Adiabatic hyperspherical approach to describing low-energy mesic-atom scattering

Abramov, D. I.; Гусев, В. В.; Ponomarev, L. I.

doi:10.1134/1.1398928

Cited by 4 publications

(13 citation statements)

References 16 publications

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“…The pure discrete character of the spectrum of had is explained by the fast decrease of the mass m(t) at large t, m(t) ∼ t −4 . Every eigenfunction of had coincides at large ρ with the wave function of certain bound state of the atom (1,3) or (2,3) [22].…”

Section: The Appropriate Coulomb Two-centre (Ctc) Hamiltonian In T-spacementioning

confidence: 98%

“…The variables ρ, χ, ϑ are the internal coordinates of the system. In the hyperspherical coordinates the kinetic energy (12) takes the form [19,22]…”

Section: Starting Equationsmentioning

confidence: 99%

“…In contrast to the traditional BO representation, the adiabatic hyperspherical one [18][19][20][21][22] is coordinated with the asymptotic conditions of the three-body scattering problem. In this approach the hyperradius ρ is used as an adiabatic parameter.…”

Section: Introductionmentioning

confidence: 99%

“…The wavefunction of two colliding clusters in any open channel is the asymptotics of the single, corresponding to that channel, term of the expansion. The adiabatic hyperspherical approach is successfully applied to the calculations of the bound states, the cross sections of the elastic and inelastic collisions and the resonances in various Coulomb three-body systems [18,[20][21][22][23][24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

“…In the general case, they are the non-factorized functions of five independent variables. In addition, for the Coulomb three-body systems the adiabatic hyperspherical terms as functions of ρ have the numerous avoiding crossings which make difficulties for the numerical calculations [20,22]. These avoiding crossings are closely connected with the exact crossings in the Coulomb two-centre problem [22].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: The Appropriate Coulomb Two-centre (Ctc) Hamiltonian In T-spacementioning

confidence: 98%

“…The variables ρ, χ, ϑ are the internal coordinates of the system. In the hyperspherical coordinates the kinetic energy (12) takes the form [19,22]…”

Section: Starting Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Hyperspherical Coulomb spheroidal representation in the Coulomb three-body problem

Abramov¹

2008

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

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

Abramov¹,

Гусев²

2005

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

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Abstract. The method of calculation of the resonance characteristics is developed for the metastable states of the Coulomb three-body (CTB) system with two disintegration channels. It is based on the numerical solution of the scattering problem in the framework of the adiabatic hyperspherical (AHS) approach. The energy dependence of K-matrix in the resonance region is calculated with the use of the stabilization method. Resonance position E 0 , partial widths Γ 1 , Γ 2 , and three additional parameters are obtained by fitting of the numerically calculated K ij (E) with the help of the generalized Breit-Wigner formula which takes into account the non-zero background inelastic scattering. The method developed is applied to the calculation of the parameters of three lowest metastable states of the mesic molecular ion dtµ.

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Auger formation of the (3Heμp)J2+molecule

Czapliński

2013

Phys. Rev. A

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Adiabatic hyperspherical approach to describing low-energy mesic-atom scattering

Cited by 4 publications

References 16 publications

Hyperspherical Coulomb spheroidal representation in the Coulomb three-body problem

Hyperspherical Coulomb spheroidal representation in the Coulomb three-body problem

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

Auger formation of the (3Heμp)J2+molecule

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