Integrodifferential equation approach. I. Triton and α-particle binding energies

Oehm, W.; Sofianos, S. A.; Fiedeldey, H.; Ripelle, M. Fabre de la

doi:10.1103/physrevc.42.2322

Cited by 29 publications

(10 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As such they allow the description of the Abody wave function in terms of a single length variable, the hyper-radius ρ, and (D − 1) hyper-angular variables Ω [62,63]. Removing the center-of-mass coordinate, the A-body dynamics can be described by A − 1 Jacobi vec-…”

Section: A the Effective-interaction Hypersphericalmentioning

confidence: 99%

Spectra and scattering of light lattice nuclei from effective field theory

et al. 2015

View full text Add to dashboard Cite

An effective field theory is used to describe light nuclei, calculated from quantum chromodynamics on a lattice at unphysically large pion masses. The theory is calibrated at leading order to two available data sets on two-and three-body nuclei for two pion masses. At those pion masses we predict the quartet and doublet neutron-deuteron scattering lengths, and the alpha-particle binding energy. For mπ=510 MeV we obtain, respectively, 4 anD = 2.3 ± 1.3 fm, 2 anD = 2.2 ± 2.1 fm, and B α = 35 ± 22 MeV, while for mπ=805 MeV 4 anD = 1.6 ± 1.3 fm, 2 anD = 0.62 ± 1.0 fm, and B α = 94 ± 45 MeV are found. Phillips-and Tjon-like correlations to the triton binding energy are established. We find the theoretical uncertainty in the respective correlation bands to be independent of the pion mass. As a benchmark, we present results for the physical pion mass, using experimental two-body scattering lengths and the triton binding energy as input. Hints of subtle changes in the structure of the triton and alpha particle are discussed.

show abstract

Section: A the Effective-interaction Hypersphericalmentioning

confidence: 99%

Spectra and scattering of light lattice nuclei from effective field theory

et al. 2015

View full text Add to dashboard Cite

show abstract

“…Therefore the use of more accurate nuclear wave functions is of utmost importance. Such realistic wave functions can be constructed, for instance, by means of the Integrodifferential Equation Approach (IDEA) [28,29], and are in progress. Table I.…”

mentioning

confidence: 99%

Threshold scattering of the η-meson off light nuclei

et al. 1995

View full text Add to dashboard Cite

The scattering lengths of η-meson collisions with light nuclei 2 H, 3 H, 3 He, and 4 He are calculated on the basis of few-body equations in coherent approximation. It is found that the η-nucleus scattering length depends strongly on the number of nucleons and the potential-range parameter. By taking into account the off-shell behavior of the ηN amplitude, the ηα scattering length increases considerably.In η-nucleus collisions at threshold energies, a large Final State Interaction (FSI) is expected due to the N * (1535) S 11 -resonance. This resonance, which is strongly coupled to the ηN and πN channels, lies only ∼ 50 MeV above the ηN threshold and has a very broad width of Γ ≈ 150 MeV [1]. The η-nucleus dynamics, thus, is of interest from the point of view of both few-body and meson-nucleon physics.In the energy region covering the S 11 -resonance, the πN and ηN scattering processes are to be considered as a coupled-channel problem [2][3][4]. The first of these channels has a long record of theoretical and experimental investigations, while the second one is understood only in a rudimentary way. The πN and ηN channels are connected to each other primarily via the N * (1535) resonance. In fact, the ηNN coupling constant was shown to be negligible [5][6][7] as compared to the one of the ηNN * vertex. This latter vertex constant, being hence crucial for determining the ηN interaction, is known only with a large uncertainty, so that the ηN scattering length inferred from it varies from (0.27 + i 0.22)fm [2] to (0.55 + i 0.30)fm [8]. The ηN near-threshold interaction, therefore, remains an interesting field of investigation. Of particular relevance in this context is the possibility of η-nucleus bound states [9,10]. Their existence would provide us with an excellent opportunity to answer the above-mentioned questions in a reliable manner.

show abstract

“…Our results will be compared to several techniques: the VAR [23] and HH [24]- [27] methods, several types of approximations for the subsystem kernels of the four-body problem by operators of finite rank (SKFR) [28]- [32], the integrodifferential equation approaches SIDE [33] and IDEA [34], the CRC [35], the DFY [1,36], the FY (PW) [3], and last, but not least, 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%

“…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

View full text Add to dashboard Cite

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.

show abstract

Integrodifferential equation approach. I. Triton and α-particle binding energies

Cited by 29 publications

References 23 publications

Spectra and scattering of light lattice nuclei from effective field theory

Spectra and scattering of light lattice nuclei from effective field theory

Threshold scattering of the η-meson off light nuclei

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

Contact Info

Product

Resources

About