Universal properties of infrared oscillator basis extrapolations

More, S. N.; Ekström, Andreas; Furnstahl, R. J.; Hagen, G.; Papenbrock, T.

doi:10.1103/physrevc.87.044326

Cited by 109 publications

(201 citation statements)

References 33 publications

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“…Clearly, the data points do not fall on a single line for either nucleus, and similar results are found for 22 O. Earlier studies [20] showed that the smoothness of E(L), when plotted for a large set of N and Ω values for which UV corrections are small, is a sensitive diagnostic of the quality of L(N, Ω). Thus, L = L 2 is not the accurate box size of the harmonic oscillator basis for fermionic many-body systems.…”

Section: Infrared Cutoffs Of the Oscillator Basissupporting

confidence: 74%

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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: Infrared Cutoffs Of the Oscillator Basissupporting

confidence: 74%

“…20 of Ref. [20] as an example. We note that all solid data points employed in the IR extrapolation in Fig.…”

Section: Extrapolations and The Coupled-cluster Methodsmentioning

confidence: 96%

Infrared extrapolations for atomic nuclei

Furnstahl

Hagen

Papenbrock

et al. 2015

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

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“…While progress toward a theoretically founded understanding of universal infrared extrapolations has been made [103], the ultraviolet situation is less clear. The SRG offers a tool for studying ultraviolet extrapolations, including suggestive but as yet unexplained scaling with the SRG flow parameter [102].…”

Section: Other Applications and Future Directionsmentioning

confidence: 99%

New applications of renormalization group methods in nuclear physics

2013

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Abstract. We review recent developments in the use of renormalization group (RG) methods in low-energy nuclear physics. These advances include enhanced RG technology, particularly for three-nucleon forces, which greatly extends the reach and accuracy of microscopic calculations. We discuss new results for the nucleonic equation of state with applications to astrophysical systems such as neutron stars, new calculations of the structure and reactions of finite nuclei, and new explorations of correlations in nuclear systems.

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“…While mature techniques to extrapolate results to infinite HO bases are available [142][143][144][145][146][147][148], we limit ourselves to finite bases here, using sufficiently large e max values to eliminate the single-particle basis truncation as a relevant source of uncertainty, typically up to e max = 14 (15 major HO shells). An additional truncation is necessary to manage the enormous memory requirements of 3N interaction matrix elements.…”

Section: Interactions and Implementationmentioning

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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Universal properties of infrared oscillator basis extrapolations

Cited by 109 publications

References 33 publications

Infrared extrapolations for atomic nuclei

Infrared extrapolations for atomic nuclei

New applications of renormalization group methods in nuclear physics

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

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