Separable Non-Local One-Body Ground State Densities for light 0⁺ Nuclei

Nucleon-nucleon (NN) interaction potentials derived from Chiral Effective Field Theory used in conjunction with the no-core shell-model (NCSM) allows ab initio predictions of light nuclei structure and scattering observables. In a multipole expansion of the non-local one-body density matrix (OBDM), nuclei with 0+ ground states are completely described by the monopole term. It is advantageous to consider these OBDMs in momentum space, specifically where the momentum transfer and the average momentum are the coordinates.

We investigate the dependence on the angle between those two momentum vectors for OBDMs for s- and p-shell nuclei (⁴He, ¹²C, and ¹⁶O) derived in the NCSM framework from different chiral NN interactions. We find that those OBDMs are separable in the chosen momentum variables. However, OBDMs in terms of the initial and final momentum (p,p') exhibit dependence on the angle between them.