Three-body optical potentials in (d,p) reactions and their influence on indirect study of stellar nucleosynthesis

Abstract

Model uncertainties arising due to suppression of target excitations in the description of deuteron scattering and resulting in a modification of the two-body interactions in a three-body system are investigated for several $(d,p)$ reactions serving as indirect tools for studying the astrophysical $(p,\ensuremath{\gamma})$ reactions relevant to $rp$ process. The three-body nature of the deuteron-target potential is treated within the adiabatic distorted-wave approximation (ADWA) which relies on a dominant contribution from the components of the three-body deuteron-target wave function with small $n\text{\ensuremath{-}}p$ separations. This results in a simple prescription for treating the explicit energy dependence of two-body optical potentials in a three-body system requiring nucleon optical potentials to be evaluated at a shifted energy with respect to the standard value of half the deuteron incident energy. In addition, the ADWA allows for leading-order multiple-scattering effects to be estimated, which leads to a simple renormalization of the adiabatic potential's imaginary part by a factor of two. These effects are assessed using both nonlocal and local optical potential systematics for $^{26}\mathrm{Al}$, $^{30}\mathrm{P}$, $^{34}\mathrm{Cl}$, and $^{56}\mathrm{Ni}$ targets at a deuteron incident energy of 12 MeV, which is typical for experiments with radioactive beams in inverse kinematics. The model uncertainties induced by the three-body nature of deuteron-target scattering are found to be within $40%$ both in the main peak of angular distributions and in total $(d,p)$ cross sections. At higher deuteron energies, around 60 MeV, model uncertainties can reach 100% in the total cross sections. A few examples of application to astrophysically interesting proton resonances in $^{27}\mathrm{Si}$ and $^{57}\mathrm{Cu}$ obtained using $(d,p)$ reactions and mirror symmetry are given.