Structure of ${}^{78}\mathrm{Ni}$ from First-Principles Computations

Doubly magic nuclei have a simple structure and are the cornerstones for entire regions of the nuclear chart. Theoretical insights into the supposedly doubly magic ${}^{78}\mathrm{Ni}$ and its neighbors are challenging because of the extreme neutron-to-proton ratio and the proximity of the continuum. We predict the $J^{\pi }=2_1^{+}$ state in ${}^{78}\mathrm{Ni}$ from a correlation with the $J^{\pi }=2_1^{+}$ state in ${}^{48}\mathrm{Ca}$ using chiral nucleon-nucleon and three-nucleon interactions. Our results confirm that ${}^{78}\mathrm{Ni}$ is doubly magic, and the predicted low-lying states of ${}^{79,80}\mathrm{Ni}$ open the way for shell-model studies of many more rare isotopes.

Figure 1

Energy of the $2_1^{+}$ state in neutron-rich nickel isotopes for ${}^{68-76}\mathrm{Ni}$ from the data (black horizontal lines) and for ${}^{78,80}\mathrm{Ni}$ from first-principles computations (red horizontal lines) based on the chiral interaction “1.8/2.0 (EM)” of Ref. [33]. The red shaded area for ${}^{78}\mathrm{Ni}$ shows the predicted range for the $2_1^{+}$ state based on a correlation between the $2_1^{+}$ in ${}^{48}\mathrm{Ca}$ and ${}^{78}\mathrm{Ni}$ using a family of chiral interactions (see the text and Fig. 2 for details).

Figure 2

Correlation between the energies of the $2_1^{+}$ excited state in ${}^{48}\mathrm{Ca}$ and ${}^{78}\mathrm{Ni}$, obtained from the interactions ${\mathrm{NNLO}}_{\text{sat}}$ (circle), “2.0/2.0 (PWA)” (square), “2.0/2.0 (EM)” (diamond), “2.2/2.0 (EM)” (triangle up), and “1.8/2.0 (EM)” (triangle down). The error bars estimate uncertainties from enlarging the model space from $N=12$ to $N=14$. The thin horizontal line marks the known energy of the $2_1^{+}$ state in ${}^{48}\mathrm{Ca}$.

Figure 3

Convergence of the first $2_1^{+}$ excited state of ${}^{48}\mathrm{Ca}$ and ${}^{78}\mathrm{Ni}$ with increasing model-space size and compared to the data for the interaction $1.8/2.0$ (EM) of Ref. [33].

Figure 4

Low-lying states in ${}^{77-80}\mathrm{Ni}$ with respect to the ground state of ${}^{78}\mathrm{Ni}$ computed with the interaction $1.8/2.0$ (EM) of Ref. [33]. The ground states are shown in black, while excited states are shown in red.