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

Background: Calculating microscopic optical potentials for elastic scattering at intermediate energies from light nuclei in an ab initio fashion within the Watson expansion has been established within the last few years.Purpose: 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.Methods: 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. In the SA-NCSM, the model space is systematically up-selected using $\mathrm{Sp}(3,\mathbb{R})$ symmetry considerations.Results: For the light nucleus of $^{6}\mathrm{He}$, 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 $^{20}\mathrm{Ne}$ and $^{40}\mathrm{Ca}$ in the energy regime between 65 and 200 MeV, and compare to available data.Conclusions: 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 $^{40}\mathrm{Ca}$ 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.