Systematical treatment of the non-relativistic n-particle scattering problem

Grassberger, Peter; Sandhas, W.

doi:10.1016/0550-3213(67)90017-x

Cited by 281 publications

(186 citation statements)

References 26 publications

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“…Surrogate reactions involving charged particles, such as (d,p) reactions are complicated because they require a correct treatment of the interaction between its constituents to all orders. A popular tool to treat these systems is the Alt-Grassberger-Sandhas (AGS) [357] formalism. They arise from the Faddeev formalism treating the system (a+b)+A, and its rearrangements a + (b + A) and b + (a + A).…”

Section: Single-particle Ab-initio Methodsmentioning

confidence: 99%

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Current Status of Nuclear Physics Research

Bertulani

Hussein

2015

Braz J Phys

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In this review we discuss the current status of research in nuclear physics which is being carried out in different centers in the World. For this purpose we supply a short account of the development in the area which evolved over the last 9 decades, since the discovery of the neutron. The evolution of the physics of the atomic nucleus went through many stages as more data become available. We briefly discuss models introduced to discern the physics behind the experimental discoveries, such as the shell model, the collective model, the statistical model, the interacting boson model, etc., some of these models may be seemingly in conflict with each other, but this was shown to be only apparent.The richness of the ideas and abundance of theoretical models attests to the important fact that the nucleus is a really singular system in the sense that it evolves from two-body bound states such as the deuteron, to few-body bound states, such as 4 He, 7 Li, 9 Be etc. and up the ladder to heavier bound nuclei containing up to more than 200 nucleons. Clearly statistical mechanics, usually employed in systems with very large number of particles, would seemingly not work for such finite systems as the nuclei, neither do other theories which are applicable to condensed matter. The richness of nuclear physics stems from these restrictions. New theories and models are presently being developed. Theories of the structure and reactions of neutron-rich and proton-rich nuclei, called exotic nuclei, halo nuclei, or Borromean nuclei, deal with the wealth of experimental data that became available in the last 35 years. Further, nuclear astrophysics and stellar and Big Bang nucleosynthesis have become a more mature subject. Due to limited space, this review only covers a few selected topics, mainly those with which the authors have worked on. Our aimed potential readers of this review are nuclear physicists and physicists in other areas, as well as graduate students interested in pursuing a career in nuclear physics.

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Section: Single-particle Ab-initio Methodsmentioning

confidence: 99%

“…In each of these channels the three-particle scattering is described in terms of the transition operators T βα , where α(β) corresponds to a set of channel permutation combination. They obey the AGS equations [357] that are a system of coupled integral equations given by…”

Section: Single-particle Ab-initio Methodsmentioning

confidence: 99%

Current Status of Nuclear Physics Research

Bertulani

Hussein

2015

Braz J Phys

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“…However, its theoretical description is technically and computationally highly challenging. Exact four-particle scattering equations have been formulated 50 years ago by Faddeev and Yakubovsky (FY) [1] and by Alt, Grassberger, and Sandhas (AGS) [2,3]. However, their numerical solution using realistic force models only became possible many years later.…”

Section: Introductionmentioning

confidence: 99%

“…However, their numerical solution using realistic force models only became possible many years later. In the last decade accurate numerical calculations for low-energy nucleon-trinucleon elastic scattering have been performed using both coordinate-space and momentum-space rigorous approaches, namely, the hyperspherical harmonics (HH) expansion method [4,5], the Faddeev-Yakubovsky (FY) equations [1] for the wave function components [6], and the Alt, Grassberger and Sandhas (AGS) equations [3] for transition operators [7,8]. The reliability of all these methods was confirmed in a benchmark calculation [9] for neutron-3 H (n-3 H) and proton-3 He (p-3 He) elastic scattering observables.…”

Section: Introductionmentioning

confidence: 99%

Reactions in the four-nucleon system above breakup threshold

Deltuva

Fonseca

2016

EPJ Web of Conferences

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Abstract. Microscopic calculations of four-body scattering become very challenging in the energy regime above the threshold for four free particles. We consider mixed-isospin four-nucleon reactions initiated by the proton-3 H, neutron-3 He, or deuteron-deuteron collisions. We solve the Alt, Grassberger, and Sandhas equations for the four-nucleon transition operators in the momentum-space framework. The complex-energy method with special integration weights is applied to deal with the complicated singularities in the kernel of AGS equations. Results for the differential cross section and spin observables in elastic, charge-exchange, transfer, and breakup reactions using realistic potentials are presented.

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“…These problems persist even when the Coulomb interaction is added [1,2,3] and seem to be insensitive to the choice of realistic 2N + 3N force model. As it has already been highlighted in the past [4,5,6], the four-nucleon scattering problem reveals further discrepancies between theory and experiment that need clarification in terms of improved calculations using modern force models and efficient numerical algorithms that allow for a numerically converged solution of the Alt, Grassberger and Sandhas (AGS) equation [7] for the transition operators.…”

Section: Introductionmentioning

confidence: 99%

Four-nucleon scattering: a new numerical approach

Deltuva

Fonseca

2007

Nuclear Physics A

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The AGS equations are solved for n 3 H and p 3 He scattering including the Coulomb interaction. Comparison with previous work confirms the accuracy of the calculation and helps clarify a number of issues related to the n 3 H total cross section at the peak of the resonance region, as well as an A y deficiency in p 3 He. Calculations are fully converged in terms of NN partial waves and involve no uncontrolled approximations.

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Systematical treatment of the non-relativistic n-particle scattering problem

Cited by 281 publications

References 26 publications

Current Status of Nuclear Physics Research

Current Status of Nuclear Physics Research

Reactions in the four-nucleon system above breakup threshold

Four-nucleon scattering: a new numerical approach

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