  We study the efficacy of a new ab initio framework that combines the
symmetry-adapted (SA) no-core shell-model approach with the resonating group
method (RGM) for unified descriptions of nuclear structure and reactions. We
obtain ab initio neutron-nucleus interactions for $^4$He, $^{16}$O, and
$^{20}$Ne targets, starting with realistic nucleon-nucleon potentials. We
discuss the effect of increasing model space sizes and symmetry-based
selections on the SA-RGM norm and direct potential kernels, as well as on phase
shifts, which are the input to calculations of cross sections. We demonstrate
the efficacy of the SA basis and its scalability with particle numbers and
model space dimensions, with a view toward ab initio descriptions of nucleon
scattering and capture reactions up through the medium-mass region.
