  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.
