Quantifying uncertainties due to irreducible three-body forces in deuteron-nucleus reactions

Abstract

Background: Deuteron-induced nuclear reactions are an essential tool for probing the structure of nuclei as well as astrophysical information such as $(n,\ensuremath{\gamma})$ cross sections. The deuteron-nucleus system is typically described within a Faddeev three-body model consisting of a neutron ($n$), a proton ($p$), and the target nucleus ($A$) interacting through pairwise phenomenological potentials. While Faddeev techniques enable the exact description of the three-body dynamics, their predictive power is limited in part by the omission of irreducible neutron-proton-nucleus three-body force ($n\text{\ensuremath{-}}p\text{\ensuremath{-}}A$ 3BF).Purpose: Our goal is to quantify systematic uncertainties stemming from the reduction of deuteron-nucleus ($d+A$) dynamics to a picture of three pointlike nuclear clusters interacting via pairwise nucleon-nucleus forces, using as testing grounds $d+\ensuremath{\alpha}$ scattering and the $^{6}\mathrm{Li}$ ground state. We particularly focus on quantifying uncertainties arising from the full antisymmetrization of the ($A+2$)-body system with the target nucleus fixed in its ground state.Methods: We adopt the ab initio no-core shell model coupled with the resonating group method (NCSM/RGM) to compute microscopic $n\text{\ensuremath{-}}\ensuremath{\alpha}$ and $p\text{\ensuremath{-}}\ensuremath{\alpha}$ interactions, and use them in a three-body description of the $d+\ensuremath{\alpha}$ system by means of momentum-space Faddeev-type equations. Simultaneously, we also carry out ab initio calculations of $d+\ensuremath{\alpha}$ scattering and $^{6}\mathrm{Li}$ ground state by means of six-body NCSM/RGM calculations to serve as a benchmark for the three-body model predictions given by the Faddeev calculations.Results: By comparing the Faddeev and NCSM/RGM results, we show that the irreducible $n\text{\ensuremath{-}}p\text{\ensuremath{-}}\ensuremath{\alpha}$ 3BF has a non-negligible effect on bound state and scattering observables alike. Specifically, the Faddeev approach yields a $^{6}\mathrm{Li}$ ground state that is approximately 600 keV shallower than the one obtained with the NCSM/RGM. Additionally, the Faddeev calculations for $d+\ensuremath{\alpha}$ scattering yield a ${3}^{+}$ resonance that is located approximately 400 keV higher in energy compared to the NCSM/RGM result. The shape of the $d+\ensuremath{\alpha}$ angular distributions computed using the two approaches also differ, owing to the discrepancy in the predictions of the ${3}^{+}$ resonance energy.Conclusions: The Faddeev three-body model predictions for $d+\ensuremath{\alpha}$ scattering and $^{6}\mathrm{Li}$ using microscopic $n\text{\ensuremath{-}}\ensuremath{\alpha}$ and $p\text{\ensuremath{-}}\ensuremath{\alpha}$ potentials differ from those computed microscopically with the NCSM/RGM. These discrepancies are due to the $n\text{\ensuremath{-}}p\text{\ensuremath{-}}\ensuremath{\alpha}$ 3BF, which arises from two-nucleon exchange terms in the microscopic $d\text{\ensuremath{-}}\ensuremath{\alpha}$ interaction and are not accounted for in the three-body model Faddeev calculations. This study lays the foundation for future parametrizations of the 3BF due to Pauli exclusion principle effects in improved three-body calculations of deuteron-induced reactions.