Ab initio multireference in-medium similarity renormalization group calculations of even calcium and nickel isotopes

We use the newly developed multireference in-medium similarity renormalization group to study all even isotopes of the calcium and nickel isotopic chains, based on two- plus three-nucleon interactions derived from chiral effective field theory. We present results for ground-state and two-neutron separation energies and quantify their theoretical uncertainties. At shell closures, we find excellent agreement with coupled-cluster results obtained with the same Hamiltonians. Our results confirm the importance of chiral $3N$ interactions to obtain a correct reproduction of experimental energy trends, and their subtle impact in neutron-rich Ca and Ni isotopes. At the same time, we uncover and discuss deficiencies of the input Hamiltonians which need to be addressed by the next generation of chiral interactions.

Figure 1

Ground-state energies of the Ca isotopes for the (a) $NN+3N$-induced and (b) $NN+3N$ full Hamiltonians, with ${\lambda }_{\mathrm{SRG}}=1.88{\mathrm{fm}}^{-1}$ (open symbols) to $2.24{\mathrm{fm}}^{-1}$ (solid symbols). The bands for the MR-IM-SRG(2) results indicate the variation of the results with the resolution scale ${\lambda }_{\mathrm{SRG}}$. Experimental data (black bars) are taken from [26, 50].

Figure 2

Two-neutron separation energies of the Ca isotopes for the (a) $NN+3N$-induced and (b) $NN+3N$-full Hamiltonian with ${\Lambda }_{3N}=350$ and $400\mathrm{MeV}/c$, for a range ${\lambda }_{\mathrm{SRG}}=1.88{\mathrm{fm}}^{-1}$ (open symbols) to $2.24{\mathrm{fm}}^{-1}$ (solid symbols). Panel (c) compares MR-IM-SRG(2) and second-order GGF [6, 7, 8] results with the same input Hamiltonian, but slightly different SRG evolution [54]. Experimental values (black bars) are taken from [26, 50].

Figure 3

Uncertainty of Ca two-neutron separation energies: (a) Variation as $E_{3\max }=12\to 14$ for different ${\Lambda }_{3N}$ and ${\lambda }_{\mathrm{SRG}}=1.88$ to $2.24{\mathrm{fm}}^{-1}$. (b) Variation $E_{3\max }=12\to 14\to 16$ for ${\Lambda }_{3N}=400\mathrm{MeV}/c,{\lambda }_{\mathrm{SRG}}=1.88{\mathrm{fm}}^{-1}$.

Figure 4

Ground-state energies of the Ni isotopes for the (a) $NN+3N$-induced and (b) $NN+3N$ full Hamiltonians, for resolution scales ${\lambda }_{\mathrm{SRG}}=1.88{\mathrm{fm}}^{-1}$ (open symbols) to $2.24{\mathrm{fm}}^{-1}$ (solid symbols). Experimental data (black bars) are taken from [50].

Figure 5

Two-neutron separation energies of the Ni isotopes for the (a) $NN+3N$-induced and (b) $NN+3N$-full Hamiltonian with ${\Lambda }_{3N}=350$ and $400\mathrm{MeV}/c$, for a range ${\lambda }_{\mathrm{SRG}}=1.88{\mathrm{fm}}^{-1}$ (open symbols) to $2.24{\mathrm{fm}}^{-1}$ (solid symbols). Experimental values (black bars) are taken from [50].