Spin dependent ab initio nonlocal no-core shell-model one-body densities

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 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 ⁴He, ⁶He, ¹²C, and ^16O and compare them with the scalar one-body density matrix. (author)