We present a comprehensive review of the In-Medium Similarity Renormalization Group (IM-SRG), a novel ab inito method for nuclei. The IM-SRG employs a continuous unitary transformation of the many-body Hamiltonian to decouple the ground state from all excitations, thereby solving the many-body problem. Starting from a pedagogical introduction of the underlying concepts, the IM-SRG flow equations are developed for systems with and without explicit spherical symmetry. We study different IM-SRG generators that achieve the desired decoupling, and how they affect the details of the IM-SRG flow. Based on calculations of closed-shell nuclei, we assess possible truncations for closing the system of flow equations in practical applications, as well as choices of the reference state. We discuss the issue of center-of-mass factorization and demonstrate that the IM-SRG ground-state wave function exhibits an approximate decoupling of intrinsic and center-of-mass degrees of freedom, similar to Coupled Cluster (CC) wave functions. To put the IM-SRG in context with other many-body methods, in particular many-body perturbation theory and non-perturbative approaches like CC, a detailed perturbative analysis of the IM-SRG flow equations is carried out. We conclude with a discussion of ongoing developments, including IM-SRG calculations with three-nucleon forces, the multi-reference IM-SRG for open-shell nuclei, first non-perturbative derivations of shellmodel interactions, and the consistent evolution of operators in the IM-SRG. We dedicate this review to the memory of Gerry Brown, one of the pioneers of many-body calculations of nuclei.3 made a significant impact on nuclear structure theory since the pioneering applications in the early 2000's. Gerry would have been quite pleased with the IM-SRG, as he long advocated for the increased use of RG and Effective Field Theory (EFT) methods in nuclear physics, dating back to when two of us (SKB and AS) were beginning Ph.D. students at Stony Brook in the late 1990's. It was then that Gerry provided our first exposure to these powerful techniques, challenging us to recast in RG language the low-momentum NN interaction V low k and to revisit the calculations of Fermi liquid parameters and shell model Hamiltonians from a modern RG perspective. This was vintage Gerry, in that his intuitive style of doing physics told him that these problems were intimately related to Wilsonian RG ideas, even if he didn't know yet the details. Indeed, if pressed on any of the formalism or technical details, he would give a wry smile and say that such things were the responsibilities of young people to work through.While Gerry's research interests shifted towards astrophysics, heavy-ion and hadronic physics in his later years, the nuclear many-body problem always held a privileged place in his heart. As students, Gerry told us on more than one occasion that his work with Tom Kuo in the 1960's deriving shell model Hamiltonians from the NN interaction [1, 2] was his proudest achievement. Gerry was similarly fond...

We use the recently proposed In-Medium Similarity Renormalization Group (IM-SRG) to carry out a systematic study of closed-shell nuclei up to 56 Ni, based on chiral two-plus three-nucleon interactions. We analyze the capabilities of the IM-SRG by comparing our results for the groundstate energy to Coupled Cluster calculations, as well as to quasi-exact results from the ImportanceTruncated No-Core Shell Model. Using chiral two-plus three-nucleon Hamiltonians whose resolution scales are lowered by free-space SRG evolution, we obtain good agreement with experimental binding energies in 4 He and the closed-shell oxygen isotopes, while the calcium and nickel isotopes are somewhat overbound.

We formulate the in-medium similarity renormalization group (IM-SRG) for open-shell nuclei using a multireference formalism based on a generalized Wick theorem introduced in quantum chemistry. The resulting multireference IM-SRG (MR-IM-SRG) is used to perform the first ab initio study of all even oxygen isotopes with chiral nucleon-nucleon and three-nucleon interactions, from the proton to the neutron drip lines. We obtain an excellent reproduction of experimental ground-state energies with quantified uncertainties, which is validated by results from the importance-truncated no-core shell model and the coupled cluster method. The agreement between conceptually different many-body approaches and experiment highlights the predictive power of current chiral two- and three-nucleon interactions, and establishes the MR-IM-SRG as a promising new tool for ab initio calculations of medium-mass nuclei far from shell closures.

