Contribution ofp-wave (3)+1 subamplitudes to4He binding energy and scattering observables below four-body breakup threshold

Fonseca, A. C.

doi:10.1007/bf01277075

Cited by 20 publications

(4 citation statements)

References 23 publications

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“…[6] and show that NN P waves not only have a strong effect in n-t elastic observables, but also that both AV14 and Bonn-B are able to describe the total n-t cross section at the peak. This may be rationalized in the following manner: as we know from 3N physics, 1 H͑ d, d͒ 1 H spin observables are strongly dependent on the NN P waves, even at low energy E d , 3 MeV; most of this dependence comes through the odd parity 3N amplitudes J 2 which, as we know from very early work on the four-nucleon system [19], make up for 50% of the total n-t cross section. This is again shown in Fig.…”

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confidence: 98%

Contribution of Nucleon-NucleonPWaves tont−nt,dd−pt<

Fonseca

1999

Phys. Rev. Lett.

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The four-body equations of Alt, Grassberger, and Sandhas [Phys. Rev. C 1, 85 (1970)] are solved for a system of four nucleons, using realistic NN interactions in channels j # 2. The results of the calculation are compared with data for the reactions dd ! dd, dd ! p 3 H, and n 3 H ! n 3 H. The calculations indicate that the NN P waves have a strong effect on 4N observables including a 10% contribution to the total n 3 H ! n 3 H cross section at the peak of the low energy resonance. PACS numbers: 21.45. + v, 13.75.Cs, 25.10. + s In a recent review article on the three-nucleon continuum [1] one finds that 1 H͑ d, d͒ 1 H elastic observables (cross sections, vector, and tensor polarizations) are insensitive to the choice of realistic NN potential. Beyond the persistent A y discrepancy at low energy, the agreement between calculations and data is excellent in the energy range up to 65 MeV. They also report that the A y discrepancy at low energy persists even when known static 3N force models are added to any realistic 2N interaction. The same conclusion is reached by others [2], where the NN interaction is modified by the coupling NN-ND. No matter what approach one follows to add a 3N force in the 3N system, the outcome is similar: beyond its effect on the 3N binding energy (about 1 MeV more binding), triton wave function related parameters (charge radii, asymptotic normalization constants), and doublet scattering length, all of which correlate almost linearly with the triton binding energy, the 3N force plays almost no role in d 1 p elastic scattering or breakup for deuteron laboratory energies up to E d Ӎ 65 MeV. This low energy behavior, though predicted by a few authors [3] 30 years ago, was confirmed in the last 10 years by the very accurate calculations of the Bochum and Pisa groups. Unlike d 1 N scattering, the triton is very sensitive to the choice of 2N or 2N 1 3N interaction. Therefore 3 H͑ n, n͒ 3 H or d͑ d, p͒ 3 H observables may show greater dependence on force models than 1 H͑ d, d͒ 1 H. Recent calculations of the four-nucleon system exist for the binding energy of the a particle [4], p 3 He and n 3 H scattering length [5] which may be considered of the same accuracy and sophistication as encountered in the 3N system. At higher energies, but still below three-body breakup threshold, there is the work of the Grenoble group [6] which calculates the cross section for 3 H͑n, n͒ 3 H using Malfliet-Tjon (MT) and Argonne V14 (AV14) potentials in channels 1 S 0 and 3 S 1 -3 D 1 . Because their calculation carries no approximations, beyond a limitation on the NN partial waves included or number of channels, the conclusions are very disturbing. They claim that, unlike MT, the realistic interaction (AV14) fails to describe the neutron-triton (n-t) total cross section at the peak of the resonance (E n 3.5 MeV) and preliminary results on the importance of NN P waves or a 3N force seem to indicate that they have almost no effect on the cross section at this energy; while the combined effect of 1 P 1 , 3 P 0 , and 3 ...

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confidence: 98%

Contribution of Nucleon-NucleonPWaves tont−nt,dd−pt<

Fonseca

1999

Phys. Rev. Lett.

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“…Tjon [213] made an interesting finding, namely that the effect of p-waves in the 3N subamplitudes is not negligible for low-energy 4N scattering. This was later confirmed in an AGS calculation [216], where it was shown that the effect is particularly strong in p-3 He elastic cross sections, but also noticeable in dd → p -3 H and dd → dd reactions. These studies of low-energy 4N scattering reactions by Fonseca with the AGS approach were continued in Ref.…”

Section: N Problem: the Early Phasementioning

confidence: 60%

Modern ab initio approaches and applications in few-nucleon physics with

Leidemann

Orlandini

2013

Progress in Particle and Nuclear Physics

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We present an overview of the evolution of ab initio methods for few-nucleon systems with A ≥ 4, tracing the progress made that today allows precision calculations for these systems. First a succinct description of the diverse approaches is given. In order to identify analogies and differences the methods are grouped according to different formulations of the quantum mechanical many-body problem. Various significant applications from the past and present are described. We discuss the results with emphasis on the developments following the original implementations of the approaches. In particular we highlight benchmark results which represent important milestones towards setting an ever growing standard for theoretical calculations. This is relevant for meaningful comparisons with experimental data. Such comparisons may reveal whether a specific force model is appropriate for the description of nuclear dynamics.

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“…Our results will be compared to several techniques: the variational method (VAR) [23], the Hyperspherical Harmonics expansion (HH) [24][25][26][27], several types of approximations for the subsystem kernels of the four-body problem by operators of finite rank (SKFR) [28][29][30][31][32], the integrodifferential equation approaches (IDEA) and the S-wave projected integrodifferential equation (SIDE) [33,34], the Coupled-RearrangementChannel (CRC) [35], the differential Faddeev-Yakubovsky (DFY) [1,36], the FY (PW) [3], and the coupled twodimensional integral equations (2DI) [20]. Our results for the triton and α-particle binding energies are shown in Tables II-V in comparison to the results of other techniques.…”

Section: A Results For N N Potential Modelsmentioning

confidence: 99%

Solutions of the bound-state Faddeev-Yakubovsky equations in three dimensions by usingNNand3Npotential models

2011

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A recently developed three-dimensional approach (without partial-wave decomposition) is considered to investigate solutions of Faddeev-Yakubovsky integral equations in momentum space for three-and four-body bound states, with the inclusion of three-body forces. In the calculations of the binding energies, spin-dependent nucleon-nucleon (NN) potential models [soft-core potential S3, Malfliet-Tjon (MT) I-III, Yamaguchi-type potentials (YS), and P 5.5 -model of Gibson-Lehman (P 55 GL)] are considered along with the scalar two-meson exchange three-body potential. The presently reported results agree well with the ones obtained by other techniques, demonstrating the advantage of an approach in which the formalism is much more simplified and easy to manage for direct computation.

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Contribution ofp-wave (3)+1 subamplitudes to4He binding energy and scattering observables below four-body breakup threshold

Cited by 20 publications

References 23 publications

Contribution of Nucleon-NucleonPWaves tont−nt,dd−pt<

Contribution of Nucleon-NucleonPWaves tont−nt,dd−pt<

Modern ab initio approaches and applications in few-nucleon physics with

Solutions of the bound-state Faddeev-Yakubovsky equations in three dimensions by usingNNand3Npotential models

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