Calculation of resonances in the Coulomb three-body system with two disintegration channels in the adiabatic hyperspherical approach

Abramov, D. I.; Гусев, В. В.

doi:10.1088/0953-4075/38/23/009

Cited by 5 publications

(3 citation statements)

References 19 publications

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“…Finally, the transition probabilities can then be calculated by equation (13) from the corresponding known S-matrix elements (22). The application of the reprojection t-matrix method to n + H collisions improves the results by two or three orders of magnitude, as shown in figure 1 by the solid lines.…”

Section: Reprojection T-matrix Methodsmentioning

confidence: 96%

“…Within the standard adiabatic approach, the process is treated in two steps: (i) consideration of electrons in the fixed-nuclei approximation, that is, calculation of quantum-chemical data, and (ii) consideration of the nuclear dynamics based on the data obtained in the first step. In contrast to the hyperspherical adiabatic approach [12,13], where hyperspherical coordinates are used for electrons and nuclei, the standard adiabatic approach uses Jacobi coordinates, in which the Hamiltonian of the entire system has the simplest form.…”

Section: Standard Interpretation Of the Bo Approachmentioning

confidence: 99%

“…The great majority of theoretical studies of slow collisions are carried out within the standard adiabatic approach [1][2][3][4][5][6] based on the Born-Oppenheimer (BO) separation of the electronic and nuclear motion. In general, inelastic collisional processes can be treated by other approaches as well: the semiclassical approach [7,8], the use of the state specific coordinates [9], solutions of the Faddeev equations [10], the hyperspherical adiabatic approach [11][12][13] to mention a few. Nevertheless, all methods are conceptionally rather complicated, as compared to Massey's original concept, and have not found wide applications so far.…”

Section: Introductionmentioning

confidence: 99%

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Nonadiabatic effects in inelastic collisional processes

Belyaev¹

2009

Phys. Scr.

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The standard adiabatic Born–Oppenheimer approach to inelastic collisional processes is revised. It is shown that the widely used standard interpretation of this approach has fundamental limitations leading to physical artefacts or to uncertainties in numerical calculations due to neglecting the electron translation problem. It is demonstrated that the Born–Oppenheimer approach itself does not have such limitations. The particular full quantum solution of the electron translation problem within the Born–Oppenheimer approach by means of the reprojection procedure is discussed in the paper together with the practical applications.

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Section: Reprojection T-matrix Methodsmentioning

confidence: 96%

Section: Standard Interpretation Of the Bo Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonadiabatic effects in inelastic collisional processes

Belyaev¹

2009

Phys. Scr.

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Hyperspherical Coulomb spheroidal representation in the Coulomb three-body problem

Abramov¹

2008

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

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The new representation of the Coulomb three-body wave function via the well-known solutions of the separable Coulomb two-centre problem φ j (ξ, η) = X j (ξ)Y j (η) is obtained, where X j (ξ) and Y j (η) are the Coulomb spheroidal functions. Its distinguishing characteristic is the coordination with the boundary conditions of the scattering problem below the three-particle breakup. That is, the wave function of the scattering particles in any open channel is the asymptotics of the single, corresponding to that channel, term of the expansion suggested. The effect is achieved due to the new relation between three internal coordinates of the three-body system and the parameters of φ j (ξ, η). It ensures the orthogonality of φ j (ξ, η) on the sphere of a constant hyperradius, ρ = const, in place of the surface R = |x 2 − x 1 | = const appearing in the traditional Born-Oppenheimer approach. The independent variables ξ and η are the orthogonal coordinates on that sphere with three poles in the coalescence points. They are connected with the elliptic coordinates on the plane by means of the stereographic projection. For the total angular momentum J ≥ 0 the products of φ j and the Wigner D-functions form the hyperspherical Coulomb spheroidal (HSCS) basis on the five-dimensional hypersphere, ρ being a parameter. The system of the differential equations and the boundary conditions for the radial functions f J i (ρ), the coefficients of the HSCS decomposition of the three-body wave function, are presented.

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S-wave resonances in positron-sodium scattering

et al. 2008

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We have calculated S-wave resonances in the positron-sodium system using the stabilization method in the framework of hyperspherical coordinates. Resonances below the Ps͑n =2͒ threshold have been investigated. We have located all the previously known S-wave resonances by Kar and Ho ͓Eur. Phys. J. D 35, 453 ͑2005͔͒ and Ward et al. ͓J. Phys. B 22, 3763 ͑1989͔͒ and observed relatively good agreement for the resonance positions. In addition, two new higher-lying resonances associated with the Ps͑n =2͒ threshold are found to be at energies of −0.066 56 and −0.063 53 a.u.

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Calculation of resonances in the Coulomb three-body system with two disintegration channels in the adiabatic hyperspherical approach

Cited by 5 publications

References 19 publications

Nonadiabatic effects in inelastic collisional processes

Nonadiabatic effects in inelastic collisional processes

Hyperspherical Coulomb spheroidal representation in the Coulomb three-body problem

S-wave resonances in positron-sodium scattering

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