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Restricted quatum-mechanical three-body problems

IV. Asymptotically exact wave functions of a helium-like ion in all singular points of its Schrödinger equation

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Abstract

On the basis of a perturbative procedure in which the eigenfunctions of a helium-like ion are expanded in the Hilbert space built up from the eigenfunctions of an electron in two fixed Coulomb charges,all asymptotic eigenfunctions are constructed for the Schrödinger equation of helium-like ions. If the nuclear chargeZ 1 is not less than 2, then our asymptotic considerations clarify the singularities of the Schrödinger equation of a helium-like ion (atr 1=0, ∞,r 2=0, ∞,r 12=0, ∞), while in the case ofZ 1=1 (negative hydrogen ion)r 2=0 will not be treated in this paper. The established order (inr 2) of asymptotics at 0 or in an exceptional case the zeroth-order term of the functions (actually the coefficients of an expansion of the desired eigenfunctions) as one of the electron coordinates (r 2, the distance of the two fixed Coulomb charges, a parameter of the set of the basic functions) enables us to classify the eigenfunctions of a helium-like ion. This classification resembles the classification scheme for one-electron configurations. The asymptotics forr 2→∞ indicate bounded, pseudobounded (auto-ionizing) and free states. (Doubly ionized continuum states are not discussed here.) The use of the asymptotic solutions is indicated for the complete solution of the problem which may be either numerical integration or a variational procedure.

Neutral muonic helium is included in the discussion.

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References

  • Barcza, S.: 1979,Astrophys. Space Sci. 66, 287 (Paper I).

    Google Scholar 

  • Barcza, S.: 1980,Astrophys. Space Sci. 72, 497 (Paper II).

    Google Scholar 

  • Barcza, S.: 1984,Astrophys. Space Sci. 100, 185 (Paper III).

    Google Scholar 

  • Bethe, H. R. and Salpeter E. E.: 1957, in S. Flügge (ed.), ‘Quantum Mechanics of One and Two Electron Systems’Handbuch der Physik, Vol. XXXV, Springer-Verlag, Berlin.

    Google Scholar 

  • Borie, E. and Rinker, G. A.: 1982,Rev. Mod. Phys. 54, 67.

    Google Scholar 

  • Gombás, P.: 1950,Theorie und Lösungsmethoden des Mehrteilchenproblems der Wellenmechanik, Birkhäuser Verlag, Basel.

    Google Scholar 

  • Jaffé, G.: 1934,Z. Phys. 87, 535.

    Google Scholar 

  • Kinoshita, T.: 1957,Phys. Rev. 105, 1490.

    Google Scholar 

  • Sholin, G. V.: 1969,Opt. Spect. (USSR) 26, 489.

    Google Scholar 

  • Souder, P. A., Casperson, D. E., Crane, T. W., Hughes, V. W., Lu, D. C., Orth, H., Reist, H. W., Yam, M. H., and Zu Putlitz, G.: 1975,Phys. Rev. Letters 34, 1417.

    Google Scholar 

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Authors and Affiliations

  1. Konkoly Observatory, Budapest, Hungary

    S. Barcza

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  1. S. Barcza
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Barcza, S. Restricted quatum-mechanical three-body problems. Astrophys Space Sci 120, 61–95 (1986). https://doi.org/10.1007/BF00653900

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  • DOI: https://doi.org/10.1007/BF00653900

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