Accurate nuclear radii and binding energies from a chiral interaction

With the goal of developing predictive ab initio capability for light and medium-mass nuclei, two-nucleon and three-nucleon forces from chiral effective field theory are optimized simultaneously to low-energy nucleon-nucleon scattering data, as well as binding energies and radii of few-nucleon systems and selected isotopes of carbon and oxygen. Coupled-cluster calculations based on this interaction, named ${\mathrm{NNLO}}_{\mathrm{sat}}$, yield accurate binding energies and radii of nuclei up to ${}^{40}\mathrm{Ca}$, and are consistent with the empirical saturation point of symmetric nuclear matter. In addition, the low-lying collective $J^{\pi }=3^{-}$ states in ${}^{16}\mathrm{O}$ and ${}^{40}\mathrm{Ca}$ are described accurately, while spectra for selected $p$- and $sd$-shell nuclei are in reasonable agreement with experiment.

Figure 1

Ground-state energy (negative of binding energy) per nucleon (top), and residuals (differences between computed and experimental values) of charge radii (bottom) for selected nuclei computed with chiral interactions. In most cases, theory predicts too-small radii and too-large binding energies. References: $a$ [40, 41], $b$ [24], $c$ [23], $d$ [22], $e$ [42], $f$ [43], $g$ [44], $h$ [45], $i$ [46]. The red diamonds are ${\mathrm{NNLO}}_{\mathrm{sat}}$ results obtained in this work.

Figure 2

Selected neutron-proton scattering phase-shifts as a function of the laboratory scattering energy $T_{\mathrm{Lab}}$. (Top) ${\mathrm{NNLO}}_{\mathrm{sat}}$ prediction (solid lines) compared to the Nijmegen phase shift analysis [95] (symbols) at low energies $T_{\mathrm{Lab}}<35$ MeV. Note the two vertical scales. (Bottom) Neutron-proton scattering phase shifts from ${\mathrm{NNLO}}_{\mathrm{sat}}$ (red diamonds) compared to the Nijmegen phase shift analysis (black squares) and the NNLO potentials (green) from Ref. [77].

Figure 3

Energies (in MeV) of selected excited states for various nuclei using ${\mathrm{NNLO}}_{\mathrm{sat}}$. For ${}^6\mathrm{Li}$ we also include spectra from the NCSM (dotted lines), and isospin quantum numbers are also given. The NCSM results were obtained with $N_{\max }=10$ and $\hslash \Omega =16$ MeV. Parenthesis denote tentative spins assignments for experimental levels. Data are from Refs. [100, 101, 102, 103].

Figure 4

Charge density in ${}^{16}\mathrm{O}$ computed as in Ref. [110] compared to the experimental charge density [111]. The inset compares computed low-lying negative-parity states with experiment.

Figure 5

Equation of state for symmetric nuclear matter from chiral interactions. Solid red line is the prediction of ${\mathrm{NNLO}}_{\mathrm{sat}}$. Blue dashed-dotted and black dashed lines: Ref. [56]. Symbols (red diamond, blue circle, black square) mark the corresponding saturation points. Triangles are saturation points from other models (upward triangles [33], rightward triangles [112], downward triangles [36]). The corresponding incompressibilities (in MeV) are indicated by numbers. Green box shows empirical saturation point.