Motivated by recent findings on the separability of optical potentials that are derived from folding off-shell densities with off-shell nucleon-nucleon amplitudes, we study the off-shell character of one-body density matrices created within the no-core shell model. Concentrating on nuclei with a $0^{+}$ ground state from ${}^4\mathrm{He}$ through ${}^{48}\mathrm{Ca}$, we investigate the off-shell character of their one-body density matrices in momentum space when using the momentum transfer and the average momentum as variables. A singular value decomposition of the one-body density matrices reveals that they can be characterized by only very few terms, depending on the mass number of the nucleus. These findings are independent of the nucleon-nucleon interactions employed, as well as of computational specifics, such as grid spacing and size of the model space.

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• Nuclear forces
• Nucleon distribution
• Shell model