The Schwinger variational principle for charged particle scattering on atomic systems

Belyaev, Vladimir; Podkopayev, A P; Wrzecionko, J.; Zubarev, Alexander L.

doi:10.1088/0022-3700/12/7/022

Cited by 14 publications

(5 citation statements)

References 10 publications

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“…The equations employed are obtained within the Finite-Rank Hamiltonian Approximation (FRHA), proposed in Refs. [18,19] as an alternative to the multiple scattering or optical potential theory. Developed originally for the treatment of pion-nucleus scattering, this technique was later on also applied to other questions of few-body physics, such as the Λ-nucleus bound state problem [20] or the NN-scattering in a six quark model [19].…”

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confidence: 99%

Threshold scattering of the η-meson off light nuclei

et al. 1995

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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.

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Threshold scattering of the η-meson off light nuclei

et al. 1995

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“…The Schwinger variational principle (SVP) [40][41][42][43] can be generalized to the case of Eq. (8).…”

Section: Schwinger Variational Principlementioning

confidence: 99%

“…The Schwinger variational principle (SVP) [40][41][42][43] can be generalized to the case of equation (8). Since the entire treatment is based on the equivalence of the SVP and the method of separable representation, we briefly describe this method.…”

Section: The Schwinger Variational Principlementioning

confidence: 99%

Hydrodynamic modes in a trapped strongly interacting Fermi gas of atoms

Kim

Zubarev

2005

J. Phys. B: At. Mol. Opt. Phys.

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The zero-temperature properties of a dilute two-component Fermi gas in the BCS-BEC crossover are investigated. On the basis of a generalization of the variational Schwinger method, we construct approximate semi-analytical formulae for collective frequencies of the radial and the axial breathing modes of the Fermi gas under harmonic confinement in the framework of the hydrodynamic theory. It is shown that the method gives nearly exact solutions.

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“…The Bateman method had drawn some interest in 1970's in the context of few-body scattering calculations [18][19][20][21][22][23]. However, almost all discussions and applications have been restricted to partial-wave (single-variable) LS equations.…”

Section: Introductionmentioning

confidence: 99%

Multi-variate Bateman method for two-body scattering without partial-wave decomposition

Kuruoglu

2014

J Math Chem

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The use of Bateman method for solving the two-variable version of the twobody Lippmann-Schwinger equation without recourse to partial-wave decomposition is investigated. Bateman method is based on a special kind of interpolation of the momentum representation of the potential on a multi-variate grid. A suitable scheme for the generation of a multi-variate Cartesian grid is described. The method is tested on the Hartree potential for electron-hydrogen scattering in the static no-exchange approximation. Our results show that the Bateman method is capable of producing quite accurate solutions with relatively small number of grid points.Keywords Quantum scattering theory · Lippmann-Schwinger equation · Few-body collisions · Multi-variate interpolation and approximation · Bateman interpolation · Degenerate-kernel methods for integral equations · Nystrom method · Faddeev equations

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The Schwinger variational principle for charged particle scattering on atomic systems

Cited by 14 publications

References 10 publications

Threshold scattering of the η-meson off light nuclei

Threshold scattering of the η-meson off light nuclei

Hydrodynamic modes in a trapped strongly interacting Fermi gas of atoms

Multi-variate Bateman method for two-body scattering without partial-wave decomposition

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