Reduction of the three-particle collision problem to multi-channel two-particle Lippmann-Schwinger equations

Alt, E. O.; Grassberger, Peter; Sandhas, W.

doi:10.1016/0550-3213(67)90016-8

Cited by 958 publications

(580 citation statements)

References 13 publications

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“…These equations, usually referred to as AGS equations (for Alt, Grassberger and Sandhas) [42], are coupled integral equations for the transition operators…”

Section: A Faddeev Theorymentioning

confidence: 99%

Improved description ofAr34,36,46(p,d) transfer reactio

2011

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An improved description of single neutron stripping from 34,36,46 Ar beams at 33 MeV/nucleon by a hydrogen target is presented and the dependence on the neutron-proton asymmetry of the spectroscopic factors is further investigated. A finite range adiabatic model is used in the analysis and compared to previous zero range and local energy approximations. Full three-body Faddeev calculations are performed to estimate the error in the reaction theory. In addition, errors from the optical potentials are also evaluated. From our new spectroscopic factors extracted from transfer, it is possible to corroborate the neutron-proton asymmetry dependence reported from knockout measurements.

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“…These equations, usually referred to as AGS equations (for Alt, Grassberger and Sandhas) [42], are coupled integral equations for the transition operators…”

Section: A Faddeev Theorymentioning

confidence: 99%

Improved description ofAr34,36,46(p,d) transfer reactio

2011

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“…Then with the Faddeev formulation of the three-body system [29] or the equivalent Alt-Grassberger-Sandhas (AGS) equations [30], where the latter ones are ideally suited for finite rank forces, a new epoch started. In the following we shall not distinguish between the two and just call them for short "Faddeev approach".…”

Section: Introductionmentioning

confidence: 99%

Electron and photon scattering on three-nucleon bound states

et al. 2005

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A big spectrum of processes induced by real and virtual photons on the 3 He and 3 H nuclei is theoretically investigated through many examples based on nonrelativistic Faddeev calculations for bound and continuum states. The modern nucleon-nucleon potential AV18 together with the threenucleon force UrbanaIX is used. The single nucleon current is augmented by explicit π-and ρ-like two-body currents which fulfill the current continuity equation together with the corresponding parts of the AV18 potential. We also employ the Siegert theorem, which induces many-body contributions to the current operator. The interplay of these different dynamical ingredients in the various electromagnetic processes is studied and the theory is compared to the experimental data.Overall we find fair to good agreement but also cases of strong disagreement between theory and experiment, which calls for improved dynamics. In several cases we refer the reader to the work of other groups and compare their results with ours. In addition we list a number of predictions for observables in different processes which would challenge this dynamical scenario even more stringently and systematically.

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“…In this way the asymptotic boundary conditions are implicitly built into the form of equations but lead to kernels with integrable singularities. Considering the three 4 He atoms as identical bosons it is most convenient to use the symmetrized form of Faddeev equations in the Alt-Grassberger-Sandhas (AGS) version [12]; formally they coincide with the ones employed for the fermionic three-nucleon system [10; 11]. The only difference is in the properties of the basis states, namely, they must be symmetric under the exchange of particles within pair (12) which is chosen as a representative pair.…”

Section: Integral Equations For Three-atom Bound State and Scatteringmentioning

confidence: 99%

“…Considering the three 4 He atoms as identical bosons it is most convenient to use the symmetrized form of Faddeev equations in the Alt-Grassberger-Sandhas (AGS) version [12]; formally they coincide with the ones employed for the fermionic three-nucleon system [10; 11]. The only difference is in the properties of the basis states, namely, they must be symmetric under the exchange of particles within pair (12) which is chosen as a representative pair. The potential v acting within this pair in the integral formulation is summed up into the respective two-particle transition matrix using the Lippmann-Schwinger equation…”

Section: Integral Equations For Three-atom Bound State and Scatteringmentioning

confidence: 99%

Momentum-Space Calculation of 4He Triatomic System with Realistic Potential

Deltuva

2015

Few-Body Syst

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The system of three 4 He atoms with realistic interactions is studied in the momentum-space framework. It is demonstrated that short and long-range difficulties encountered in the coordinatespace calculations can be reliably resolved in the momentum-space calculations. Well-converged and accurate results are obtained for the ground and excited trimer energies, atom-dimer scattering length, phase shifts, inelasticity parameters, and elastic and breakup cross sections. A significant correction to previously published results is found for the elastic cross section at very low energy.

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Reduction of the three-particle collision problem to multi-channel two-particle Lippmann-Schwinger equations

Cited by 958 publications

References 13 publications

Improved description ofAr34,36,46(p,d) transfer reactio

Improved description ofAr34,36,46(p,d) transfer reactio

Electron and photon scattering on three-nucleon bound states

Momentum-Space Calculation of 4He Triatomic System with Realistic Potential

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