Ab initio leading order effective potential for elastic proton scattering based on the symmetry-adapted no-core shell model

Abstract

Based on the Watson expansion of the multiple scattering series, we employ a nonlocal translationally invariant nuclear density derived within the symmetry-adapted no-core shell model (SA-NCSM) framework from a chiral next-to-next-to-leading order (NNLO) nucleon-nucleon interaction and the very same interaction for a consistent full-folding calculation of the effective (optical) potential for nucleon-nucleus scattering for medium-heavy nuclei. The leading order effective (optical) folding potential is computed by integrating over a translationally invariant SA-NCSM one-body scalar density, spin-projected momentum distribution, and the Wolfenstein amplitudes $A$, $C$, and $M$. The resulting nonlocal potentials serve as input for a momentum space Lippmann-Schwinger equation, whose solutions are summed up to obtain nucleon-nucleus scattering observables. In the SA-NCSM, the model space is systematically up-selected using $\SpR{3}$ symmetry considerations. For the light nucleus of $^6$He, we establish a systematic selection scheme in the SA-NCSM for scattering observables. Then, we apply this scheme to calculations of scattering observables, such as differential cross sections, analyzing powers, and spin rotation functions for elastic proton scattering from $^{20}$Ne and $^{40}$Ca in the energy regime between 65 and 200 MeV, and compare to available data. Our calculations show that the leading order effective nucleon-nucleus potential in the Watson expansion of multiple scattering theory obtained from an up-selected SA-NCSM model space describes $^{40}$Ca elastic scattering observables reasonably well to about 60 degrees in the center-of-mass frame, which coincides roughly with the validity of the NNLO chiral interaction used to calculate both the nucleon-nucleon amplitudes and the one-body scalar and spin nuclear densities.