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 + 1 /3 + 1 inversion problem in 22 Na and 46 V. This approach extends the reach of ab initio nuclear structure calculations to essentially all light-and medium-mass nuclei.The development of a first-principles, or ab initio, theoretical description of atomic nuclei is a central challenge in nuclear physics. This task is complicated by the combined difficulties of not having an exact form for nuclear interactions and the great complexity in solving the nuclear many-body problem. Regardless, controlled predictions with uncertainty estimates are vital to guide efforts of rare-isotope beam facilities [1,2], to constrain nucleosynthesis models predicting the origin of heavy elements in the universe [3,4], and to quantify nuclear structure effects in searches for beyond-standard-model physics such as neutrinoless double-beta decay [5], dark matter [6,7], and superallowed beta decay [8]. Developments in chiral effective field theory [9, 10], similarity renormalization group (SRG) [11], and ab initio many-body techniques [12][13][14][15][16][17] provide a unified picture for these efforts, while three-nucleon (3N) forces have emerged as an essential component of nuclear forces [2,[18][19][20][21][22][23][24][25][26][27][28][29].One promising approach to the many-body problem is offered by the shell-model paradigm, where a valencespace Hamiltonian of tractable dimension is decoupled from the much larger Hilbert space and diagonalized. This allows the treatment of excited states, deformation, and transitions in open-shell systems within a single framework. Building upon earlier perturbative approaches [30][31][32], ab initio methods now provide shellmodel Hamiltonians in a nonperturbative manner [33][34][35][36][37][38][39], similar to recent work for chemical systems, see e.g., [40]. However, the inclusion of residual 3N forces [41] among valence particles [42,43] remains problematic in nonperturbative methods and leads to a loss in accuracy compared to large-space ab initio calculations [38].A first attempt to address this shortcoming within the in-medium similarity renormalization group (IM-SRG) framework [38] used normal ordering with respect to closed sub-shells in the valence space, but gave no clear prescription for sys...

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 O. Similarly, natural-parity spectra in 21,22,23,24 O are in agreement with experiment, and we present predictions for excited states in 25,26 O. The results exhibit a weak dependence on the harmonic-oscillator (HO) basis parameter and reproduce spectroscopy within the standard sd valence space.PACS numbers: 21.30. Fe, 21.60.Cs, 21.60.De, With the next generation of rare-isotope beam facilities, the quest to discover and understand the properties of exotic nuclei from first principles is a fundamental challenge for nuclear theory. This challenge is complicated in part because the proper inclusion of three-nucleon (3N) forces plays a decisive role in determining the structure of medium-mass nuclei [1,2]. While ab initio many-body methods based on nuclear forces from chiral effective field theory (EFT) [3][4][5] have now reached the medium-mass region and beyond [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], restrictions in the nuclei and observables accessible to these methods have limited their application primarily to ground-state properties in semimagic isotopic chains.For open-shell systems, rather than solving the full Abody problem, it is profitable to follow the shell-model paradigm by constructing and diagonalizing an effective Hamiltonian in which the active degrees of freedom are A v valence nucleons confined to a few orbitals near the Fermi level. Both phenomenological and microscopic implementations of the shell model have been used with success to understand and predict the evolution of shell structure, properties of ground and excited states, and electroweak transitions [21][22][23].Recent microscopic shell-model studies have revealed the impact of 3N forces in predicting ground-and excited-state properties in neutron-and proton-rich nuclei [1,2,[24][25][26][27][28]. Despite the novel insights gained from these studies, they make approximations which are difficult to benchmark. The microscopic derivation of the effective valence-space Hamiltonian relies on many-body perturbation theory (MBPT) [29], where order-by-order convergence is unclear. Even with efforts to calculate particular classes of diagrams nonperturbatively [30], results are sensitive to the HO frequency ω (due to the core), and the choice of valence space [2,24,25]. A nonperturbative method to address these issues was developed in [31,32], which generates valence-space interactions and operators by projecting their full no-core shell model (NCSM) counterparts into a given valence space.To overcome these limitations in heavier systems, the in-medium similarity renormalization group (IM-SRG), originally developed for ab initio calculations of ground states in closed-shell syste...

