Nucleus-Dependent Valence-Space Approach to Nuclear Structure

We present a nucleus-dependent valence-space approach for calculating ground and excited states of nuclei, which generalizes the shell-model in-medium similarity renormalization group to an ensemble reference with fractionally filled orbitals. Because the ensemble is used only as a reference, and not to represent physical states, no symmetry restoration is required. This allows us to capture 3N forces among valence nucleons with a valence-space Hamiltonian specifically targeted to each nucleus of interest. Predicted ground-state energies from carbon through nickel agree with results of other large-space ab initio methods, generally to the 1\% level. In addition, we show that this new approach is required in order to obtain convergence for nuclei in the upper $p$ and $sd$ shells. Finally, we address the $1^+$/$3^+$ ground-state inversion problem in $^{22}\text{Na}$ and $^{46}\text{V}$. This approach extends the reach of ab initio nuclear structure calculations to essentially all light- and medium-mass nuclei.