Properties of Nuclei up to $A=16$ using Local Chiral Interactions

We report accurate quantum Monte Carlo calculations of nuclei up to $A=16$ based on local chiral two- and three-nucleon interactions up to next-to-next-to-leading order. We examine the theoretical uncertainties associated with the chiral expansion and the cutoff in the theory, as well as the associated operator choices in the three-nucleon interactions. While in light nuclei the cutoff variation and systematic uncertainties are rather small, in ${}^{16}\mathrm{O}$ these can be significant for large coordinate-space cutoffs. Overall, we show that chiral interactions constructed to reproduce properties of very light systems and nucleon-nucleon scattering give an excellent description of binding energies, charge radii, and form factors for all these nuclei, including open-shell systems in $A=6$ and 12.

Figure 1

Ground-state energies per nucleon for $3\le A\le 16$ up to ${\mathrm{N}}^2\mathrm{LO}$ $(E\tau )$ with the $R_0=1.0\mathrm{fm}$ cutoff. Smaller error bars (indistinguishable from the symbols up to $A=6$) indicate the statistical Monte Carlo uncertainty, while larger error bars are the uncertainties from the truncation of the chiral expansion.

Figure 2

Charge radii for $3\le A\le 16$ up to ${\mathrm{N}}^2\mathrm{LO}$ $(E\tau )$ with the $R_0=1.0\mathrm{fm}$ cutoff. Error bars are as in Fig. 1.

Figure 3

Charge form factor for ${}^{16}\mathrm{O}$ at ${\mathrm{N}}^2\mathrm{LO}$ for $R_0=1.0$ and 1.2 fm compared to experimental data [44, 48, 49]. For $R_0=1.0\mathrm{fm}$, both $E\tau$ and $E\mathbb{1}$ three-body operators give consistent results. The shaded area indicates the statistical Monte Carlo uncertainty combined with the (dominant) uncertainty from the truncation of the chiral expansion. For ${}^{12}\mathrm{C}$, AFDMC results are shown in the inset for $R_0=1.0\mathrm{fm}$ versus experimental data from Ref. [50] and the GFMC results employing the $\mathrm{AV}18+\mathrm{IL}7$ potentials [46].

Figure 4

Coulomb sum rules for ${}^{12}\mathrm{C}$ and ${}^{16}\mathrm{O}$ at ${\mathrm{N}}^2\mathrm{LO}$ $(E\tau )$ compared to experimental data as derived in Ref. [51]. Results are shown for $R_0=1.0$ and 1.2 fm for ${}^{16}\mathrm{O}$, and for $R_0=1.0\mathrm{fm}$ for ${}^{12}\mathrm{C}$. Shaded areas indicate only the statistical Monte Carlo uncertainty. In addition, we compare our results to GFMC calculations for ${}^{12}\mathrm{C}$ with $\mathrm{AV}18+\mathrm{IL}7$ [46].