Few-Body Systems

, Volume 54, Issue 7–10, pp 1533–1536 | Cite as

Quadrupole Transitions in the Bound Rotational-Vibrational Spectrum of the Hydrogen Molecular Ion



The three-body Schrödinger equation of the \({{\rm H}_{2}^{+}}\) hydrogen molecular ion is solved in perimetric coordinates using the Lagrange-mesh method. Energies and wave functions of the four lowest vibrational bound or quasibound states for total orbital momenta from 0 to 40 are calculated with high accuracy. A simple calculation using the associated Gauss quadrature provides accurate quadrupole transition probabilities per time unit between those states over the whole rotational bands.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Posen A.G., Dalgarno A., Peek J.M.: The quadrupole vibration-rotation transition probabilities of the molecular hydrogen ion. At. Data Nucl. Data Tables 28, 265 (1983)ADSCrossRefGoogle Scholar
  2. 2.
    Olivares Pilón H., Baye D.: Quadrupole transitions in the bound rotational-vibrational spectrum of the hydrogen molecular ion. J. Phys. B 45, 065101 (2012)ADSCrossRefGoogle Scholar
  3. 3.
    Hesse M., Baye D.: Lagrange-mesh calculations of the ground-state rotational bands of the \({{\rm H}_{2}^{+}}\) and \({{\rm D}_{2}^{+}}\) molecular ions. J. Phys. B 36, 139 (2003)ADSCrossRefGoogle Scholar
  4. 4.
    Baye D., Heenen P.-H.: Generalised meshes for quantum mechanical problems. J. Phys. A 19, 2041 (1986)MathSciNetADSMATHCrossRefGoogle Scholar
  5. 5.
    Baye D., Hesse M., Vincke M.: The unexplained accuracy of the Lagrange-mesh method. Phys. Rev. E 65, 026701 (2002)MathSciNetADSCrossRefGoogle Scholar
  6. 6.
    Pekeris C.L.: Ground state of two-electron atoms. Phys. Rev. 112, 1649 (1958)MathSciNetADSMATHCrossRefGoogle Scholar
  7. 7.
    Moss R.E.: Calculations for the vibration-rotation levels of \({{\rm H}_{2}^{+}}\) in its ground and first excited electronic states. Mol. Phys. 80, 1541 (1993)ADSCrossRefGoogle Scholar
  8. 8.
    Olivares Pilón H., Baye D.: Static and dynamic polarizabilities of the non-relativistic hydrogen molecular ion. J. Phys. B 45, 235101 (2012)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 2012

Authors and Affiliations

  1. 1.Physique Quantique C.P. 165/82, and Physique Nucléaire Théorique et Physique Mathématique, C.P. 229Université Libre de Bruxelles (ULB)BrusselsBelgium

Personalised recommendations