Nonperturbative Shell-Model Interactions from the In-Medium Similarity Renormalization Group

We present the first ab initio construction of valence-space Hamiltonians for medium-mass nuclei based on chiral two- and three-nucleon interactions using the in-medium similarity renormalization group. When applied to the oxygen isotopes, we find experimental ground-state energies are well reproduced, including the flat trend beyond the drip line at ${}^{24}\mathrm{O}$. Similarly, natural-parity spectra in ${}^{21,22,23,24}\mathrm{O}$ are in agreement with experiment, and we present predictions for excited states in ${}^{25,26}\mathrm{O}$. The results exhibit a weak dependence on the harmonic-oscillator basis parameter and reproduce spectroscopy within the standard $sd$ valence space.

Figure 1

Single-particle energy evolution (a) and ground-state energies (b) for the indicated $A$-dependent Hamiltonians with ${\lambda }_{\mathrm{SRG}}=1.88{\mathrm{fm}}^{-1}$. The range of $\text{NN}+3\mathrm{N}$-full (${\mathrm{\Lambda }}_{3\mathrm{N}}=400\mathrm{MeV}$) results for $\hslash \omega =20,24\mathrm{MeV}$ is given by the shaded bands.

Figure 2

Excited-state spectrum of ${}^{21}\mathrm{O}$ for IM-SRG Hamiltonians based on $\text{NN}+3\mathrm{N}$-induced and $\text{NN}+3\mathrm{N}$-full Hamiltonians for ${\mathrm{\Lambda }}_{3\mathrm{N}}=400,500\mathrm{MeV}$, with $\hslash \omega =20\mathrm{MeV}$ (dotted) and $\hslash \omega =24\mathrm{MeV}$ (solid), compared with MBPT ($\text{NN}+3\mathrm{N}$) and experiment [48]. $\text{NN}+3\mathrm{N}$-full results are given in two columns: ${\lambda }_{\mathrm{SRG}}=1.88{\mathrm{fm}}^{-1}$ (left) and ${\lambda }_{\mathrm{SRG}}=2.24{\mathrm{fm}}^{-1}$ (right). The neutron-separation threshold is given by black dot-dashed lines.

Figure 3

Excited state spectrum for ${}^{22}\mathrm{O}$ as in Fig. 2, with experimental values from Refs. [48, 49].

Figure 4

Excited state spectrum of ${}^{23}\mathrm{O}$ as in Fig. 2, with experimental values from Refs. [50, 51].

Figure 5

Excited state spectra of ${}^{24–26}\mathrm{O}$ for ${\mathrm{\Lambda }}_{3\mathrm{N}}=400,500\mathrm{MeV}$ $\text{NN}+3\mathrm{N}$-full Hamiltonians with $\hslash \omega =20\mathrm{MeV}$ (dotted), $\hslash \omega =24\mathrm{MeV}$ (solid), and ${\lambda }_{\mathrm{SRG}}$ dependence as in Fig. 2, compared to experiment for ${}^{24}\mathrm{O}$ [52, 53].