  We explore the impact of nuclear matter saturation on the properties and
systematics of finite nuclei across the nuclear chart. Using the ab initio
in-medium similarity renormalization group (IM-SRG), we study ground-state
energies and charge radii of closed-shell nuclei from $^4$He to $^{78}$Ni,
based on a set of low-resolution two- and three-nucleon interactions that
predict realistic saturation properties. We first investigate in detail the
convergence properties of these Hamiltonians with respect to model-space
truncations for both two- and three-body interactions. We find one particular
interaction that reproduces well the ground-state energies of all closed-shell
nuclei studied. As expected from their saturation points relative to this
interaction, the other Hamiltonians underbind nuclei, but lead to a remarkably
similar systematics of ground-state energies. Extending our calculations to
complete isotopic chains in the $sd$ and $pf$ shells with the valence-space
IM-SRG, the same interaction reproduces not only experimental ground states but
two-neutron-separation energies and first excited $2^+$ states. We also
calculate radii with the valence-space IM-SRG for the first time. Since this
particular interaction saturates at too high density, charge radii are still
too small compared with experiment. Except for this underprediction, the radii
systematics is, however, well reproduced. Our results highlight the importance
of nuclear matter as a theoretical benchmark for the development of
next-generation chiral interactions.
