Separable Character of ab initio No-Core Shell-Model densities for 0⁺ ground states.

When the momentum space off-shell one-body density for 0⁺ nuclei constructed from an ab initio no-core shell model (NCSM) is written as function of the momentum transfer and the average momentum, it turns out that it does not depend on the angle between those two momenta. This leads to a hypothesis that this off-shell one-body density may be separable. We explore this assumption by using a Singular Value Decomposition (SVD), and compute a Preserved Variance (PV) to determine which rank a separable representation of the density matrix may have. Our findings, when considering light and medium heavy nuclei, indicate that the rank of a separable representation of the momentum space one-body density is quite low and mainly depends on the number of shells filled. We also find that this rank neither depends on the grid-spacing, the size of the model space or the nucleon-nucleon interaction employed. We are also able to connect one of lowest rank singular vectors to the probability of finding a nucleon with a specific momentum in the nucleus. We will present results for neutron densities from ⁴He to ⁴⁸Ca based on the NNLO_opt and Daejeon16 nucleon-nucleon interactions.