Ground and excited states of doubly open-shell nuclei from ab initio valence-space Hamiltonians

We present ab initio predictions for ground and excited states of doubly open-shell fluorine and neon isotopes based on chiral two- and three-nucleon interactions. We use the in-medium similarity renormalization group to derive mass-dependent $sd$ valence-space Hamiltonians. The experimental ground-state energies are reproduced through neutron number $N=14$, beyond which a new targeted normal-ordering procedure improves agreement with data and large-space multireference calculations. For spectroscopy, we focus on neutron-rich ${}^{23-26}\mathrm{F}$ and ${}^{24-26}\mathrm{Ne}$ isotopes near $N=14,16$ magic numbers. In all cases we find agreement with experiment and established phenomenology. Moreover, yrast states are well described in ${}^{20}\mathrm{Ne}$ and ${}^{24}\mathrm{Mg}$, providing a path toward an ab initio description of deformation in the medium-mass region.

Figure 1

Ground-state energies of fluorine and neon isotopes from the $A$-dependent IM-SRG valence-space Hamiltonian with ${\lambda }_{\text{SRG}}=1.88{\text{fm}}^{-1}$ and $\hslash \omega =24\text{MeV}$ compared with the 2012 Atomic Mass Evaluation (AME2012) [34] and the phenomenological USDB interaction [35]. Blue circles indicate results obtained with the new targeted normal ordering (Targeted NO) scheme, yellow triangles are the results of the self-consistent Green's function (SCGF) method [4], and green diamonds indicate ground-state energies calculated with the multireference (MR-IM-SRG).

Figure 2

Excited-state spectra for ${}^{19,23,25,26}\mathrm{F}$ from IM-SRG Hamiltonians based on $NN+3N$-ind and $NN+3N$-full Hamiltonians for ${\mathrm{\Lambda }}_{3N}=400$ MeV with $\hslash \omega =20$ MeV (dotted) and $\hslash \omega =24$ MeV (solid), compared with experiment [51] and results from the phenomenological USDB interaction [35].

Figure 3

Excited-state spectra of ${}^{19,24,25,26}\mathrm{Ne}$, as in Fig. 2.

Figure 4

Yrast states for deformed ${}^{20}\mathrm{Ne}$ and ${}^{24}\mathrm{Mg}$ compared to experimental data and phenomenological USDB predictions.