Local chiral interactions, the tritium Gamow-Teller matrix element, and the three-nucleon contact term

Baroni, Alessandro; Schiavilla, R.; Marcucci, L. E.; Girlanda, L.; Kievsky, A.; Lovato, Alessandro; Pastore, Saori; Piarulli, M.; Pieper, Steven C.; Viviani, M.; Wiringa, R. B.

doi:10.1103/physrevc.98.044003

Cited by 80 publications

(114 citation statements)

References 58 publications

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“…[67] for the two-nucleon, and in Refs. [1,68] for the thee-nucleon interaction. The two-nucleon models are labeled NVIa, NVIIa, NVIb and NVIIb depending on the cutoff value and the maximum laboratory energy of the considered N N database.…”

Section: Selected Resultsmentioning

confidence: 99%

The Hyperspherical Harmonics Method: A Tool for Testing and Improving Nuclear Interaction Models

et al. 2020

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The Hyperspherical Harmonics (HH) method is one of the most accurate techniques to solve the quantum mechanical problem for nuclear systems with A ≤ 4. In particular, by applying the Rayleigh-Ritz or Kohn variational principle, both bound and scattering states can be addressed, using either local or non-local interactions. Thanks to this versatility, the method can be used to test the two-and three-nucleon components of the nuclear interaction.In the present review we introduce the formalism of the HH method, both for bound and scattering states. In particular, we describe the implementation of the method to study the A = 3 and 4 scattering problem. Second, we present a selected choice of results of the last decade, most representative of the latest achievements. Finally, we conclude with a discussion of what we believe will be the most significant developments within the HH method for the next five-to-ten years.on Monte Carlo techniques, as the variational Monte Carlo (VMC) or the Green's function Monte Carlo (GFMC) methods (see Ref. [7], and references therein). There are then the methods linked to the shell model, as the no-core shell model (NCSM) or the realistic shell model (RSM), see Refs. [8] and [9,10], respectively. All these methods are quite powerful to study medium-mass nuclear bound states, but less accurate, apart from the GFMC and NCSM, for very light nuclei, as those with A = 3, 4. Furthermore, their extension to the scattering systems is not so trivial, and, in some cases, still not at reach.Restricting ourselves to the A = 3, 4 nuclear systems, both bound and scattering states, we have at hand very few accurate ab-initio methods, i.e. the Faddeev (Faddeev-Yakubovsky for A = 4) equations (FE) technique, solved in coordinate-or in momentum-space, the method based on the Alt-Grassberger-Sandhas (AGS) equations solved in momentum space, and the Hyperspherical Harmonics (HH) method presented here. We refer the reader to Refs. [11, 12] for the FE method in coordinate space, to Refs. [13,14] for the FE method in momentum space, to Refs. [15,16] for recent reviews on the AGS method. Clearly, each method has advantages and drawbacks. For instance, the FE method in momentum space can be applied to A = 3, 4 bound and scattering states in a wide energy range. However, the inclusion of the Coulomb interaction for charged particle scattering states is quite problematic. The FE method in coordinate space can handle the Coulomb interaction, but it has not yet been applied to scattering problems at very low-energy, and it has been applied only recently to study systems with larger A values [17]. It is though a method with in principle great possibilities of extension [12]. The AGS method, although working in momentum space, can handle the Coulomb interaction, and can be applied to a large variety of A = 3, 4 scattering states, in a wide energy range. However, the very low energy range, that of interest for nuclear astrophysics, i.e. below ∼ 100 keV, is still not accessible with the AGS method. The method has ...

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Section: Selected Resultsmentioning

confidence: 99%

The Hyperspherical Harmonics Method: A Tool for Testing and Improving Nuclear Interaction Models

et al. 2020

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“…The contact terms are implemented via a Gaussian representation of the three-dimensional delta function with R S as the Gaussian parameter [92,10,96]. The pion-range operators are regularized at high-value of momentum transfer via a special radial function characterized by the cutoff R L [92,10,96]. There are two classes of these potentials.…”

Section: Nuclear Interactionsmentioning

confidence: 99%

“…In the first, the 3N unknown LECs were determined by simultaneously reproducing the experimental trinucleon ground-state energies and neutron-deuteron (nd) doublet scattering length for each of the 2N models considered, namely NV2-Ia/b and NV2-IIa/b [11,97]. In the second set, these LECs were constrained by fitting, in addition to the trinucleon energies, the empirical value of the Gamow-Teller matrix element in tritium β-decay [96]. The resulting Hamiltonians were labelled as NV2+3-Ia/b and NV2+3-IIa/b (or Ia/b and IIa/b for short) in the first case, and as NV2+3-Ia * /b * and NV2+3-IIa * /b * (or Ia * /b * and IIa * /b * ) in the second.…”

