A stochastic variational method for few-body systems

Kukulin, V. I.; Krasnopolsky, Vladimir M.

doi:10.1088/0305-4616/3/6/011

Cited by 184 publications

(158 citation statements)

References 15 publications

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“…[105], enabling the first few energy levels of non-strange baryons for a linearly rising potential to be determined, was helped by the assumed link between the quark-antiquark potential in mesons and the quark-quark potential appearing in baryons. Early potential models paved the way to more sophisticated analyses by the introduction of converged variational methods [115][116][117] and the use of Faddeev equations [19,[117][118][119]. Connections to the heavy quark sector of QCD have been established on the one hand via heavy quark effective theory and nonrelativistic QCD, see e.g.…”

Section: The Quark Modelmentioning

confidence: 99%

Baryons as relativistic three-quark bound states

Eichmann

Sanchis-Alepuz

Williams

et al. 2016

Progress in Particle and Nuclear Physics

406

530

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We review the spectrum and electromagnetic properties of baryons described as relativistic three-quark bound states within QCD. The composite nature of baryons results in a rich excitation spectrum, whilst leading to highly non-trivial structural properties explored by the coupling to external (electromagnetic and other) currents. Both present many unsolved problems despite decades of experimental and theoretical research. We discuss the progress in these fields from a theoretical perspective, focusing on nonperturbative QCD as encoded in the functional approach via Dyson-Schwinger and Bethe-Salpeter equations. We give a systematic overview as to how results are obtained in this framework and explain technical connections to lattice QCD. We also discuss the mutual relations to the quark model, which still serves as a reference to distinguish 'expected' from 'unexpected' physics. We confront recent results on the spectrum of non-strange and strange baryons, their form factors and the issues of two-photon processes and Compton scattering determined in the DysonSchwinger framework with those of lattice QCD and the available experimental data. The general aim is to identify the underlying physical mechanisms behind the plethora of observable phenomena in terms of the underlying quark and gluon degrees of freedom.

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Section: The Quark Modelmentioning

confidence: 99%

Baryons as relativistic three-quark bound states

Eichmann

Sanchis-Alepuz

Williams

et al. 2016

Progress in Particle and Nuclear Physics

406

530

View full text Add to dashboard Cite

show abstract

“…Although it involves the solution of a complex eigenvalue problem which causes some difficulties in practice, the CSM has been widely and successfully used to study resonances in atomic and molecular systems [11,12,13] and atomic nuclei [9,10,14,15,16]. The analytical continuation in the coupling constant (ACCC) approach is based on an intuitive idea that a resonant state can be lowered to be bound when the potential becomes more attractive or equivalently the coupling constant stronger, thus a resonant state being related to a series of bound states via an analytical continuation in the coupling constant [17,18,19]. Combined with the cluster model, the ACCC approach has been used to calculate the resonant energies and widths in some light nuclei [20,21].…”

Section: Introductionmentioning

confidence: 99%

Real stabilization method for nuclear single-particle resonances

et al. 2008

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We develop the real stabilization method within the framework of the relativistic mean field (RMF) model. With the self-consistent nuclear potentials from the RMF model, the real stabilization method is used to study single-particle resonant states in spherical nuclei. As examples, the energies, widths and wave functions of low-lying neutron resonant states in 120 Sn are obtained. These results are compared with those from the scattering phase shift method and the analytic continuation in the coupling constant approach and satisfactory agreements are found.

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“…For two particles in this case it is known [22] that ξ = 1 for a S-wave and ξ = 1 2 for P -waves and higher ones. For a three-body system and the three-body break-up threshold we are not aware of an analytical insight into the value ξ.…”

Section: Resonance Prediction Via Padémentioning

confidence: 95%

“…The interesting idea to predict low lying resonances with the help of Padé approximants from a sequence of (auxiliary) bound state energies has been proposed in [22] and exemplified for instance in [23]. We also applied it to the system of 3n's.…”

Section: Resonance Prediction Via Padémentioning

confidence: 99%

Indications for the Nonexistence of Three-Neutron Resonances Near the Physical Region

Hemmdan

Glöckle

Kamada

2003

Few-Body Problems in Physics ’02

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The pending question of the existence of three-neutron resonances near the physical energy region is reconsidered. Finite rank neutron-neutron forces are used in Faddeev equations, which are analytically continued into the unphysical energy sheet below the positive real energy axis. The trajectories of the three-neutron S-matrix poles in the states of total angular momenta and parity J π = 1 2 ± and J π = 3 2 ± are traced out as a function of artificial enhancement factors of the neutron-neutron forces. The final positions of the S-matrix poles removing the artificial factors are found in all cases to be far away from the positive real energy axis, which provides a strong indication for the nonexistence of nearby three-neutron resonances. The pole trajectories close to the threshold E = 0 are also predicted out of auxiliary generated three-neutron bound state energies using the Padé method and agree very well with the directly calculated ones.

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A stochastic variational method for few-body systems

Cited by 184 publications

References 15 publications

Baryons as relativistic three-quark bound states

Baryons as relativistic three-quark bound states

Real stabilization method for nuclear single-particle resonances

Indications for the Nonexistence of Three-Neutron Resonances Near the Physical Region

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