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In-Medium Similarity Renormalization Group for Closed and Open-Shell Nuclei

We present a pedagogical introduction to the In-Medium Similarity Renormalization Group (IM-SRG) framework for ab initio calculations of nuclei. The IM-SRG performs continuous unitary transformations of the nuclear many-body Hamiltonian in second-quantized form, which can be implemented with polynomial computational effort. Through suitably chosen generators, it is possible to extract eigenvalues of the Hamiltonian in a given nucleus, or drive the Hamiltonian matrix in configuration space to specific structures, e.g., band- or block-diagonal form. Exploiting this flexibility, we describe two complementary approaches for the description of closed- and open-shell nuclei: The first is the Multireference IM-SRG (MR-IM-SRG), which is designed for the efficient calculation of nuclear ground-state properties. The second is the derivation of nonempirical valence-space interactions that can be used as input for nuclear Shell model (i.e., configuration interaction (CI)) calculations. This IM-SRG+Shell model approach provides immediate access to excitation spectra, transitions, etc., but is limited in applicability by the factorial cost of the CI calculations. We review applications of the MR-IM-SRG and IM-SRG+Shell model approaches to the calculation of ground-state properties for the oxygen, calcium, and nickel isotopic chains or the spectroscopy of nuclei in the lower $sd$ shell, respectively, and present selected new results, e.g., for the ground- and excited state properties of neon isotopes.