• Українська
  • English

< | >

Current issue   Ukr. J. Phys. 2016, Vol. 61, N 11, p. 950-955
https://doi.org/10.15407/ujpe61.11.0950    Paper

Simulik V.M.1, Zajac T.M.2, Tymchyk R.V.3

1 Institute of Electron Physics, Department of the Theory of Elementary Interactions,
Nat. Acad. of Sci. of Ukraine
(21, Universytets’ka Str., Uzhgorod 88000, Ukraine; e-mail: vsimulik@gmail.com)
2 Uzhgorod National University, Chair of Electron Systems
(13, Kapitul’na Str., Uzhgorod 88000, Ukraine)
3 Institute of Electron Physics, Department of Electron Processes, Nat. Acad. of Sci. of Ukraine
(21, Universytets’ka Str., Uzhgorod 88000, Ukraine; e-mail: vsimulik@gmail.com)

Choice of the Wave Function for the Helium Ground State for Precision Calculations of Quasistationary State Parameters

Section: Atoms and Molecules
Original Author's Text: Ukrainian

Abstract: In the problems of ionization of atoms by photons and electrons, the necessity of choosing the multiparametric wave functions for the description of an atom in the ground state has been substantiated. The helium atom is taken as an example. The energies, widths, and partial widths of the lowest 1p autoionizing state of helium, located above the excited ions formation threshold, are calculated. The results obtained with the use of different ground state wave functions are compared. It is shown that, contrary to the total widths of autoionizing states, the partial widths are substantially different for different ground-state wave functions.

Key words: autoionizing states, quasistationary states, overlapping configurations, multiparametric wave functions.


  1. P.G. Burke. Effects of configuration interaction on electron and photon interactions with atoms. In Electron and Photon Interactions with Atoms (Plenum Press, 1976) [ISBN 978-1-4899-5024-6].  https://doi.org/10.1007/978-1-4899-5022-2_1
  2. T.M. Luke. Calculation of doubly excited resonances in neon. J. Phys. B: At. Mol. Phys. 8, 1501 (1975).  https://doi.org/10.1088/0022-3700/8/9/016
  3. U. Fano. Effects of configuration interaction on intensities and phase shifts. Phys. Rev. 124, 1866 (1961).  https://doi.org/10.1103/PhysRev.124.1866
  4. C. Froese Fischer. The Hartree–Fock Method for Atoms – a Numerical Approach (Wiley, 1977) [ISBN 0-471-25990-X].
  5. E.A. Hylleraas. Neue Berechnung der Energie des Heliums im Grundzustande, sowie des tiefsten Terms von Ortho-Helium, Z. Phys. 54, 347 (1929).  https://doi.org/10.1007/BF01375457
  6. E.A. Hylleraas. Uber den Grundterm der Zweielektronenprobleme von H?, He, Li+, Be++ usw, Z. Phys. 65, 209 (1930).  https://doi.org/10.1007/BF01397032
  7. V.I. Reshetnyak. On the trial functions of the ground state of He atom. Dokl. Akad. Nauk SSSR 263, 1356 (1982).
  8. V.A. Fock. On the Schr?odinger for He atom. Izv. Akad. Nauk SSSR 18, 161 (1954).
  9. C. Froese Fischer. The MCHF atomic-structure package. Comput. Phys. Commun. 128, 635 (2000).  https://doi.org/10.1016/S0010-4655(00)00009-6
  10. C.L. Pekeris. Excited S states of helium. Phys. Rev. 127, 509 (1962).  https://doi.org/10.1103/PhysRev.127.509
  11. S.A. Alexander, R.L. Coldwell. Atomic wave function forms. Int. J. Quant. Chem. 63, 1001 (1997).  https://doi.org/10.1002/(SICI)1097-461X(1997)63:5<1001::AID-QUA9>3.0.CO;2-1
  12. P.A. Golovinskii, P.Yu. Kiyan. Negative ion in a strong optical field. Sov. Phys. Usp. 33 (6), 453 (1990).  https://doi.org/10.1070/PU1990v033n06ABEH002600
  13. M.K. Evseev, V.I. Matvyeyev. Study of the analytic wave functions of a two-electron system in dynamical interacions with multiсharge ions and ultrashort pulses of the elecromagnetic fields. Zh. Tekhn. Fiz. 78, 28 (2008).
  14. R.J. Tweed. Correlated wavefunctions for helium-like atomic systems. J. Phys. B 5, 810 (1972).  https://doi.org/10.1088/0022-3700/5/4/015
  15. S.M. Burkov, N.A. Letyaev, S.I. Strakhova, T.M. Zajac. Photon and electron ionization of helium to the = 2 state of He+. J. Phys. B: At. Mol. Opt. Phys. 21, 1195 (1988).  https://doi.org/10.1088/0953-4075/21/7/014
  16. T.M. Zajac. Method of interacting configurations in the representation by complex numbers in the problem of ionization of atoms by the electron impact in the region above the threshold of formation of excited ions. Nauk. Visnyk Uzhgorod. Univ. Ser. Fiz. 11, 72 (2002).
  17. V.S. Senashenko, A. Vague. Resonance photoabsorption of the helium atom in the vicinity of the (3 3) 1 resonance. J. Phys. B: At. Mol. Phys. 12, L269 (1979).  https://doi.org/10.1088/0022-3700/12/8/002