The shell model of electron structure of negative hydrogen ion

In the frame of non-relativistic approximation, a compact approximate solution of the Schrödinger equation for the ion of $H^{-}$ has been obtained in the form of product for Legendre polynomials and variational functions of the Schull--Löwdin type. The accuracy of calculation of ion energy is of the same order that the results obtained using the multiparametric functions of Hylleraas and Pekeris.

  1. Wildt R.  The Continuous Spectrum of Stellar Atmospheres Consisting Only of Atoms and Negative Ions of Hydrogen.  Astrophys. Journ. 93, 47--51 (1941).
  2. Chandrasekhar S., Breen F. H.  On the Continuous Absorption Coefficient of the Negative Hydrogen Ion. III.  Astrophys. Journ. 104, 430--445 (1946).
  3. Geltman S.  The Bound-Free Absorption Coefficient of the Hydrogen Negative Ion.  Astrophys. Journ. 136, 935--945 (1962).
  4. Wishart A. W.  The Bound-Free Photodetachment Cross Section of $H^-$.  J. Phys. B: Atom. Molec. Phys. 12 (21), 3511--3519, (1979).
  5. Vavrukh М. V., Vasil'eva І. Е., Stelmakh О. М., Tyshko N. L.  Continuous Absorption and Depression in the Solar Spectrum at Wavelengths from 650 to 820 nm.  Kinematics and Physics of Celestial Bodies. 32 (3), 129--144 (2016).
  6. Hylleraas E. A.  Die Elektronenaffinität des Wasserstoffatoms nach der Wellenmechanik.  Zeitschrift für Physik. 60, 624--630 (1930).
  7. Pekeris C. L.  $1^1S$, $2^1S$ and $2^3S$ States of $H^-$ and of He.  Phys. Rev. 126, 1470--1476 (1962).
  8. Massey H. S. W.  Negative Ions.  Cambridge University Press (1976).
  9. Schull H., Löwdin P.-O.  Correlation Splitting in Helium-Like Ions.  J. Chem. Phys. 25, 1035--1040 (1956).
  10. Kinoshita T.  Ground State of the Helium Atom.  Phys. Rev. 105, 1490--1502 (1957).
  11. Hart J. F., Herzberg G.  Twenty-Parameter Eigenfunctions and Energy Values of the Ground States of He and He-Like Ions.  Phys. Rev. 106, 79--82 (1957).
  12. Tweed R. J. Correlated wavefunctions for helium-like atomic systems.  J. Phys. B: Atom. Molec. Phys. 5, 810--819 (1972).
Math. Model. Comput. Vol.6, No.1, pp.144-151 (2019)