Ab Initio Calculations of Even Oxygen Isotopes with Chiral Two-Plus-Three-Nucleon Interactions

We formulate the in-medium similarity renormalization group (IM-SRG) for open-shell nuclei using a multireference formalism based on a generalized Wick theorem introduced in quantum chemistry. The resulting multireference IM-SRG (MR-IM-SRG) is used to perform the first ab initio study of all even oxygen isotopes with chiral nucleon-nucleon and three-nucleon interactions, from the proton to the neutron drip lines. We obtain an excellent reproduction of experimental ground-state energies with quantified uncertainties, which is validated by results from the importance-truncated no-core shell model and the coupled cluster method. The agreement between conceptually different many-body approaches and experiment highlights the predictive power of current chiral two- and three-nucleon interactions, and establishes the MR-IM-SRG as a promising new tool for ab initio calculations of medium-mass nuclei far from shell closures.

Figure 1

Convergence of the MR-IM-SRG(2) ground-state energies of ${}^{18}\mathrm{O}$ (a) and ${}^{26}\mathrm{O}$ (b) with respect to the single-particle basis size $e_{\max }$, for the $NN+3N$-full Hamiltonian at ${\lambda }_{\mathrm{SRG}}=2.0{\mathrm{fm}}^{-1}$.

Figure 2

Dependence of the MR-IM-SRG(2) oxygen ground-state energies for the $NN+3N$-full Hamiltonian on the resolution scale and the initial cutoff ${\Lambda }_{3N}$. For each ${\Lambda }_{3N}$, the band is obtained by varying ${\lambda }_{\mathrm{SRG}}$ from 2.24 (open symbols) to $1.88{\mathrm{fm}}^{-1}$ (closed symbols). Experimental values are indicated by black bars [28, 36].

Figure 3

IT-NCSM ground-state energies of the even oxygen isotopes for the $NN+3N$-induced (a) and $NN+3N$-full Hamiltonians (b) at ${\lambda }_{\mathrm{SRG}}=1.88{\mathrm{fm}}^{-1}$. Solid lines indicate the energy extrapolation based on $N_{\max }=8–12$ data; dotted lines guide the eye for smaller $N_{\max }$. Uncertainties due to the importance truncation are smaller than the symbols used to represent the data. All energies are obtained at optimal $\hslash \Omega$.

Figure 4

Oxygen ground-state energies for the $NN+3N$-induced (a) and $NN+3N$-full (b) Hamiltonian with ${\Lambda }_{3N}=400\mathrm{MeV}/c$. MR-IM-SRG(2), CCSD, and $\Lambda$-CCSD(T) results are obtained at optimal $\hslash \Omega$, using 15 major oscillator shells and $E_{3\max }=14$. The IT-NCSM energies are extrapolated to infinite model space. Experimental values are indicated by black bars [28, 36].