Many-body calculations with Deuteron based single-particle bases and their associated natural orbits

We use the recently introduced single-particle states obtained from localized Deuteron wave-functions as a basis for nuclear many-body calculations. We show that energies can be substantially lowered if the natural orbits obtained from this basis are used. We use this modified basis for ${}^{10}B$, ${}^{16}O$ and ${}^{24}Mg$ employing the bare $NNLO_{opt}$ Nucleon-Nucleon interaction. The lowering of the energies increases with the mass. Although in principle natural orbits require a full scale preliminary many-body calculation, we found that an approximate preliminary many-body calculation, with a marginal increase in the computational cost, is sufficient. The use of natural orbits based on an harmonic oscillator basis leads to a much smaller lowering of the energies for a comparable computational cost.