In-medium similarity renormalization group with chiral two- plus three-nucleon interactions

Hergert, H.; Bogner, S. K.; Binder, Sven; Calci, Angelo; Langhammer, Joachim; Roth, Robert; Schwenk, A.

doi:10.1103/physrevc.87.034307

Cited by 214 publications

(417 citation statements)

References 53 publications

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“…First, we want to study in more detail whether L eff is also the relevant length scale when approximate many-body solutions (such as CCSD) are employed. We note that most ab initio methods that presently compute nuclei beyond the p shell employ approximate solutions of the many-body problem [29,30,7,25,24]. Second, we want to probe the extrapolation formula (6) over a large energy range and see how large the model space needs to be for a reliable and accurate extrapolation.…”

Section: Extrapolations and The Coupled-cluster Methodsmentioning

confidence: 99%

Infrared extrapolations for atomic nuclei

Furnstahl

Hagen

Papenbrock

et al. 2015

J. Phys. G: Nucl. Part. Phys.

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Abstract. Harmonic oscillator model-space truncations introduce systematic errors to the calculation of binding energies and other observables. We identify the relevant infrared scaling variable and give values for this nucleus-dependent quantity. We consider isotopes of oxygen computed with the coupled-cluster method from chiral nucleon-nucleon interactions at next-to-next-to-leading order and show that the infrared component of the error is sufficiently understood to permit controlled extrapolations. By employing oscillator spaces with relatively large frequencies, well above the energy minimum, the ultraviolet corrections can be suppressed while infrared extrapolations over tens of MeVs are accurate for ground-state energies. However, robust uncertainty quantification for extrapolated quantities that fully accounts for systematic errors is not yet developed.

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Section: Extrapolations and The Coupled-cluster Methodsmentioning

confidence: 99%

Infrared extrapolations for atomic nuclei

Furnstahl

Hagen

Papenbrock

et al. 2015

J. Phys. G: Nucl. Part. Phys.

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“…Truncations in the SRG flow equation cause a violation of unitarity that manifests as a (residual) dependence of many-body results on λ. By varying this parameter, the size of the missing contributions can be assessed (see, e.g., [33,55,57,61,91,[99][100][101][102]). State-of-the-art SRG evolutions of nuclear interactions are nowadays performed in the three-body system, using relative (Jacobi) harmonic oscillator [54,100,103], relative momentum plane wave [101], or momentum-space hypherspherical harmonics representations [104].…”

Section: Srg Evolution Of Nuclear Interactionsmentioning

confidence: 99%

“…This leads us to the socalled In-Medium SRG (IMSRG), which is the main focus of the present work [60][61][62]. In a nutshell, we want to use SRG-like flow equations to decouple physics at different excitation energy scales of the nucleus, and render the Hamiltonian matrix in configuration space block or band diagonal in the process.…”

Section: Introductionmentioning

confidence: 99%

In-medium similarity renormalization group for closed and open-shell nuclei

Hergert¹

2016

Phys. Scr.

145

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Abstract. We present a pedagogical introduction to the In-Medium Similarity Renormalization Group (IMSRG) framework for ab initio calculations of nuclei. The IMSRG 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 IMSRG (MR-IMSRG), 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 IMSRG+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-IMSRG and IMSRG+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.Submitted to: Phys. Scr.

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“…An ab initio calculations of the quark mass dependence of the ground state energies of 4 He, 8 Be and 12 C, and of the energy of the Hoyle state in 12 C have been performed [22,23]. The sensitivity of the production rate of carbon and oxygen in red giant stars to the fundamental constants of nature was investigated by considering the impact of variations in the light quark masses and the electromagnetic fine-structure constant on the reaction rate of the triple-alpha process.…”

Section: The Fate Of Carbon-based Lifementioning

confidence: 99%

“…For going beyond light nuclei, one can either combine these forces with standard many-body methods like the no-core-shell-model, the coupled cluster approach, and so on (for some recent such works see Refs. [5][6][7][8][9][10][11]) or develop a novel scheme that uses lattice methods to tackle the nuclear many-body problem. This is the approach I will discuss here.…”

Section: Introductionmentioning

confidence: 99%