Renormalization of Hamiltonians

Głazek, Stanisław D.; Wilson, Kenneth G.

doi:10.1103/physrevd.48.5863

Cited by 488 publications

(489 citation statements)

References 14 publications

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“…The many-body data, e.g., selected radii, are chosen in order to improve the deficient saturation behavior of chiral interactions that are used as input for nuclear many-body calculations. The first interaction optimized with this protocol is NNLO sat [26], which is able to accurately describe the ground-state energies and charge radii of 40,48 Ca at the same time. Following the same philosophy but not the same approach, Shirokov et al have produced Daejeon16, a softened chiral N N interaction that has been tuned for the description of light nuclei without explicit 3N forces [27][28][29][30].…”

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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Section: Introductionmentioning

confidence: 99%

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

Hergert¹

2016

Phys. Scr.

145

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“…As shown by the red lines in Fig. 3(a), the further inclusion of square integrable energy-eigenstates of the 7 He nucleus (in the present calculation four 3/2 − states, of which only the first produces a substantial effect on the 2 P 3/2 resonance) compensates for missing higher 6 He excitations, leading to a much faster convergence rate. Finally, the present NCSMC calculation yields the well established 3/2 − g.s.…”

Section: The Unbound 7 He Nucleus As a Testing Groundmentioning

confidence: 74%

“…[11] is augmented by coupling fourteen (of which three 3/2 − and one 1/2 − ) NCSM eigenstates of the 5 He compound nucleus [15]. As for the 7 He nucleus in the previous section, the convergence with respect to the number of target states is now excellent. Further, the total cross section, presented in Fig.…”

Section: Three-nucleon Forces and Continuummentioning

confidence: 85%

“…To achieve this, we soften the chiral interactions using the similarity renormalization group (SRG) method [7][8][9][10]. This employes a continuous unitary transformation of the Hamiltonian…”

Section: Similarity Renormalization Group Methodsmentioning

confidence: 99%

“…An ideal system to showcase new achievements made possible by the ab initio NCSMC is 7 He [14]. The unified description of the structural and reaction properties of this unbound nucleus cannot be realized within the traditional NCSM.…”

Section: The Unbound 7 He Nucleus As a Testing Groundmentioning

confidence: 99%

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Toward a Fundamental Understanding of Nuclear Reactions and Exotic Nuclei

Quaglioni¹,

Hupin²,

Langhammer³

et al. 2015

Proceedings of the Conference on Advances in Radioactive Isotope Science (ARIS2014)

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Nuclear systems near the drip lines offer an exciting opportunity to advance our understanding of the interactions among nucleons, which has so far been mostly based on the study of stable nuclei. However, this is not a goal devoid of challenges. From a theoretical standpoint, it requires the capability to address within an ab initio framework not only bound, but also resonant and scattering states, all of which can be strongly coupled. In recent years, significant progress has been made in ab initio nuclear structure and reaction calculations based on input from Quantum Chromodynamics employing Hamiltonians constructed within chiral effective field theory. In this contribution, we present a brief overview of one of such methods, the ab initio no-core shell model with continuum, and its applications to nucleon and deuterium scattering on light nuclei. The first investigation of the low-lying continuum spectrum of 6 He within an ab initio framework that encompasses the 4 He+n+n three-cluster dynamics characterizing its lowest particle-decay channel will also be briefly presented.KEYWORDS: ab initio calculations, exotic nuclei, low-energy reactions Ab initio nuclear theory including the continuumLight exotic nuclei offer an exciting opportunity to test our understanding of nuclear properties in terms of forces emerging from the underlying theory of Quantum Chromodynamics (QCD). This is not a goal devoid of challenges. Experimentally, the study of rare nuclei is challenged by their short half lives and minute production cross sections. A major stumbling block in nuclear theory has to deal with the low breakup thresholds, which can lead to multi-particle emissions, and can cause bound, resonant and scattering states to be strongly coupled. Even worse, many of the systems we are interested in are simply unbound. Hence, to achieve a fundamental understanding of exotic nuclei we need both advanced experimental techniques and an ab initio nuclear theory including the continuum. In the following we briefly outline the elements of one of such theories, the ab initio no-core shell model with continuum (NCSMC). Nuclear forcesTo develop such an ab initio theory, we start from nuclear interactions grounded in the underlying theory of Quantum Chromodynamics via chiral effective field theory [1][2][3], where nucleons and pions are the only explicit degrees of freedom and the strong interaction is systematically expanded in terms of positive powers of small momenta Q (the generic momentum in the nuclear process or the pion mass) over the chiral symmetry breaking scale Λ ∼ 1 GeV. The nuclear forces emerging from such a procedure order by order are schematically represented by the diagrams of Fig. 1. In particular, we 1

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Dimensional Transmutation and Dimensional Regularization in Quantum Mechanics

et al. 2001

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This is the first in a series of papers addressing the phenomenon of dimensional transmutation in nonrelativistic quantum mechanics within the framework of dimensional regularization. Scale-invariant potentials are identified and their general properties are derived. A strategy for dimensional renormalization of these systems in the strong-coupling regime is presented, and the emergence of an energy scale is shown, both for the bound-state and scattering sectors. Finally, dimensional transmutation is explicitly illustrated for the two-dimensional delta-function potential.

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Renormalization of Hamiltonians

Cited by 488 publications

References 14 publications

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

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

Toward a Fundamental Understanding of Nuclear Reactions and Exotic Nuclei

Dimensional Transmutation and Dimensional Regularization in Quantum Mechanics

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