  Constructing microscopic effective interactions (`optical potentials') for
nucleon-nucleus (NA) elastic scattering requires in first order off-shell
nucleon-nucleon (NN) scattering amplitudes between the projectile and the
struck target nucleon and nonlocal one-body density matrices. While the NN
amplitudes and the {\it ab intio} no-core shell-model (NCSM) calculations
always contain the full spin structure of the NN problem, one-body density
matrices used in traditional microscopic folding potential neglect spin
contributions inherent in the one-body density matrix. Here we derive and show
the expectation values of the spin-orbit contribution of the struck nucleon
with respect to the rest of the nucleus for $^{4}$He, $^{6}$He, $^{12}$C, and
$^{16}$O and compare them with the scalar one-body density matrix.
