Integral Equations for Deuteron-Induced Nuclear Reactions

Abstract

A new treatment of deuteron-induced nuclear reactions is presented. Uncoupled Fredholm integral equations for the reaction amplitudes are derived. Approximating the neutron-proton $T$ matrix by a simple separable form gives the optical potential for deuterons, in terms of the neutron-target and proton-target interactions. All reaction amplitudes can be expressed, in this approximation, in terms of the off-shell ($d, d^{\prime }$) scattering matrix. For the special case of a spinless, inert, infinitely heavy target, the optical potential can be constructed by quadratures. This is done explicitly, and the numerical behavior of the partial-wave deuteron elastic-scattering equations is investigated for a simple model. Finally, the philosophy of this approach to the study of direct reactions is discussed, and extensions of the theory (for the treatment of local neutron-target and proton-target potentials) are suggested.