Ab initio no-core properties of ${}^7\mathrm{Li}$ and ${}^7\mathrm{Be}$ with the JISP16 and chiral ${\mathrm{NNLO}}_{\mathrm{opt}}$ interactions

We investigate the properties of ${}^7\mathrm{Li}$ with the JISP16 and chiral ${\mathrm{NNLO}}_{\mathrm{opt}}$ at next-to-next-to-leading order (NNLO) nucleon-nucleon interactions and ${}^7\mathrm{Be}$ with the JISP16 interaction in the ab initio no-core full configuration approach. We calculate selected observables that include energy spectra, point proton root-mean-square radii, electromagnetic moments, and transitions. We compare our results with experimental results, where available, as well as with results obtained using nucleon-nucleon plus three-nucleon interactions. We obtain reasonable agreement between theory and experiment for low-lying states that are dominated by $p$-shell configurations.

Figure 1

Energy of the ground state ($J=\frac{3}{2}$) for ${}^7\mathrm{Be}$ and ${}^7\mathrm{Li}$ with the JISP16 and ${\mathrm{NNLO}}_{\mathrm{opt}}$ interactions as a function of HO energy. In this figure and the following figures, for ${}^7\mathrm{Li}$ and ${}^7\mathrm{Be}$, the $N_{\max }$ value ranges from 8 to 16. The increment of $N_{\max }$ is 2. Extrapolated ground-state energies are shown in purple with uncertainties depicted as vertical bars. Horizontal red lines indicate the lowest breakup thresholds as calculated with the same interactions; black lines are experimental data.

Figure 2

Energies of the four lowest excited states ($J^{\pi }={\frac{1}{2}}^{-},{\frac{7}{2}}^{-},{\frac{5}{2}}^{-},{\frac{5}{2}}^{-},$) with JISP16 and ${\mathrm{NNLO}}_{\mathrm{opt}}$ for ${}^7\mathrm{Be}$ and ${}^7\mathrm{Li}$ as a function of the HO energy. The corresponding experimental values are shown as a horizontal solid line. The $Y$ axis indicates the energy gap between the excited and ground state.

Figure 3

Point proton rms radius (in fm) of the ground state as a function of HO energy with JISP16 and ${\mathrm{NNLO}}_{\mathrm{opt}}$ for a sequence of $N_{\max }$ values.

Figure 4

Magnetic dipole moment of the ground state shown as a function of the HO energy for ${}^7\mathrm{Be}$ and ${}^7\mathrm{Li}$ with the JISP16 and ${\mathrm{NNLO}}_{\mathrm{opt}}$ interactions.

Figure 5

Quadrupole moment of the ground state as a function of the HO energy with a sequence of $N_{\max }$ values for ${}^7\mathrm{Be}$ and ${}^7\mathrm{Li}$.

Figure 6

$B\left(E2\right)$ to the ground state ($J^{\pi }={\frac{3}{2}}^{-}$) from the states $J^{\pi }={\frac{1}{2}}^{-}$ (top) and $J^{\pi }={\frac{7}{2}}^{-}$ (bottom) as a function of the HO energy with a sequence of $N_{\max }$ values. The abbreviation “g.s.” signifies the ground state.

Figure 7

$B\left(M1\right)$ to the ground state ($J^{\pi }={\frac{3}{2}}^{-}$) from the states ($J^{\pi }={\frac{1}{2}}^{-}$) (top), ($J^{\pi }={\frac{5}{2}}_1^{-}$) (middle), and ($J^{\pi }={\frac{5}{2}}_2^{-}$) (bottom) as a function of the HO energy for ${}^7\mathrm{Li}$ and ${}^7\mathrm{Be}$ with JISP16 and ${\mathrm{NNLO}}_{\mathrm{opt}}$. Note the expanded scales used to reveal similarities and differences in the details.

Figure 8

Spin decompositions and total magnetic moments for ${}^7\mathrm{Li}$ with JISP16, ${}^7\mathrm{Li}$ with ${\mathrm{NNLO}}_{\mathrm{opt}}$, and ${}^7\mathrm{Be}$ with JISP16. They are presented as a function of the HO energy with a sequence of $N_{\max }$ values. We show the contributions from the proton orbital motion (red), neutron orbital motion (blue), proton intrinsic spin (orange), and neutron intrinsic spin (green) to their respective angular momenta in units with $\hslash =1$ so the vertical axis is dimensionless. The purple symbols with connecting lines present the total magnetic moment in units of ${\mu }_N$.