Ab initio nucleon-nucleus elastic scattering with chiral effective field theory uncertainties

Abstract

Background: Effective interactions for nucleon-nucleus elastic scattering from first principles require the use of the same nucleon-nucleon interaction in the structure and reaction calculations and a consistent treatment of the relevant operators at each order.Purpose: Systematic investigations of the effect of truncation uncertainties of chiral nucleon-nucleon ($NN$) forces have been carried out for scattering observables in the two- and three-nucleons system as well as for bound-state properties of light nuclei. Here we extend this type of study to proton and neutron elastic scattering for $^{16}\mathrm{O}$ and $^{12}\mathrm{C}$.Methods: Using the frameworks of the spectator expansion of multiple scattering theory as well as the no-core shell model, we employ one specific chiral interaction from the LENPIC collaboration and consistently calculate the leading-order effective nucleon-nucleus interaction up to the third chiral order, from which we extract elastic scattering observables. Then we apply pointwise as well as correlated uncertainty quantification for the estimation of the chiral truncation error.Results: We calculate and analyze proton elastic scattering observables for $^{16}\mathrm{O}$ and $^{12}\mathrm{C}$ as well as neutron elastic scattering observables for $^{12}\mathrm{C}$ between 65 and 185 MeV projectile kinetic energy. We find in all cases qualitatively similar results for the chiral truncation uncertainties as in few-body systems and assess them using similar diagnostic tools. The order-by-order convergence of the scattering observables for $^{16}\mathrm{O}$ and $^{12}\mathrm{C}$ is very reasonable around 100 MeV, while for higher energies the chiral expansion parameter becomes too large for convergence. Comparing proton and neutron differential cross sections reveals that their description is comparable up to around 100 MeV. We also find a nearly perfect correlation between the differential cross section for neutron scattering and the $NN$ Wolfenstein amplitudes for small momentum transfers.Conclusions: The diagnostic tools for studying order-by-order convergence in observables in few-body systems can be employed for observables in nucleon-nucleus scattering with only minor modifications provided the momentum scale in the problems is not too large. We also find that the chiral $NN$ interaction on which our study is based gives a very good description of differential cross sections for $^{16}\mathrm{O}$ and $^{12}\mathrm{C}$ as low as 65-MeV projectile energy, particularly in the forward direction. In addition, the very forward direction of the neutron differential cross section mirrors the behavior of the $NN$ interaction amazingly well.