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 multi-reference calculations. For spectroscopy, we focus on neutron-rich 23−26 F and 24−26 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 Ne and 24 Mg, providing a path towards an ab initio description of deformation in the medium-mass region. PACS numbers: 21.30.Fe, 21.60.Cs, 21.60.De, 21.10.-k With hundreds of undiscovered nuclei to be created and studied at rare-isotope beam facilities, the development of an ab initio picture of exotic nuclei is a central goal of modern nuclear theory. Three-nucleon (3N) forces are a key input to understand and predict the structure of medium-mass nuclei, from the neutron dripline in oxygen to the evolution of magic numbers in oxygen and calcium [1-11]. In addition, advances in large-space many-body methods have extended the scope of ab ini-tio theory to open-shell calcium and nickel isotopes, and beyond [12-14]. While ground-state properties of even-even isotopes are captured with these methods, excited states and/or odd-mass systems away from closed shells are more challenging. Furthermore, doubly open-shell nuclei may exhibit deformation, which is challenging to capture in large-space ab initio methods built on spherical reference states [15, 16]. These difficulties can be addressed straightforwardly within the framework of the nuclear shell model [17-19], where an effective valence-space Hamiltonian is constructed for particles occupying a small singe-particle space above some closed-shell configuration. Exact di-agonalization then accesses all nuclei and their structure properties in a given region and naturally captures deformation [20]. While the shell model approach is traditionally phenomenological, valence-space Hamiltonians obtained with many-body perturbation theory (MBPT) [21] including 3N forces describe separation energies and first-excited 2 + energies in the sd shell above 16 O [22, 23]. However, order-by-order convergence of is difficult to verify , especially for T = 0 components, and a successful description of exotic nuclei requires the use of extended valence spaces [24-27]. All-order diagrammatic extensions provide further insights [28] but exhibit dependence on the harmonic-oscillator spacing ω and have not been benchmarked with 3N forces. Recently, nonperturbative methods have been developed [29-33], which provide a promising path toward an ab initio description of nuclei between semi-magic isotopic chains, but have not been applied systematically beyond oxygen. In this article we p...

We use the newly developed Multi-Reference In-Medium Similarity Renormalization Group to study all even isotopes of the calcium and nickel isotopic chains, based on two-plus three-nucleon interactions derived from chiral effective field theory. We present results for ground-state and twoneutron separation energies and quantify their theoretical uncertainties. At shell closures, we find excellent agreement with Coupled Cluster results obtained with the same Hamiltonians. Our results confirm the importance of chiral 3N interactions to obtain a correct reproduction of experimental energy trends, and their subtle impact in neutron-rich Ca and Ni isotopes. At the same time, we uncover and discuss deficiencies of the input Hamiltonians which need to be addressed by the next generation of chiral interactions.

We present a systematic study of both nuclear radii and binding energies in (even) oxygen isotopes from the valley of stability to the neutron drip line. Both charge and matter radii are compared to state-of-the-art ab initio calculations along with binding energy systematics. Experimental matter radii are obtained through a complete evaluation of the available elastic proton scattering data of oxygen isotopes. We show that, in spite of a good reproduction of binding energies, ab initio calculations with conventional nuclear interactions derived within chiral effective field theory fail to provide a realistic description of charge and matter radii. A novel version of two- and three-nucleon forces leads to considerable improvement of the simultaneous description of the three observables for stable isotopes but shows deficiencies for the most neutron-rich systems. Thus, crucial challenges related to the development of nuclear interactions remain.