Few-channel models of nuclear reactions: Three-body model for deuteron elastic scattering and breakup

This paper is concerned with the reduction of the general deuteron-nucleus collision problem to a three-body model describing deuteron elastic scattering and elastic breakup. A formally exact reduction is carried out using an antisymmetrized, multiparticle scattering theory, viz., the Bencze-Redish-Sloan theory in precursor form. All effects of the Pauli principle due to the target nucleons are thus included in the Hamiltonian $H_3$ describing the three-body model. Since deuteron elastic scattering and breakup have been treated for quite some time via an empirical, three-body model Hamiltonian $H_M$, the main purpose of this work has been to establish the relation between $H_3$ and $H_M$. It is shown that, even with inclusion of the Pauli principle, $H_3$ has exactly the form conjectured some years ago by Austern and Richards using a distinguishable particle ansatz. That is, $H_3$ is a sum of the following terms: the two kinetic energy operators, the neutron-proton interaction $V_{\mathrm{np}}$ binding the deuteron, the sum of the exact (antisymmetrized) neutron-nucleus and proton-nucleus optical potentials, each evaluated at an ‘‘energy’’ shifted by the kinetic energy operator of the other (spectator) nucleon, and a three-body interaction. Contrary to other conjectures, the Pauli principle does not give rise to a term $V_{\mathrm{np}\mathrm{Q}}$ (or ${\mathrm{QV}}_{\mathrm{np}}$), where Q is a Pauli blocking factor, projecting off states occupied in the (exact) target ground state. The deuteron in a deuteron-nucleus collision is thus not like a nucleon pair in the structure problem described by the Bethe-Goldstone theory. The three-body interaction $W_{\mathrm{np}}$ is sufficiently complicated to necessitate approximate evaluation. Some relatively simple approximations to $W_{\mathrm{np}}$ are described within a multiple scattering type of framework.