Impact of three-body forces on elastic nucleon-nucleus scattering observables

Abstract

Background: In a previous series of papers we investigated the domain of applicability of chiral potentials to the construction of a microscopic optical potential (OP) for elastic nucleon-nucleus scattering. The OP was derived at the first order of the spectator expansion of the Watson multiple scattering theory and its final expression was a folding integral between the nucleon-nucleon (NN) t matrix and the nuclear density of the target. In the calculations NN and three-nucleon (3N) chiral interactions were used for the target density and only the NN interaction for the NN t matrix. Purpose: The purpose of this work is to achieve another step towards the calculation of a more consistent OP introducing the 3N force also in the dynamic part of the OP. Methods: The full treatment of the 3N interaction is beyond our present capabilities. Thus, in the present work it is approximated with a density dependent NN interaction obtained after the averaging over the Fermi sphere. In practice, in our model the 3N force acts as a medium correction of the bare NN interaction used to calculate the t matrix. Even if the 3N force is treated in an approximate way, this method naturally extends our previous model of the OP and allows a direct comparison of our present and previous results. Results: We consider as case studies the elastic scattering of nucleons off 12 C and 16 O. We present results for the differential cross section and the spin observables for different values of the projectile energy. From the comparison with the experimental data and with the results of our previous model we assess the importance of the 3N interaction in the dynamic part of the OP. Conclusions: Our analysis indicates that the contribution of the 3N force in the t matrix is small for the differential cross section and it is sizable for the spin observables, in particular, for the analyzing power. We find that the two-pion exchange term is the major contributor to the 3N force. A chiral expansion order-by-order analysis of the scattering observables confirms the convergence of our results at the next-to-next-to-next-to-leading-order, as already established in our previous work.

Chiral uncertainties in ab initio elastic nucleon-nucleus scattering

“…This has been the case in the microscopic calculations of the 1990s (see e.g. [9][10][11][12][13][14]) and a set of recent calculations with specific chiral NN interactions [40,41,46]. Attempts to go beyond the leading order by incorporating 3NFs in a density dependent fashion into the many-body propagator [46] indicate that effects at 200 MeV are only visible at higher momentum transfer.…”

“…At at the next-to-leading order three-nucleon forces will naturally enter the effective interaction. At present this step has only been attempted in approximative fashions, namely by approximating the next-to-leading order in the propagator expansion via a nuclear mean field force [54] or by introducing an effective, density dependent NN potential in the scattering part of the calculation [46]. Since we are not considering next-to-leading order terms in the spectator expansion, we restrict our analysis to N2LO in the chiral interaction and only consider two-nucleon forces.…”

“…Including three-nucleon forces consistently in both, the structure and scattering calculations requires going beyond the leading-order optical potential, and is beyond the scope of this work. Though initial attempts of incorporating three-nucleon forces as an effective density-dependent NN force in the scattering part have been presented [46], they can not yet be considered as systematic consideration of three-nucleon forces in NA scattering. For similar reasons, we restrict most of our results to N2LO since three-nucleon force contributions at N3LO and N4LO are significant [71].…”

“…The theoretical and computational developments leading to ab initio NA effective interactions (in leading order in the spectator expansion) are described in a serious of publications by the authors [39][40][41][42][43] and others (see e.g. [44][45][46][47]). Thus the aim of this review is to shed light on truncation uncertainties in the chiral expansion, and within that context give a perspective on intricacies of the spectator expansion as well as the explicit content of its leading order term, which can now be calculated ab initio.…”

Modern approaches to optical potentials

“…In the top two panels of Figure 40 is shown the differential elastic scattering cross sections for proton projectiles on a 12 C target at energies E = 122 MeV and 200 MeV computed within a multiple-scattering formalism [Vorabbi et al(2021)] compared to experimental data. The proton-nucleon T -matrix, t pN , is derived from nucleon-nucleon interactions at N4LO in the chiral power counting together with a density-dependent two-body force [Holt et al(2010)] derived from the chiral effective field theory three-body force at N2LO.…”