Exploring $sd$-shell nuclei from two- and three-nucleon interactions with realistic saturation properties

We study ground- and excited-state properties of all $sd$-shell nuclei with neutron and proton numbers $8\le N,Z\le 20$, based on a set of low-resolution two- and three-nucleon interactions that predict realistic saturation properties of nuclear matter. We focus on estimating the theoretical uncertainties due to variation of the resolution scale, the low-energy couplings, as well as from the many-body method. The experimental two-neutron and two-proton separation energies are reasonably well reproduced, with an uncertainty range of $\sim 5\text{MeV}$. The first excited $2^{+}$ energies also show overall agreement, with a more narrow uncertainty range of $\sim 500\text{keV}$. In most cases, this range is dominated by the uncertainties in the Hamiltonian.

Figure 1

Ground-state energies of the magnesium (top) and chlorine isotopes (bottom panel) relative to ${}^{16}\mathrm{O}$ at second (blue, darker band) and third order (cyan, lighter band) in MBPT and compared to the Atomic Mass Evaluation (AME 2012) [50]. The uncertainty bands are spanned by the five different $\mathrm{NN}+3\mathrm{N}$ interactions (see text for details). The ordering in the legend is with decreasing ground-state energies.

Figure 2

Uncertainty estimates for the two-neutron separation energies $S_{2\mathrm{n}}$ of $sd$-shell isotopic chains at second (blue, darker band) and third order (cyan, lighter band) in MBPT and compared to the Atomic Mass Evaluation (AME 2012) [50].

Figure 3

Uncertainty estimates for two-proton separation energies $S_{2\mathrm{p}}$ of $sd$-shell isotonic chains at second (blue, darker band) and third order (cyan, lighter band) in MBPT and compared to the Atomic Mass Evaluation (AME 2012) [50].

Figure 4

Uncertainty estimates for excitation energies of the first $2_1^{+}$ states in even-even $sd$-shell isotopes at second (blue, darker band) and third order (cyan, lighter band) and compared to experimental data from ENSDF [57].