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Coulomb spheroidal representation in the hyperspherical approach to the three-body problem

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Abstract

The construction of the most simple representation coordinated with the physical asymptotic conditions is considered for the Coulomb three-body scattering wave function at energies below the threshold of the three-particle breakup. It is shown that such a representation can be constructed with the use of the well-known solutions of the separable Coulomb two-centre (CTC) problem if the role of the intercentre distance is given to the hyperradius. For the simplest version of the approach (Abramov, J Phys B 41:175201, 2008) the corresponding system of radial differential equations and the statement of the three-body scattering problem for the total angular momentum J ≥ 0 are presented.

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References

  1. Abramov, D.I.: Hyperspherical Coulomb spheroidal representation in the Coulomb three-body problem. J. Phys. B 41, 175201 (2008)

    Article  ADS  Google Scholar 

  2. Macek, J.: Properties of autoionizing states of He. J. Phys. B 1, 831–843 (1968)

    Article  ADS  Google Scholar 

  3. Kadomtzev, M.B., Vinitsky, S.I.: Adiabatic representation for the three-body problem in hyperspherical coordinates: I. Statement of the problem. J. Phys. B 20, 5723–5736 (1987).

    Article  MathSciNet  ADS  Google Scholar 

  4. Lin, C.D.: Hyperspherical coordinate approach to atomic and other Coulombic three-body systems. Phys. Rep. 257, 1–83 (1995)

    Article  ADS  Google Scholar 

  5. Gusev, V.V., Puzynin, V.I., Kostrykin, V.V., Kvitsinsky, A.A., Merkuriev, S.P., Ponomarev, L.I.: Adiabatic hyperspherical approach to the Coulomb three-body problem: theory and numerical method. Few-Body Syst. 9, 137–153 (1990)

    Article  ADS  Google Scholar 

  6. Abramov, D.I., Gusev, V.V., Ponomarev, L.I.: Relationship between the adiabatic hyperspherical and the Born-Oppenheimer approach to the Coulomb three-body problem. Phys. At. Nucl. 60, 1133–1144 (1997)

    Google Scholar 

  7. Abramov, D.I., Gusev, V.V., Ponomarev, L.I.: Symmetric elastic and spin-flip low-energy collisions of the hydrogen isotope mesic atoms in the adiabatic hyperspherical approach. Phys. At. Nucl. 67, 226–240 (2004)

    Article  Google Scholar 

  8. Vinitsky, S.I., Ponomarev, L.I.: Adiabatic representation in the three-body problem with Coulomb interaction. Sov. J. Part. Nucl. 13, 557–587 (1982)

    Google Scholar 

  9. Power, J.D.: Fixed nuclei two centre problem in quantum mechanics. Philos. Trans. R. Soc. Lond. A274, 663–702 (1973)

    ADS  Google Scholar 

  10. Komarov, I.V., Ponomarev, L.I., Slavyanov, S.Yu.: Spheroidal and Coulomb Spheroidal Functions. Nauka, Moscow (1976, in Russian)

    Google Scholar 

  11. Slavyanov, S.Yu., Lay, W.: Special Functions: A Unified Theory Based on Singularities. Oxford University Press, Oxford (2000)

    MATH  Google Scholar 

  12. Melezhik, V.S., Ponomarev, L.I., Faifman, M.P.: Elastic scattering in a three-particle system with Coulomb interaction. Sov. Phys. JETP 58, 254–261 1983

    Google Scholar 

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  1. V.A. Fock Institute of Physics, St. Petersburg State University, St. Petersburg, 198504, Russia

    D. I. Abramov

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  1. D. I. Abramov
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Correspondence to D. I. Abramov.

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Abramov, D.I. Coulomb spheroidal representation in the hyperspherical approach to the three-body problem. Hyperfine Interact 193, 129–133 (2009). https://doi.org/10.1007/s10751-009-0052-3

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