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

Abstract

Background: Effective interactions for nucleon-nucleus ($NA$) elastic scattering from first principles require the use of the same nucleon-nucleon ($NN$) interaction in the structure and reaction calculations, and a consistent treatment of the relevant operators at each order. Purpose: Truncation uncertainties of chiral $NN$ forces have been studied for scattering observables in few-body systems and for bound state properties of light nuclei. We extend this to $NA$ elastic scattering. Methods: With the spectator expansion of multiple scattering theory and the no-core shell model, we use a chiral interaction from the LENPIC collaboration to consistently calculate the leading order effective $NA$ interaction up to third chiral order (N2LO) and extract elastic scattering observables. We quantify the chiral truncation error using pointwise and correlated methods. Results: We analyze proton-${}^{16}$O and neutron-${}^{12}$C elastic scattering observables between 65 and 185 MeV projectile kinetic energy. We find qualitatively similar results for the chiral truncation uncertainties as in few-body systems, which we assess using similar diagnostic tools. The order-by-order convergence of the scattering observables for ${}^{16}$O and ${}^{12}$C is reasonable near 100 MeV, but for higher energies the expansion parameter becomes too large to converge. We find a near-perfect correlation between the neutron differential cross section and the $NN$ Wolfenstein amplitudes for small momentum transfers. Conclusions: The tools used to study the convergence of a chiral $NN$ interaction in few-body systems can be applied to $NA$ scattering with minor changes. The $NN$ interaction used here gives a good description of ${}^{16}$O and ${}^{12}$C scattering observables as low as 65 MeV. The very forward direction of the neutron differential cross section mirrors the behavior of the $NN$ interaction amazingly well.

arXiv comment17 pages, 13 figures, 1 table

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Cited by in corpus (2)

• Microscopic optical potential from the relativistic Brueckner-Hartree-Fock theory: Proton-nucleus scattering
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