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 (N N ) 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 O and 12 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 (N2LO), 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 O and neutron elastic scattering observables for 12 C between 65 and 185 MeV projectile kinetic energy. We find qualitatively similar results for the chiral truncation uncertainties as in few-body systems, and assess them using similar diagnostic tools. The orderby-order convergence of the scattering observables for 16 O and 12 C is very reasonable around 100 MeV, while for higher energies the chiral expansion parameter becomes too large for convergence. We also find a nearly perfect correlation between the differential cross section for neutron scattering and the N N Wolfenstein amplitudes for small momentum transfers. Conclusions:The diagnostic tools for studying order-by-order convergence of a chiral N N interaction 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 N N interaction on which our study is based on, gives a very good description of differential cross sections as well as spin observables for 16 O and 12 C as low as 65 MeV projectile energy. In addition, the very forward direction of the neutron differential cross section mirrors the behavior of the N N interaction amazingly well.

Microscopic nucleus-nucleus optical potentials from nuclear matter with uncertainty analysis from chiral forces

“…Optical potentials play a central role in the theoretical modeling of nuclear reactions and the interpretation of experimental data. There has been much recent development in the area of microscopic nucleon-nucleus optical potentials [1][2][3][4][5]. However, most reaction experiments in the rare isotope era will involve nucleus-nucleus interactions and therefore require nucleus-nucleus optical potentials.…”