Section: Nuclear Interactionsmentioning

confidence: 99%

Atomic Nuclei From Quantum Monte Carlo Calculations With Chiral EFT Interactions

et al. 2020

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Quantum Monte Carlo methods are powerful numerical tools to accurately solve the Schrödinger equation for nuclear systems, a necessary step to describe the structure and reactions of nuclei and nucleonic matter starting from realistic interactions and currents. These ab-initio methods have been used to accurately compute properties of light nuclei -including their spectra, moments, and transitions -and the equation of state of neutron and nuclear matter. In this work we review selected results obtained by combining quantum Monte Carlo methods and recent Hamiltonians constructed within chiral effective field theory. Keywords: Quantum Monte Carlo methods, variational Monte Carlo, Green's function Monte Carlo, auxiliary field diffusion Monte Carlo, chiral effective field theory, nuclear Hamiltonians, nuclear structure 1 arXiv:2001.01374v1 [nucl-th] 6 Jan 2020 Gandolfi et al.Atomic nuclei from QMC calculations with χEFT interactions potentials that are consistent with the symmetries of QCD. The solution of nuclear many-body problems requires two main ingredients: an Hamiltonian that accurately models the interactions among the nucleons, and reliable numerical many-body methods to solve the corresponding Schrödinger equation.Microscopic nuclear Hamiltonians, capable of reproducing nucleon-nucleon scattering data and the properties of few-body systems, have been successfully used to describe light nuclei. For example the highly-realistic Argonne v 18 two-body potential [3] combined with the phenomenological Illinois-7 three-body force have been employed to predict several properties of nuclei up to A = 12 with great accuracy [4]. Several calculations of energies, rms radii, transitions, and densities turn out to be in excellent agreement with experimental data. The main limitation of these phenomenological Hamiltonians is that it is not clear how they can be systematically improved, and how to quantify theoretical, i.e., systematic, uncertainties related to the specific interaction model. Another approach that became very popular in the last two decades consist in deriving nuclear interactions within the framework of chiral Effective Field Theory (χEFT). The advantage of this approach is that it provides the necessary tools to systematically improve the interaction models, to estimate uncertainties related to the truncation of the chiral expansion, and to consistently derive electroweak currents. Frontiers

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“…At this order, as we have mentioned above, 3N forces are characterized by the presence of two unknown LECs that have to be determined. The two LECs -namely c D in the OPE-contact and c E in the 3N contact interaction -have been constrained either by fitting exclusively strong-interaction observables [90,91,92,93] or by relying on a combination of strong-and weak-interaction observables [94,95,96]. This last approach is made possible by the relation between c D in the OPE-contact interaction and the LEC in the NN contact axial current [94,95], established in chiral EFT [97].…”

Section: Chiral Effective Field Theorymentioning

confidence: 99%

“…Note that these observables have been calculated with hyperspherical-harmonics (HH) expansion methods [5] as described in Refs. [93,96].…”

Section: With Delta Isobarsmentioning

confidence: 99%

Local Nucleon-Nucleon and Three-Nucleon Interactions Within Chiral Effective Field Theory

Piarulli¹,

Tews

2020

Front. Phys.

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To obtain an understanding of the structure and reactions of nuclear systems from first principles has been a long-standing goal of nuclear physics. In this respect, few-and many-body systems provide a unique laboratory for studying nuclear interactions. During the past decades, the development of accurate representations of the nuclear force has undergone substantial progress. Particular emphasis has been devoted to chiral effective field theory (EFT), a low-energy effective representation of quantum chromodynamics (QCD). Within chiral EFT, many studies have been carried out dealing with the construction of both the nucleon-nucleon (NN ) and three-nucleon (3N ) interactions. The aim of the present article is to give a detailed overview of the chiral interaction models that are local in configuration space, and show recent results for nuclear systems obtained by employing these local chiral forces. Keywords: nuclear interactions, chiral effective field theory, local interactions, three-body forces, ab-initio calculations arXiv:2002.00032v1 [nucl-th] 31 Jan 2020 Piarulli et al. Local chiral interactionsIn fact, chiral symmetry is broken twofold. First, it is broken spontaneously, leading to the formation of Goldstone bosons, that can be identified with the pions. Second, chiral symmetry is also explicitly broken by the finite quark masses, which leads to the pion being pseudo-Goldstone bosons with finite but small mass. In contrast, isospin symmetry remains a good symmetry, because the ratio (m d − m u )/Λ QCD is very small, where m u 2.4 MeV and m d 4.8 MeV.These symmetries only allow certain operator structures for nuclear interactions. Galilean invariance, for instance, implies that nuclear interactions depend only on relative momenta between two nucleons, p = p i − p j , while symmetry under parity transformations implies that nuclear interactions cannot be Frontiers

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Local chiral interactions, the tritium Gamow-Teller matrix element, and the three-nucleon contact term

Cited by 80 publications

References 58 publications

The Hyperspherical Harmonics Method: A Tool for Testing and Improving Nuclear Interaction Models

The Hyperspherical Harmonics Method: A Tool for Testing and Improving Nuclear Interaction Models

Atomic Nuclei From Quantum Monte Carlo Calculations With Chiral EFT Interactions

Local Nucleon-Nucleon and Three-Nucleon Interactions Within Chiral Effective Field Theory

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