. At high energy, however, the latter interaction becomes negligible and, to lowest order, the deuteron optical potential reduces to the sum of two one-body optical potentials, as expected. The correct energy dependence of these potentials is explicitly exhibited. Deuteron stripping is also discussed in some detail within the context of our formalism. We obtain the lowest-order expression for the stripping amplitude and we indicate a certain class of corrections to this lowest-order term. The various approximations which are necessary to make contact with phenomenological distorted-wave treatments are indicated.