Covariant equations for the three-body bound state

Stadler, Alfred; Gross, Franz; Frank, Michael R.

doi:10.1103/physrevc.56.2396

Cited by 78 publications

(104 citation statements)

References 41 publications

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“…One specific realization of this approach is the covariant spectator approach of Ref. [24]. In this paper the relativistic three-body problem is formulated within the framework of Poincaré invariant quantum mechanics.…”

Section: Introductionmentioning

confidence: 99%

First order relativistic three-body scattering

et al. 2007

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Relativistic Faddeev equations for three-body scattering at arbitrary energies are formulated in momentum space and in first order in the two-body transition-operator directly solved in terms of momentum vectors without employing a partial wave decomposition. Relativistic invariance is incorporated within the framework of Poincaré invariant quantum mechanics, and presented in some detail. Based on a Malfliet-Tjon type interaction, observables for elastic and break-up scattering are calculated up to projectile energies of 1 GeV. The influence of kinematic and dynamic relativistic effects on those observables is systematically studied. Approximations to the two-body interaction embedded in the three-particle space are compared to the exact treatment.

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Section: Introductionmentioning

confidence: 99%

First order relativistic three-body scattering

et al. 2007

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“…[5]. One obtains a homogeneous equation for the vertex function of the 3N bound state, shown graphically in Fig.…”

Section: Covariant Spectator Theory Of Two-and Three-nucleon Systemsmentioning

confidence: 99%

A Relativistic Theory of Few-Nucleon Systems

Stadler

2010

Few-Body Syst

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This talk provides an overview of recent results for two-and three-nucleon systems obtained within the framework of the covariant spectator theory (CST). The main features of two recently published models for the neutron-proton interaction, that fit the 2007 world data base containing several thousands of neutron-proton scattering data below 350 MeV with χ 2 /N data ≈ 1, are presented. These one-boson-exchange models, called WJC-1 and WJC-2, have a considerably smaller number of adjustable parameters than are present in realistic nonrelativistic potentials. When applied to the three-nucleon bound state, the correct binding energy is obtained without additional three-body forces. First calculations of the electromagnetic form factors of helium-3 and the triton in complete impulse approximation also give very reasonable results. One can conclude that the CST yields a very efficient description of few-nucleon systems, in which the relativistic formulation of the dynamics is an essential element. The Fundamental Ideas of the Covariant Spectator TheoryIn low-energy few-body nuclear physics, relativity is often considered an unwelcome complication that gives rise to only small effects, which can be either neglected or included perturbatively. The argument is usually based on the observation that typical kinetic energies of nucleons in light nuclear systems are small compared to their rest mass. However, a relativistic description of such systems becomes unavoidable when they are investigated with hadronic or electromagnetic probes at high momentum transfer and the final nuclear states reach relativistic velocities.This talk intends to show that relativity can also lead to a significant simplification of the description of fewnucleon systems. This will be demonstrated for the case of the covariant spectator theory (CST), where simple one-boson-exchange (OBE) models of the nucleon-nucleon (N N) interaction can be derived that provide a more efficient description of the N N observables than nonrelativistic models. This efficiency applies also to the 3N bound state, which can be well described without 3N forces. The obtained simplification depends crucially on relativity.The basic idea of the CST is to reorganize the manifestly covariant Bethe-Salpeter (BS) equation with its complete kernel to another equivalent form, in which a different propagator and an accordingly modified kernel is used. The specific propagator of the CST places all particles but one in intermediate states on their mass shells [1][2][3]. This reduces the dimension of the integration over intermediate momenta from four to

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“…The details of the partial-wave decomposition ideology for the quasi-potential equation can be found in the paper [6]. All steps should be made if the particles are considered as spin-one-half with corresponding spinor propagators S (i) .…”

Section: Two-particle Casementioning

confidence: 99%

On the relativistic³D₁partial-wave contribution to the bound three-nucleon system

2017

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Abstract. The bound state of three nucleons is investigated using the Faddeev equations within the Bethe-Salpeter approach. The relativistic and nonrelativistic nucleon-nucleon interaction is chosen in a multirank separable form. The extension for partial-states with L > 0 is done. Three partial-wave states -1 S 0 , 3 S 1 and 3 D 1 -are taken into account. The Gauss quadrature method is used to calculate the integrals and find the triton binding energy by iterations.

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Covariant equations for the three-body bound state

Cited by 78 publications

References 41 publications

First order relativistic three-body scattering

First order relativistic three-body scattering

A Relativistic Theory of Few-Nucleon Systems

On the relativistic³D₁partial-wave contribution to the bound three-nucleon system

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Covariant equations for the three-body bound state

Cited by 78 publications

References 41 publications

First order relativistic three-body scattering

First order relativistic three-body scattering

A Relativistic Theory of Few-Nucleon Systems

On the relativistic3D1partial-wave contribution to the bound three-nucleon system

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On the relativistic³D₁partial-wave contribution to the bound three-nucleon system