Structure of $A=7$–8 nuclei with two- plus three-nucleon interactions from chiral effective field theory

We solve the ab initio no-core shell model (NCSM) in the complete $8\hslash \Omega$ ($N_{\max }=8$) basis for $A=7$ and $A=8$ nuclei with two-nucleon and three-nucleon interactions derived within chiral effective field theory (EFT). We find that including the chiral EFT three-nucleon interaction in the Hamiltonian improves overall agreement with experimental binding energies, excitation spectra, transitions, and electromagnetic moments. We predict states that exhibit sensitivity to including the chiral EFT three-nucleon interaction but are not yet known experimentally.

Figure 1

Calculated ground-state energy of ${}^7$Li in the NCSM with chiral EFT $NN$ and $NNN$ interactions that reproduce the triton binding energy and half-life. The dependence on the HO frequency and size of the basis is presented.

Figure 2

Calculated excitation energies of the lowest five excited states of ${}^7$Li in the NCSM with chiral EFT $NN$ and $NNN$ interactions that reproduce the triton binding energy and half-life. The dependence on the HO frequency is presented at the two highest values of basis-space truncation $N_{\max }=6$ (dashed lines) and 8 (solid lines). The experimental excitation energies are shown on the left for comparison.

Figure 3

Calculated and experimental excitation energies of ${}^7$Li. Dependence on the size of the basis is presented. The chiral EFT $NN$ and $NNN$ interaction was used. The isospin of the states is $T=1/2$ unless shown otherwise. See the text for further details.

Figure 4

Calculated and experimental excitation energies of ${}^8$B. Dependence on the size of the basis is presented. The chiral EFT $NN$ and $NNN$ interaction was used. The isospin of the states is $T=1$ unless shown otherwise. See the text for further details.

Figure 5

Calculated and experimental ground-state energies for $A=8$. Calculated results are obtained with the chiral EFT $NN$ and $NN+NNN$ interactions at $\hslash \Omega =13$ MeV and $N_{\max }=6$ and 8.

Figure 6

Calculated and experimental excitation energies of ${}^8$Be. Dependence on the size of the basis is presented. The chiral EFT $NN$ and $NNN$ interaction was used. The isospin of the states is $T=0$ unless shown otherwise. See the text for further details.