Impact of Three-Body Forces on Elastic Nucleon-Nucleus Scattering Observables.

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 final expression of the OP was a folding integral between the nucleon-nucleon ($NN$) $t$ matrix and the nuclear density of the target. In these calculations $NN$ and three-nucleon ($3N$) chiral interactions were used for the target density and only the $NN$ interaction for the $NN$ $t$ matrix. 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. In the present work this 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 $NN$ $t$ 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. 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. 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. 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.