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Viviani, M.; Deltuva, A.; Lazauskas, Rimantas; Fonseca, A. C.; Kievsky, A.; Marcucci, L. E.

doi:10.1103/physrevc.95.034003

Cited by 29 publications

(20 citation statements)

References 72 publications

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“…Just a few years later Faddeev's revolutionary work has been generalized to any number of particles by Yakubovsky [7]. Regardless these revolutionary mathematical developments progress in solution of Faddeev-Yakubovsky equations (FYe) is slow and for long years was limited to A=3 and A=4 cases [8,9]. The main difficulty is related to the complexity of these equations.…”

Section: Solution Of Nuclear Bound State Problem By Ab-initio Methodsmentioning

confidence: 99%

Solution of the n−He4 elastic scattering problem using the Faddeev-Yakubovsky equations

Lazauskas

2018

Phys. Rev. C

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Section: Solution Of Nuclear Bound State Problem By Ab-initio Methodsmentioning

confidence: 99%

Solution of the n−He4 elastic scattering problem using the Faddeev-Yakubovsky equations

Lazauskas

2018

Phys. Rev. C

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“…The functions Ω λ LSJJz have been given in Eq. (40). Note that, with the above definition, the reactance K-matrix elements can be related to the S-matrix elements as…”

Section: The a = 3 And 4 Scattering Statesmentioning

confidence: 99%

“…Also in this case, recently, in Ref. [40], a benchmark calculation has been performed with the HH, AGS and FE methods, using the N3LO-I interaction. Good agreement among the three methods has been found, with discrepancies smaller than the uncertainties in the experimental data.…”

Section: A a = 3 4 Bound Statesmentioning

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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“…The first solution of the scattering problem for the elastic 1+3, 2+2, and 1+3→ 2+3 rearrangement channels within the isospin approximation and S-wave interactions dated from 1998 [7], and it took twenty years more to obtain a full solution of the four-nucleon scattering problem with (i) realistic interactions [8][9][10] (ii) including charge-dependent (CD) and non local terms [11], (iii) Coulomb effects [12][13][14][15], (iv) three-and four-body breakup amplitudes [13,[16][17][18], and (v) a proper ab-initio determination of the 4N resonant states (e.g., 4n or 4 H) as S-matrix poles in the complex energy plane [6,[19][20][21][22][23]. There remains only the computation and analysis of the three-and four-body breakup differential cross-sections, since only the integrated cross-sections are nowadays available.…”

Section: Introductionmentioning

confidence: 99%

Description of Four- and Five-Nucleon Systems by Solving Faddeev-Yakubovsky Equations in Configuration Space

Lazauskas

Carbonell

2020

Front. Phys.

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The Faddeev-Yakubovsky equations constitute a rigorous formulation of the quantum mechanical N-body problem in the framework of non-relativistic dynamics. They allow the exact solutions of the Schrödinger equation for bound and scattering states to be obtained. In this review, we will present the general formalism as well as the numerical tools we use to solve Faddeev-Yakubovsky equations in configuration space. We will consider in detail the description of the four-and five-nucleon systems based on modern realistic nuclear Hamiltonians. Recent achievements in this domain will be summarized. Some of the still controversial issues related with the nuclear Hamiltonians as well as the numerical methods traditionally employed to solve few-nucleon problems will be highlighted.

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Benchmark calculation ofp−H3andn−He3

Cited by 29 publications

References 72 publications

Solution of the n−He4 elastic scattering problem using the Faddeev-Yakubovsky equations

Solution of the n−He4 elastic scattering problem using the Faddeev-Yakubovsky equations

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

Description of Four- and Five-Nucleon Systems by Solving Faddeev-Yakubovsky Equations in Configuration Space

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